Quantum Physics Paper Analysis

Strong light-matter interactions in optical microcavities give rise to hybrid light-matter states known as polaritons. While actively used in modern technologies, theoretical descriptions of such systems are often restricted to the single-excitation case, limiting their ability to capture many-excitation physics and hindering further technological advancements. Here, by exploiting the combinatorial structure of quantum emitters, we investigate the Tavis-Cummings model with arbitrary number of excitations. We derive the structure and properties of its eigensystem and identify allowed radiative transitions in systems of realistic size scales. Our work reveals new behavior inaccessible to the few-excitation regime, while also providing a framework to reduce the computational complexity of similar systems with exponentially growing Hilbert spaces.

We propose the high-fidelity preparation of single bosonic molecules in optical tweezers starting from small tweezer-trapped molecular ensembles. Our scheme combines a static electric field and a microwave field to generate strong, tunable, anisotropic interactions that shield the molecules against two-body collisional loss. We show that this shielding eliminates all long-range bound states, preventing three-body recombination. This elimination persists for all microwave ellipticities, including the experimentally practical limit of linear polarization. Application of an additional electric field gradient can be used to induce controlled spilling of strongly interacting molecules out of the trap until one remains. With realistic experimental parameters, we estimate that single tweezer-trapped NaCs molecules can be isolated from a pair with fidelities exceeding 99\%, and $> 95\%$ per site across an array. These results establish collisional shielding with electric fields as an effective tool for preparing highly-filled tweezer arrays of polar molecules.

Supersolids are exotic quantum states in which long-range phase coherence coexists, and may interplay, with emergent spatial orders. A particularly rich phase diagram featuring several competing spatial orders is predicted for dipolar supersolids with two-dimensional crystals, yet the experimental observation of this structural variety has remained limited. Here we experimentally form competing triangular and stripe density-modulated states in a quantum gas of highly magnetic atoms confined in a surfboard-shaped trap by tuning contact interaction strength and dipole orientation. We define a structural order parameter and study its statistical behavior. Thereby, we identify both the triangular and stripe phases and the transition between them, the associated critical behavior being marked by enhanced non-Gaussian fluctuations. Furthermore, we observe each spatial structure in both the phase-coherent supersolid regime and the phase-incoherent insulating one, near and far from the unmodulated-to-modulated transition, respectively. Our results establish a versatile platform in which multiple phases of the two-dimensional-supersolid phase diagram, and more generally, intertwined symmetry-breaking phenomena, can be investigated.

Heisenberg uncertainties lead to inevitable fluctuations in the measurement outcomes for quantum-mechanical observables. For quantum fields, these uncertainties result in random spatial structures in snapshots of a field, even when the field is in its ground (vacuum) state. Such `vacuum fluctuations' are at the heart of a wide range of phenomena, from spontaneous decay processes to the Casimir force and Hawking radiation. Their existence is a key manifestation of the quantumness of the physical world, but usually it is only their consequences that are directly observed. Here, we directly observe spatial vacuum fluctuations of a bosonic quantum field. Our experiments are based on a homogeneous planar atomic Bose--Einstein condensate. The condensate comprises two coherently coupled interacting components (spin states), and the quantum field describes its spin degrees of freedom. In the regime where the interactions dominate over the coherent coupling, our system emulates a (massive relativistic) sine-Gordon field. Images of the field reveal simultaneous fluctuations on different length scales, with scale-dependent amplitudes consistent with theoretical predictions for a vacuum state. Observing such fluctuations in the sine-Gordon limit opens many possibilities for laboratory simulations of relativistic fields in regimes that are presently not theoretically tractable.

In the article a new approach to construction of generalized coherent states in quantum billiards is proposed. The coherent states are defined as the projections of a Gaussian wave function on the basis of the eigenstates of the quantum billiard, continued outside. The continuation is built as the solution of the equivalent Balian--Bloch equation, defined on the entire $\mathbb{R}^2$ and the projection operator is built using the resolvent of the Balian--Bloch equation. In the case of the one--dimensional potential well and billiards, belonging to the Coxeter group, the wave functions of the coherent states were expressed analytically via the Jacobi and Riemann theta functions.

Aaronson and Ambainis (Theory of Computing, 2014) conjectured that quantum query algorithms admit efficient almost-everywhere classical simulation: for any $T$-query quantum algorithm, its acceptance probability can be approximated on a $(1-δ)$ fraction of inputs, up to $ε$ additive error, using $\mathrm{poly}(T, 1/ε, 1/δ)$ classical queries. At a high level, the conjecture suggests that exponential quantum speedups are possible only on sufficiently structured inputs. In this work, we make progress on this conjecture by proving it for quantum algorithms that make massively parallel quantum queries. In contrast, Yamakawa and Zhandry (Journal of the ACM, 2024) showed that quantum algorithms restricted to parallel queries can still achieve exponential speedups over classical algorithms for sampling problems. We establish our simulation theorem by proving the stronger statement that parallel-query quantum algorithms cannot distinguish the uniform distribution over oracles from oracles drawn from so-called "dense distributions". Our main technical contribution is a coupling theorem that relates the uniform distribution over oracles to oracles drawn from dense distributions. We further extend this approach beyond the purely parallel setting, obtaining simulation theorems both for algorithms with a bounded quantum-query prefix followed by a massively parallel quantum-query stage, and for hybrid algorithms that make an arbitrary polynomial number of adaptive classical queries before the massively parallel quantum-query stage. Finally, using the parallel-query simulation theorem as a base case, we obtain simulation theorems for quantum algorithms with constant rounds of adaptivity.

Strong atom-photon interactions in optical cavities are a key resource for quantum information processing, quantum networking, and the exploration of quantum optical effects. Optical tweezer arrays offer scalable, site-resolved control of neutral atoms, but their integration with high-cooperativity cavity QED systems remains challenging. Here we combine a twelve-site $^{87}$Rb optical tweezer array with a high-cooperativity fiber Fabry-Pérot microcavity. The array is positioned within the cavity mode and individual sites are controlled with subwavelength precision, enabling continuous tuning of the single-atom coupling strength via deterministic displacement through the standing-wave field. For up to five atoms coupled to the cavity, we measure collectively enhanced vacuum Rabi splitting and implement cavity-based non-destructive readout of the number of coupled atoms. These results establish a scalable architecture for cavity-mediated entanglement generation and many-body cavity QED with single-atom control, and they lay the foundation for fiber-integrated quantum network nodes.

It is known that the attractive singular inverse-square potential gives rise to the critical quantum collapse in the framework of the three-dimensional (3D) linear Schroedinger equation. This article summarizes theoretical results which demonstrate suppression of the collapse, caused by this singular potential, and the creation of the otherwise missing ground state (GS) in a 3D gas of bosonic particles, carrying an electric dipole moment, which are pulled to the central electric charge, with repulsive contact interactions between the particles. In the mean-field approximation, the repulsive interactions are represented by the cubic term in the respective Gross-Pitaevskii (GP) equation. In addition to the GS, excited states with angular momentum are briefly considered too. Another topic considered in the article is 1D and 2D bound states in the linear Schroedinger and GP equations with the repulsive potential, which demonstrates a singularity at r --> infinity. A very recent result is that such a potential, growing faster than the negative harmonic-oscillator potential, produces a full spectrum of counter-intuitive normalizable (localized) bound states. The article puts forward perspectives for further studies of linear and nonlinear bound states existing under the action of the potentials with the singularity at r --> 0 or r --> infinity.

In this study, we present an analytical approach based on the extended Nikiforov-Uvarov method to solve the generalized Klein-Gordon oscillator in the presence of a uniform magnetic field within the Som-Raychaudhuri space-time. Exact eigenstate solutions are obtained for two distinct potential models, namely the linear potential and the Cornell potential. The corresponding energy eigenvalues are determined, and the associated eigenfunctions are analyzed and illustrated graphically.

Motivated by a previous Ising study, we identify a ${\it higher}$ Nishimori line in the learning phase diagram of the $2D$ $q$-state Potts model $(2 < q\leq 4)$ under bond-energy measurements. This ${\it higher}$ Nishimori line meets the critical temperature line of the Potts model, in a ${\it higher}$ Nishimori critical point -- a tricritical point at finite inference strength that separates a paramagnetic, a ferromagnetic and a 'spin-glass' phase. With analytical tools, we discuss the general structure of the rich phase diagram, which contains two unstable and three stable fixed points, and obtain a number of exact results for universal quantities, including the decay exponent of the Edwards-Anderson correlator, using a Gaussian measurement protocol which allows for exact calculations. Using extensive numerical tools, we confirm these statements for a generic, discrete $q$-state measurement protocol and determine precise numerical estimates for the location of higher and ordinary Nishimori critical points as well as RG flows between the various fixed points. We also discuss the Casimir effective central charges of the critical points in the learning phase diagram, and their monotonic ${\it decrease}$ along measurement-induced RG flows, as established non-perturbatively by the c-effective theorem and its extensions, and contrast it to the monotonic increase along the corresponding RG flows in the random-bond Potts model. Finally, we discuss a general argument based on ${\it Elitzur's \; theorem}$ that establishes stability of the ordinary Nishimori critical points in their respective learning phase diagrams. Equivalently, our results describe a monitored deformed $\mathbb{Z}_q$ toric code where the tricritical ${\it higher}$ Nishimori point is an 'information' critical point that separates stable quantum, classical, and no memory phases.

Noisy intermediate-scale quantum computers are constrained by circuit depth, while product-formula simulation of spin systems leads to narrow and deep circuits. Here we introduce a fan-out-based gadget compiler that trades circuit depth for width in simulations of Heisenberg-type nuclear magnetic resonance (NMR) Hamiltonians. Each logical spin is encoded into a small repetition-code register sized by its interaction degree, so that all pairwise interactions of a given Pauli type execute in parallel after a logarithmic-depth CNOT fan-out, and the redundant registers provide error detection for post-selection at no additional algorithmic overhead. The central result is a fixed-protocol resource comparison of the two compilations, transpiled to heavy-hex superconducting and all-to-all trapped-ion targets across a set of NMR spin systems. For interaction graphs with a high-degree hub the volume-optimal schedule halves the two-qubit depth and reduces the volume 1.7-fold for the 13-spin demonstration, which on heavy-hex also lowers the two-qubit gate count, and the depth reduction rises to 2.5-fold on all-to-all for the highest-degree molecule studied. On all-to-all the two-qubit gate count rises for every system, so the volume reduction is a benefit on depth-limited hardware. The gain grows with the degree inhomogeneity of the interaction graph and vanishes for dense uniform graphs, where the optimum is the sequential circuit. We simulate the zero-field NMR spectrum of tetramethylsilane, a 13-spin star system. Under a noise model scaled from a published present-day processor calibration, the shallower gadget circuits match or surpass the sequential compilation only after post-selection on their built-in error detection, once error rates improve by one to one and a half orders of magnitude. We verify the spectra against an independent classical computation.

Relativistic causality in certain spacetime configurations permits jamming - superluminal causal influences that nevertheless do not enable superluminal signaling. We fully characterize the correlations compatible with relativistic causality (RC) by extending the operator framework of PRL 104, 140404. When the underlying state is required to be quantum, we prove that any nontrivial jamming - whether state-independent or state-dependent - necessarily leads to hidden superluminal signaling. Thus, the only consistent possibilities are standard quantum correlations without jamming or the full relativistically causal correlation set, with intermediate jamming extensions of quantum correlations leading to signaling. As an application of our characterization, we investigate the security of device-independent (DI) cryptographic primitives against adversaries constrained only by relativistic causality. We construct explicit RC attacks that break DI bit commitment and DI secret sharing in jamming geometries, even when these protocols remain secure against no-signaling adversaries. Our results show that security against relativistic adversaries requires behaviors to be specified together with the spacetime locations of their measurement events; input-output statistics alone are insufficient.

We investigate dynamics of a linear chain of Rydberg atoms driven by a constrained four-body interaction, where two neighboring atoms are excited simultaneously from the electronic ground state $|0\rangle$ to Rydberg state $|1\rangle$ only when their closest neighbors are in $|0\rangle$ state. By employing an ansatz for the many-body ground state, the low-energy Hamiltonian is given by a tridiagonal form. The many-body ground state energy, which scales linearly with the chain length $L$, is obtained analytically in the thermodynamic limit and agrees with the one of the exact diagonalization. Our model supports quantum many-body scar eigenstates that are nearly equally spaced energetically. The scar states overlap strongly with the basis state $|\mathbf{0}\rangle=|0\cdots 0\rangle$. We show that the overlap distribution is tilted by the state-dependent four-body interaction. This leads to non-ergodic dynamics, evidenced by the revival of the initial state. The four-body constrained model can be realized with Rydberg atoms in a Peierls array with alternating bond lengths, where atoms on the shorter and longer bonds experience Rydberg blockade and antiblockade, respectively. Our study provides a pathway to explore constrained non-ergodic dynamics with four-body interactions by combining the Rydberg blockade and antiblockade.

A $U(1)$ quantum rotor pairs a periodic angle with an integer-valued conjugate momentum, and occurs in molecular rotation, superconducting phase-charge circuits, and compact gauge fields. Coupling such a rotor coherently to qubits gives a hybrid register whose control structure is not inherited from either the oscillator-qubit or the qudit case. We develop a Clifford theory, together with a universal-control result, for registers of $n$ qubits and $r$ rotors. We classify all automorphisms of the hybrid phase space $\mathbb{F}_2^{2n}\times\mathbb{Z}^r\times\mathbb{T}^r$ that preserve the Weyl commutation relations, and give an explicit finite Clifford circuit for each one. The classification is directional: rotor momentum parity may control qubit Pauli operations within the Clifford group, while every nonzero qubit-controlled rotor momentum shift is non-Clifford. It also yields normal forms for the mixed qubit-rotor couplings and the exact minimum number of elementary mixed gates needed to synthesize them. Adding a rotor cosine potential and one fixed qubit-rotor conditional phase to the local Clifford operations gives universal control on the full Hilbert space in the strong operator topology. We then apply this structure in three settings: an exact controlled-shift realization of gauge-covariant matter hopping, which is necessarily non-Clifford; rotor phase estimation with direct angle readout and probe optimization under momentum-support and energy constraints; and finite Fourier transforms on rotor momentum codes, where the one-rotor transform for $d=2^s$ compiles into $O(s)$ momentum-selective and controlled-shift instructions and each cross-register Fourier factor is implemented by one quadratic rotor Clifford gate.

We extend the analysis of the class of quantum phase transitions (QPTs) that can be interpreted as condensations in state space, first introduced in [M. Ostilli and C. Presilla, J. Phys. A 54, 055005 (2021)], by generalizing the arguments of [M. Ostilli and C. Presilla, Phys. Rev. Lett. 127, 040601 (2021)] to prove the existence and determine the location (via simple bounds) of QPTs in general one-parameter lattice Hamiltonians. Unlike our original formulation, this extension also encompasses second-order QPTs, for which we provide the explicit example of the transverse-field Ising model. Our analysis suggests that, under conditions typically satisfied in physical contexts, any QPT taking place in lattice systems can be interpreted as a condensation in state space.

Non-unital noise is a fundamental feature of open quantum systems, governing energy exchange and inducing state translations on the Bloch sphere. While such translations can be useful for tasks such as state preparation and channel capacity, unital dynamics where no translation occurs are often preferred in quantum information processing, particularly for error correction. Phase-covariant dynamics provide a general framework encompassing dissipation, excitation, and dephasing processes in qubit systems; however, commonly used models such as the generalized amplitude damping (GAD) channel offer only limited control over these features. In this work, we present a constructive framework for generating a broader class of phase-covariant dynamics by mixing amplitude-damping and anti-damping channels with unequal decay parameters and time-dependent mixing probabilities. This approach enables independent control over contraction and translation, allows continuous tuning between non-unital and unital regimes, and yields an effective dephasing contribution absent in GAD. To characterize these dynamics, we employ the general theorem for P-divisibility and show that it can be used constructively by evaluating it in suitably chosen Hilbert space bases, leading to simplified conditions for both unital and non-unital cases. The framework captures a wide range of behaviors, including CP-divisible, P-divisible but not CP-divisible, and non-P-divisible dynamics. We further show that appropriate mixing can reduce the deviation from the ideal noiseless evolution and that such improvement persists even after tuning the dynamics to the unital regime. Our results provide a flexible approach to engineering open system dynamics beyond standard thermal models, with potential applications in noise control and quantum information processing.

Identifying the entanglement structure of a many-body quantum state, namely how its constituents partition into unentangled blocks, is a central task in quantum information science, yet conventional tomography scales exponentially with system size. Here we introduce a scalable framework that recognizes large-scale entanglement structures directly from local correlation fingerprints. By choosing a representative local Pauli basis that satisfies a boundary-matching condition p_1 = p_R, the entire chain is read out in a single measurement configuration, keeping the measurement effort independent of system size. In noisy simulations, this single-basis protocol classifies GHZ-, W-, and cluster-type structures among 30 candidate partitions with a mean accuracy exceeding 95% for systems of up to 100 qubits. We further validate the protocol on a superconducting quantum processor, where it reliably classifies block structures for systems of up to 13 qubits before noise- and depth-induced degradation sets in at larger sizes. By mapping these failure modes explicitly, our results delineate the boundary of hardware-level scalability and point to a concrete strategy for characterizing entanglement structure on near-term quantum devices.

Whether a quantum system with a double-well effective potential undergoes spontaneous symmetry breaking depends not only on the potential landscape but also on the kinetics and the coupling with additional degrees of freedom. Here we introduce a quasi-exactly solvable model to study this problem in the context of ferroelectrics, with results that apply to a broad class of quantum phase transitions. Exploiting the analytical solutions, we provide a strict definition of the quantum paraelectric regime and identify a distinct quantum ferroelectric regime in which symmetry breaking can be realized without tunneling features. We then show that explicit symmetry breaking cannot be inferred from the order-parameter Hamiltonian alone, but requires additional couplings. This leads us to identify a regime of \emph{quantum dissipative paraelectricity}, in which observable symmetry breaking is suppressed during the evolution toward the ground state, even when the double-well structure dominates over zero-point quantum fluctuations.

Achieving fault-tolerant quantum computing at a practical scale demands quantum error correction (QEC) codes with high encoding rates. Quantum low-density parity-check (qLDPC) codes emerge as a promising candidate, especially given the rise of neutral atom arrays that provide dynamic long-range connectivity via atom movements. In general, synthesizing valid and efficient physical execution plans for QEC is a provably hard combinatorial problem, forming a critical compilation bottleneck that worsens as code sizes grow. To overcome this complexity, we focus on an important product family of qLDPC codes with dimension-reduction properties, and propose ONEX. This framework decomposes complex 2D physical execution planning into independent 1D subproblems, each solved to optimal execution depth within practical compilation time. First, we formulate the 1D execution plan with an explicit satisfiability modulo theories (SMT) encoding. This protocol produces provably depth-optimal solutions with substantial duration reduction. Second, we develop a multi-stage compilation pipeline featuring anytime optimization, movement compaction, and iterative feedback. This pipeline maintains practical wall-clock times while providing progressive refinement and on-demand retrieval of quality solutions. Third, we evaluate ONEX in the application of hypergraph product (HGP) code memory mapped onto neutral atom arrays, achieving 3.7x to 6.1x and 29.8x to 42.1x higher clock rates than the constructive 1D algorithm and the general 2D compiler, respectively, while scaling efficiently to codes with 2,500 data qubits. Finally, we extend ONEX to zoned layouts, revealing architectural insights into the associated trade-offs, and demonstrate its applicability to the broader lifted-product (LP) code family through a representative example.

This work considers a variation on the problem of learning shallow quantum circuits. Given query access to the circuit, as well as knowledge of its gate layout, we consider the task of learning the specific gates used in the circuit, producing an operationally-equivalent circuit matching this structure. Building on recent work for learning Haar random brickwork circuits, we identify a meta-algorithmic framework for learning broad classes of circuits based on iterative local gate inversions at the front and back of the circuit. We apply these techniques to study random, all-to-all, two-local circuits, and provide analytical and numerical evidence that this ensemble undergoes a sharp learnability transition at depth $d^* \sim \log_2 n + \log_2\log_2 n$ in the large size limit, based on an analysis of lightcone growth. These results have implications for recently proposed quantum cryptographic schemes based on the difficulty of circuit learning, though there are important distinctions with respect to our setting that suggest avenues for future study.

What is the relation between subsystem quantum complexity and the emergence of computationally useful structure? We address this by studying a family of minimally tunable postvariational quantum circuits, and show how spectral nonflatness and metrological response directly control the ensemble-typical information processing power. This unveils an intermediate "learning phase" that precedes the onset of quantum chaos, characterized by pronounced nonflatness and sensitivity of readout states. The optimal information processing capacity improves with system size, while deep scrambling suppresses observable response. The results reveal how such features of random quantum dynamics can be viewed as computational resources for scalable nonlinear computation.

We explore quantum Turing pattern zoology, where the same Lindblad equation supports a morphology atlas of stripes, spots, holes, labyrinths, and defects. The stable stripe species provides a quantitatively controlled case in which morphology and Gaussian witness loss separate parametrically. In particular, visible Turing stripes can remain after two Gaussian witness margins associated with the same $k_*$ mode cross zero in a completely positive Lindblad lattice. The witness thresholds on the exact shell fall as $\mathcal{N}^{-1}$. The stripe nematic threshold tends to a nonzero value at fixed lattice size, time window, and morphology criterion. The ratio of the morphology threshold to either witness threshold therefore grows with $\mathcal{N}$. Imaging and momentum-resolved covariance measurements probe these sectors separately.

Our present investigation into a rather rudimentary problem is motivated by two classes of problems studied since the 70's, cosmological particle creation and its more accessible analog, the dynamical Casimir effect on the one hand, and quantum friction a neutral atom moving along a dielectric surface would experience, on the other. The backreaction effects of produced particles being able to isotropize the expansion of the universe, or to slow down the moving mirror can be understood via the concept of vacuum viscosity arising from fluctuations of the quantum field. We want to track down the origin of this effect by asking the question whether a moving massive $M$ object with a charged internal degrees of freedom $χ$ interacting with a free unbounded classical field $φ$ at zero temperature would experience a viscous force, similar to the said precedents. Adopting a microphysics model for optomechanics which can treat the unequal tripartite $χ$-$φ$-$M$ interactions, we first perform a nonrelativistic calculation, which seems perfectly legitimate considering the needs of atomic physics, and found the answer to be yes, but a relativistic covariant calculation says no. We identify where the nonrelativistic framework is defective. The resolution of this latent yet real conflict is technically nontrivial but physically quite inspirational. It results in added enriched contents to Newton's first and second laws when the principles of special relativity are enforced, and rules to follow to get the correct nonrelativistic answer

Accurate digital quantum simulation at long times is limited by the accumulation of errors inherent to approximate simulation. Here we introduce RL-Trotter, a reinforcement-learning framework that treats unavoidable approximation errors as resources for error correction rather than merely imperfections to suppress. We show that low-dimensional information from conservation laws, such as the energy and energy variance, provides a sufficient learning signal to guide the agent, which learns to adapt a single scalar---the next Trotter step size---without access to the target wave function. By optimizing the entire long-time evolution rather than individual steps, RL-Trotter discovers self-correcting sequences in which later errors compensate for those accumulated earlier, increasing the accuracy of the long-time dynamics. The learned policies are intrinsically robust to measurement noise, substantially reducing measurement overhead. They also generalize to previously unseen, physically similar initial states and transfer from small, classically simulable systems to systems an order of magnitude larger. This enables a practical protocol based on classical pretraining followed by direct deployment or limited fine-tuning on quantum hardware. Our results establish a broader perspective for quantum algorithms: errors in approximate evolution can be orchestrated into resources for accurate and resource-efficient quantum dynamics.

We introduce a geometric entropy for quantum preparations, defined as the logarithm of the Hilbert-space volume of pure states compatible with a given set of constraints. This construction extends Boltzmann's counting perspective to the quantum setting, where compatible states need not be orthogonal and the relevant notion of "number of states" is naturally replaced by a volume in state space. We analyze three classes of constraints: restriction to a subspace, fixed expectation values, and coarse-grained subsystem descriptions. For representative examples, including subspace projection, spin expectation values, partial trace, and an imperfect detector map, we obtain explicit scaling laws and closed-form expressions for the associated volumes. The resulting framework provides a geometric measure of quantum ignorance at the level of the preparation and complements entropy notions based on density matrices and coarse graining.

Large Fock states are important resources for bosonic quantum information and quantum-enhanced metrology, but preparing them with high probability at large excitation numbers remains challenging, as deterministic methods become increasingly control-intensive, while measurement-based approaches typically suffer from low heralding probabilities. Here we propose a protocol that combines quantum nondemolition photon-number encoding with quantum amplitude amplification to enable high-probability heralded generation of large Fock states. Starting from a cavity mode prepared in a coherent state, Quantum Phase Estimation encodes photon-number information into a multi-qubit register, while Quantum Amplitude Amplification boosts the probability of a desired target outcome before measurement. The scheme has an immediate implementation in dispersive circuit-QED, but can be analogously adapted to other bosonic platforms with QND photon-number readout, such as cavity-QED. With a register of up to eight qubits, near-deterministic preparation of Fock states with hundreds of excitations is possible. We also show that the protocol can serve as the first stage of an extension toward generating a two-mode NOON state via a conditional beam-splitter operation.

We introduce the Spectral Autodiff Kernel Expansion (SAKE), a differentiable computational framework for transporting nonlinear spectroscopic response between neighboring quantum dynamical models. Rather than recomputing multidimensional spectra independently for each Hamiltonian or Liouvillian, SAKE constructs local transport expansions about a reference model by combining forward-mode automatic differentiation with Duhamel transport theory. Automatic differentiation generates first-, second-, and third-order derivatives of the parameter-dependent Liouvillian, which are assembled into a pathway transport operator that maps the nonlinear response of a reference model onto neighboring systems. The framework is validated for a four-level excitonic dimer possessing an $su(2)\times su(2)$ symmetry by comparing second- and third-order transported pathway operators with exact projected transport matrices obtained from direct calculations. The third-order expansion accurately reproduces the projected transport operator and its associated pathway mixing. Beyond providing an efficient computational strategy, the transport operator reveals how coherent and dissipative perturbations redistribute amplitude among double-sided Feynman pathways, exposing mechanistic information that is not directly apparent from the nonlinear spectrum. SAKE thereby establishes a differentiable computational framework for nonlinear spectroscopy that supports efficient local parameter exploration, sensitivity analysis, and future inverse-design applications.

High-harmonic generation (HHG) provides a powerful platform for exploring the interaction between intense laser fields and matter on ultrafast timescales. Beyond its conventional description in terms of emitted radiation and electron dynamics, a fully quantum treatment of HHG reveals that the nonlinear light-matter interaction can modify the quantum state of the driving field itself, establishing correlations between the fundamental and harmonic modes. This perspective opens new possibilities for using HHG as a tool to engineer and control nonclassical states of light. In this work, we investigate the geometric properties of optical Schroedinger cat states generated in HHG via conditioning and post-selection. By analyzing the coherent-state displacements induced by different structured driving fields, we characterize the resulting phase-space evolution and the associated geometric phases of the generated quantum states. Particular emphasis is placed on how the polarization and spatial-mode structure of the driving light influence the geometry and evolution of displaced coherent states. Our results demonstrate that structured light offers a versatile means of controlling the geometric dynamics of HHG-generated cat states across the parameter space. Furthermore, we discuss the prospects for realizing genuinely topological optical cat states by exploiting more complex structured light configurations.

Fractional graph colorings are useful for the Shadow tomography of Pauli observables. In practice, it is desirable that any experimentally interesting set of Pauli operators has a small fractional chromatic number $χ_{f}$ for its anticommutation graph. Conjecture 13 in King, Gosset, Kothari, and Babbush [PRX Quantum 6, 010336 (2025)] states that if $B_ε(\varrho)$ is the set of Pauli observables having expectation value magnitude at least $ε$ in some given quantum state $\varrho$, then the fractional chromatic number of the anticommutation graph $G$ induced by $B_ε(\varrho)$ is $O(ε^{-2})$. In other words, it asserts that there exists a constant $C$ such that $χ_{f} \cdot ε^2 \leq C$ on all states and graphs. If the conjecture were true, it would imply that there exists a triply efficient Pauli shadow tomography algorithm for {\it any} subset $S$ of Pauli observables, provided that there is also an efficient fractional coloring algorithm for the set $B_ε$. Here we show that the conjecture is false by constructing a family of states and observables for which no finite $C$ satisfying the bound exists. We also give a more general construction relying on the commutation index or $β$ number of a graph. The key ingredient in the proofs can be seen as an instance of the amplification trick, where fractional chromatic numbers, $β$ numbers, and expectation values are amplified through lexicographic graph products.

Quantum networks will combine optical fibre with free-space links, yet continuous-variable quantum key distribution (CV-QKD) has been developed predominantly for one medium or the other, while operation across concatenated fibre-free-space channels remains largely unexplored. The two media impose contrasting requirements: fibre transmission is stable and permits long processing intervals, whereas atmospheric propagation imposes transmittance fluctuations that degrade security and must be resolved on short timescales. Here we demonstrate a locally generated local oscillator CV-QKD with both Gaussian-modulated coherent and squeezed states over a deployed hybrid channel comprising a 620-m free-space link and 2 km of deployed fibre, with a total loss up to 20 dB. Rather than adapting the optics to each medium, we move channel adaptation to the post-processing, through a unified adaptive post-processing framework coupling transmittance-based clustering, residual-fading mitigation by covariance-matrix averaging or de-fading, and rate-adaptive blind reconciliation, which alone recovers up to 19% additional key. The same adaptive-processing principle is applied to both protocols, while accounting for their different security analyses and statistical requirements, yielding asymptotic secret-key rates of 0.42 Mbit per sec for the coherent-state protocol and 0.93 Mbit per sec for the squeezed-state protocol under the respective channel conditions, and establishing squeezed-state CV-QKD over a deployed atmospheric channel. These results show that adaptation to the transmission medium can largely be transferred to the data-processing layer, providing a route towards heterogeneous quantum networks spanning fibre, terrestrial free-space and satellite links.

Quantum computing is a quickly growing field that is promising various advantages compared to conventional computing. However, currently stand-alone quantum applications are scarce and hybrid (quantum-classical) computing is needed, especially in quantum machine learning (QML). Due to current limitations of quantum computing hardware and the coupling between HPC and quantum devices, integrating a trained (QML) model in classical applications is challenging. In this case, it is helpful to couple so-called shadows of the QML model instead, i.e., classical models that imitate the input-output relations of QML models such that quantum resources are only needed during the training stage. Here we consider constructive shadowing processes without an explicit training or regression stage to avoid rendering the QML model redundant, and apply them to a previously developed QML model for cloud cover [1] to allow for an efficient coupling to a climate model. We compare classical interpolation methods to an approximation of the quantum Fourier model, the representation of the circuit as a partial Fourier series. The encoding strategy in [1] allows the use of the discrete Fourier transform to efficiently reconstruct the circuits classically. Truncating the partial Fourier series further reduces the size of the shadow models. Both methods have the effect of mitigating finite sampling noise under certain conditions, which yields a motivation to use shadow models also beyond the era of limited hardware availability. Further, we compute the shadow models on the quantum system Euro-Q-Exa, based on the IQM Radiance system with superconducting qubits, where error mitigating effects can also be observed, albeit it is still difficult to distinguish them from errors connected to the calibration of the system.

By combining coherence thermofield dynamics with the single-Hessian approximation, we enable simulations of low- to medium-resolution vibronic spectra of weakly anharmonic systems at nonzero temperatures, at negligible additional cost relative to zero-temperature calculations. Single-Hessian coherence thermofield Gaussian wavepacket dynamics is exact in any harmonic potential, provided that the reference Hessian is that of the final surface. When applied to Morse systems of increasing anharmonicity and varying temperature, this method successfully captures excited-state anharmonicity and key temperature-dependent spectral features, including hot bands and broadening. By combining the method with on-the-fly ab initio dynamics, we demonstrate its utility by computing the absorption spectra of naphthalene, aminocoumarin C450, and phenyl radical, and the photoelectron spectrum of SeO$_{2}^{-}$ . Within the ab initio single-Hessian approximation, after the zero-temperature spectrum is obtained at the cost of classical molecular dynamics (on the order of hours), all nonzero-temperature spectra are computed in seconds.

The Dicke model is a paradigmatic setting for collective light-matter physics and the superradiant phase transition. Yet extracting the critical exponents is challenging at experimentally accessible mesoscopic sizes, due to the slow divergence of the correlation time under all-to-all coupling and a photon-loss-driven crossover to a distinct dissipative universality class. Here, we perform a large-$N$ analysis that identifies distinct coherent and dissipative fixed points for the closed and open Dicke models. We then develop a unified mesoscopic scaling framework that incorporates the leading irrelevant correction and, going beyond static and spectral probes, brings ramping dynamics under the same scaling description. It recovers the corresponding exponents, verifies Kibble-Zurek scaling, and clarifies how finite size, dissipation, and speed compete in the ramping dynamics. Our work thus establishes a unified framework for resolving static and dynamical critical scaling in closed and open quantum systems, with broader applicability to mesoscopic systems with long-range interactions.

Quantum catalysts can overcome otherwise impossible quantum state transformations without being consumed, and allowing them to become correlated with the output makes this assistance substantially more powerful. This raises a fundamental question for entanglement theory: which limitations on state manipulation remain when such correlated catalysts are freely available? We answer this question in the positive-partial-transpose (PPT) resource theory, which allows a substantially broader class of operations than local operations and classical communication (LOCC). We identify general conditions under which regularized relative-entropy measures become strongly superadditive, and use them to construct monotones that constrain correlated catalytic PPT transformations without any knowledge of the catalyst. In particular, we prove that the regularized PPT relative entropy is fully additive and strongly superadditive, resolving an open problem in entanglement theory. Most importantly, these constraints show that even arbitrary correlated catalysts cannot restore asymptotic reversibility: for an explicit state, the optimal entanglement distillation rate remains strictly smaller than the entanglement cost. Thus, substantial catalytic assistance does not remove some of the fundamental limitations of mixed-state entanglement manipulation.

We study bipartite entanglement from the convex geometry of quantum states. Taking the maximally mixed state as a reference point, we define a geometric entangled-space quantity $G(ρ)=[1-L(ρ)]/L(ρ)$ from the relative positions of the separable and quantum-state boundaries, and introduce a relative entanglement degree $Q(ρ)=[(1-p)/p]/G(ρ)$ by comparing it with the robustness relative to the maximally mixed state. We apply this geometric construction to the Best Separable Approximation (BSA). For the optimal decomposition, we derive the general bound $(1-p)L_B/[p(1-L_B)]\leq p_0\leq Q(ρ)$ and show that the entangled component of the BSA has an entangled-space size no smaller than that of the original mixed state, namely $[1-L_R]/L_R\leq[1-L_B]/L_B$. For two-qubit states, the BSA entangled component is a pure entangled state. Using the PPT criterion, its geometric parameter can be evaluated explicitly, giving the bound $(1-p)/(2p)\leq p_0\leq Q(ρ)$. These results provide a simple geometric description of the relation between BSA, robustness, and the entangled region of the quantum-state space.

We propose and demonstrate a general mechanism for nanoscale lensing based on the phase gradient imposed by a single nanostructure scattering light in its near-field. We verify this effect using an optical waveguide on a substrate, with single atoms serving as quantum probes that sample the near-field intensity through their fluorescence. This quantum probing technique provides a unique, non-destructive approach to characterizing focused optical fields and reveals a 4-fold enhancement in single atom detection efficiency. This work establishes on-chip nanostructures as a multi-functional quantum optics platform that can efficiently route photons, localize fields, and enhance atom-photon coupling, offering new opportunities for trapping and manipulating single atoms and realizing hybrid nanophotonic-atomic systems for quantum applications.

Quantum imaging with undetected photons (QIUP) allows an object to be probed at mid-infrared frequencies by only measuring interference in the visible range, thus leveraging silicon camera technology. We show that non-collinear phase-matching in a silver thiogallate (AgGaS$_2$) crystal enables wide-field QIUP in the wavelength range of 6-10 $μ$m (1670-1000 cm$^{-1}$). A combination of coherent detection and infrared photons being ``undetected'' enables imaging at ${\sim}$100 times better than the background-limited infrared photodetection (BLIP) limit. At 8 $μ$m, our images have over 8000 $\pm$ 100 resolvable elements with a 297 $\pm$ 5 $μ$m resolution, and 10 s acquisition time. Our results pave the way to fast, background-noise-free, room-temperature, spectrally-selective mid-infrared imaging.

Retrodiction is the act of inferring a cause from its effects, the most common example of which is Bayesian inference. Retrodiction can be defined by its structural process-theoretic properties, which are mathematically captured by category theory. This categorical definition of retrodiction has recently been shown to potentially isolate the Petz recovery map as a unique universal candidate for quantum Bayesian inference. This paper extends these results to the infinite-dimensional setting on von Neumann algebras. In the process, we provide a pedagogical review of the Petz recovery map in infinite dimensions and its relation to the more commonly used expression in the finite-dimensional setting. We formalize the open question as to whether these categorical axioms for retrodiction do in fact uniquely characterize the Petz recovery map. If such a characterization holds, this would show that Bayesian inversion and the Petz recovery map are structural necessities and not simply useful algorithms for classical and quantum inference.

Practical quantum single-parameter estimation is rarely a pristine task; it almost invariably involves nuisance parameters, casting it as a one-from-many problem. Existing approaches to this problem rely on multi-parameter metrology, reducing the matrix quantum Cramér-Rao bound to obtain scalar quantum precision limits. However, these methods are often hampered by the demanding inversion of the quantum Fisher information (QFI) matrix and the requisite choice of a weight matrix, and they break down when the QFI matrix becomes singular. Here, we show that for dynamical one-from-many estimation, a previously overlooked sum rule connecting the QFI about all model parameters to the QFI about time necessitates including the latter to consider an augmented QFI matrix while simultaneously rendering it inherently singular--precisely the scenario where conventional approaches fail. To meet this challenge, we derive a tight, matrix-free quantum precision bound that involves only scalar quantities, offers broad applicability, and subsumes existing results as special cases. Validated in both unitary and noisy settings, our findings provide a refined operational framework for practical quantum single-parameter metrology.

We present a practical, ab initio time-dependent method using Hagedorn wavepackets to simulate resonance Raman (RR) spectra of polyatomic molecules. Hagedorn functions---Gaussians multiplied by specific polynomials---are used to represent RR initial and final states because these functions are exact solutions to the time-dependent Schrödinger equation for at-most-quadratic potentials and can be propagated at zero cost beyond that of propagating the guiding Gaussian. Using efficient recursive formulae to compute overlaps between Hagedorn wavepackets, we can evaluate RR excitation profiles for arbitrary spectral signals, such as fundamental, overtone, combination, and hot bands. We then construct the Stokes and anti-Stokes RR spectra from these profiles. We first validate the method in a two-dimensional displaced, distorted, and Duschinsky-rotated harmonic model against numerically exact split-operator calculations. Then, we apply the method to compute RR spectra of anthracene by performing dynamics on a 66-dimensional harmonic potential energy surface constructed from density functional theory calculations.

The paper investigates entangling operations acting on two qudits of arbitrary dimension, with one encoded in the states of a spatially multimode optical field, the other in those of atomic collective spin coherence, both carrying orbital angular momentum (OAM). We demonstrate the generation of a wide range of entangling operations within a protocol consisting of two Faraday interactions and a rotation of atomic and light quadratures between them. All generated gates can be represented as rational powers of the d-dimensional gate $SWAP^α_d$. The probabilities of two-qudit transformations are calculated for various dimensions of the logical space and for different entangling powers of the logical gates.

Though quantum computing naturally offers an advantage for simulations of real-time quantum systems, implementing Imaginary-Time Evolution (ITE) is comparatively more difficult. Nevertheless, quantum implementations of ITE are useful both in cases where classical implementations have associated sign problems, and also as an exact method of preparing eigenstates on quantum computers. In this work we present an algorithm to obtain ITE of a generic quantum Hamiltonian by performing analytic continuation of measured real-time correlation functions. We present simulations and demonstrations on IBM quantum hardware of 1D Fokker-Planck equations for classical diffusion process and imaginary-time evolution of integrated correlation functions in 1D quantum mechanical scattering as examples to demonstrate the effectiveness of the method.

Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computing, but their practical implementation requires efficient circuits for syndrome extraction. Many qLDPC families are assembled from a small set of components through explicit constructions that imprint edge symmetries on their Tanner graphs. We show that these symmetries can be exploited to design syndrome-extraction circuits from the underlying components, rather than from the full quantum code. For Lifted Product and Balanced Product codes this approach yields an analytical construction with provably optimal or near-optimal CNOT depth. For Quantum Tanner codes it produces depth-optimal circuits on every instance we test, including codes up to nearly 600 data qubits.

Molecular docking is a vital computational task in drug discovery, wherein the objective is to efficiently identify optimal binding poses between a ligand and a target receptor protein. Due to the combinatorial explosion of possible binding configurations, docking of large and flexible molecules remains a computationally intensive problem, especially at scale. Early studies have revealed that the molecular docking can be re-cast as a maximum vertex-weighted clique problem (MVWCP) problem on a compatibility graph to be solved classically. In this work, we proposed a hybrid quantum-classical approach for molecular docking leveraging the MVWCP formalism with a variational full-basis encoding (FBE) strategy, which enables efficient encoding of classical binary variables with Bloch sphere vectors. We further prove that a global minimizer of the FBE objective can always be chosen to be a pure product state, thereby providing a rigorous justification for its optimization using a unitary variational circuit. The molecular docking problem is first mapped to a cost Hamiltonian that is minimized within a variational framework, optimized via a randomized imaginary time evolution (ITE)-inspired warm start, and gradient-based techniques. Finally, we also executed the circuit on an IBM quantum computer, underlying the feasibility and of quantum-assisted optimization for structure-based drug design and point towards the broader utility of advanced encoding techniques in quantum optimization for computational biology.

Variational Quantum Eigensolver requires many circuit executions, making it ideal for distributed parallelization. However, heterogeneous noise in NISQ devices can skew results and efficiency. Using the CUNQA platform for emulation of virtual QPUs, we evaluate three embarrassingly parallelization strategies (shot-level, circuit-level for gradients and observables and candidate level for population-based optimizers) across metrics like speedup and accuracy.

We consider the combined effect of a Duffing nonlinearity and the optomechanical interaction on the cavity density of states (DOS), which is directly observable in optomechanically induced transparency (OMIT) experiments. Both nonlinearities introduce the same type of interaction between polaritons, producing a distinct feature in the optical response. We derive the resonant condition that enhances the nonlinear scattering between polaritons and study the parameter dependence of the cavity DOS in detail. This allows us to characterize the typical strength and optimal conditions for observing the quantum effects of the Duffing nonlinearity in OMIT experiments.

Developed as a workhorse for classical simulations of quantum algorithms and quantum many-body systems, Tensor Network methods have entered the scientific mainstream in quantum physics. Among various types of tensor networks, Tensor Trains (commonly know as Matrix Product States in the quantum computing community) have already found applications in machine learning. These methods often rely on a powerful linear algebra tool called the Singular Value Decomposition (SVD). Several conditional GAN architectures for image denoising incorporate SVD as a single-cut decomposition step applied to generator feature maps. In this work we introduce TT-Net, which replaces the per-channel SVD denoising block with a two-cut tensor-train decomposition capable of accessing cross-channel information directly, a capability absent from contemporary alternatives. In a controlled comparison differing only in this decomposition mechanism, TT-Net outperforms SVD-Net on PSNR and SSIM across all three noise types tested (Gaussian, motion blur, and salt-and-pepper), supporting the hypothesis that cross-channel access improves denoising quality. Training-dynamics analysis further shows that TT-Net's adversarial loss term consistently saturates to a stagnant state across all three noise types, more so than SVD-Net's, while reconstruction quality continues to improve regardless, raising an open question about the adversarial component's contribution that this work identifies but does not resolve. Furthermore, for Gaussian noise our method outperforms both the EigenGAN and the state of the art Pix2pix method which does not assume any linear algebra decompositions and does not retain any linear algebra information. Our manuscript shows how quantum inspired tools can be used as practical real world feature filters for deep learning applications.

We show that there exists a total function for which there is a polynomial gap between the randomized and the constant-round quantum communication complexity. Previously, such a separation was known only for quantum protocols using polynomially many rounds.

World models provide digital simulacra of the true world, allowing agents to be trained and tested before costly real-world deployment. At each time step, they receive an action and generate an observation and reward matching the statistics of the true world. In complex environments where present outcomes depend on events far in the past, this requires memory. One might expect that, by increasing memory, we can always build a model accurately enough to align the optimal agent policies of the real and virtual worlds. We show that this is false for classical world models, even when the true world itself is classical. We construct true worlds for which every finite classical model fails along the same possible trajectory: it either loses the ability to distinguish actions when the true world clearly prefers one, or repeatedly assigns the highest expected reward to suboptimal actions. Its expected-reward estimates also retain a nonvanishing average error. In contrast, each such true world admits a quantum world model using a single qutrit that reproduces it exactly: its reward estimates and preferred actions always match those of the true world, ensuring that the optimal policies of the real and virtual worlds remain perfectly aligned.

We propose a gradient-flow method for quantum states in lattice models, generated by an action consisting of the quantum-metric and the square of the Berry curvature. These two terms drive the spectral projector toward Bogomolny saturation and uniform Berry curvature, respectively. We show that, due to a no-go theorem for finite-dimensional projectors, the two conditions cannot in general be satisfied simultaneously in lattice models. Hence the flow is expected to approach a nontrivial fixed point that balances the two geometric requirements. For the Wilson-Dirac model, we demonstrate that the flowed projector exhibits almost uniform Berry curvature while remaining close to the Bogomolny bound. We further construct a short-range truncated flattened Hamiltonian from the flowed projector and obtain a lattice model with nearly flat bands and nearly uniform Berry curvature. We also apply the method to the Hofstadter model and confirm the roles of the metric and Berry-curvature terms in a Chern band with higher Chern number.

The recent creation of a Bose-Einstein condensate (BEC) of dipolar molecules has opened a new frontier for many-body quantum systems in which dipolar interactions can drive novel self-organization phenomena. Here, we observe electrostriction in a molecular BEC, an elliptical deformation driven by anisotropic dipolar interactions. We use double microwave dressing, involving $σ$- and $π$-polarized fields, to control non-axially symmetric dipolar interactions. We compare the experimental observations of electrostriction to a model based on an extended Gross-Pitaevskii equation and find excellent agreement in the regime of weak to moderate interactions. Using electrostriction, we demonstrate that the molecular BEC can be torqued by dynamically changing the orientation of the elliptical $σ$ microwave field. This provides a route to setting molecular quantum gases into rotation, opening opportunities to probe vorticity, superfluidity, and supersolidity in strongly dipolar matter.

We develop a geometry for transporting stationary-state response across the control space of an open quantum system. A physical model is represented by the ordered pair of its stationary state and dynamical generator. Embedding these pairs in a common ambient space induces a metric, a response one-form, and a closed two-form on the control manifold. The ambient space admits a canonical complex structure that exchanges state and generator directions, but the Liouvillian null-state condition restricts physical models to a submanifold that need not preserve this structure. For an amplitude-damped optical Bloch model, the metric and response two-form are compatible at the single point $ω=0$ and $g/Γ=1/\sqrt{2}$; the physical manifold is non-Kähler elsewhere. The induced metric defines the Levi--Civita connection, geodesics, and parallel transport without requiring Kähler compatibility. We compute the connection by automatic differentiation through the stationary Liouvillian solve and recover the symbolic result to machine precision. A two-point calculation then shows that the resulting geodesic differs from linear interpolation in control space and follows a shorter path through the family of state--generator models. This geometry supplies the intrinsic derivative and transport structure needed to carry observable response, including multidimensional spectra, between admissible stationary models.

One of the most basic conjectures in quantum complexity theory states that every $t$-query quantum algorithm can be simulated on most inputs by a $\mathrm{poly}(t)$-query classical algorithm. If true, this would provide broad justification for the need for structure in quantum speedups. We settle this conjecture for parallel quantum algorithms, showing that every $t$-query $d$-round quantum algorithm can be simulated on most inputs with $t^{O(d^2)}$ classical queries. This suggests that for unstructured problems, superpolynomial speedups would require quantum circuits of superconstant depth, and exponential speedups would further require polynomial depth. In contrast, most known speedups for structured problems are achieved by highly parallel, low-depth algorithms. Our techniques also carry new implications for the status of $\mathsf{BPP}$ vs. $\mathsf{BQP}$ relative to a random oracle, a similarly longstanding problem.

In this work, we study the limitations and advantages of using entanglement battery and entanglement catalyst in local state discrimination problems. We consider both cases of such tools, i.e., exact and approximate cases. We show that to distinguish any set of orthogonal pure bipartite entangled states perfectly under local operations and classical communication using an (exact) entanglement battery or an (exact) entanglement catalyst, it is necessary to consider that the cardinality of the set must be smaller than the total dimension of the given Hilbert space. Then, we construct a nontrivial case where an exact entanglement battery can provide huge advantage. We also construct other nontrivial cases where exact or approximate entanglement battery or entanglement catalyst can be useful. In fact, we find that the approximate tools are particularly useful in the local discrimination of certain sets which can be derived from many-copy indistinguishable ensembles.

Adding links generally improves classical transport by increasing the number of available paths. We show that coherent quantum transport can display the opposite behavior. Using continuous-time quantum walks on a percolated hierarchical small-world network, we identify a coherent overconnectivity penalty: root-to-boundary transport is maximized at intermediate bond probability and decreases as the network approaches full connectivity. The effect is quantified by the final-layer limiting probability $χ_N$ and by the penalty $P_Q=1-χ_N(p=1)/\max_pχ_N(p)$, which measures the loss caused by making the architecture fully connected. The optimum results from a competition between shortcut-assisted spreading and interference-induced intra-layer recirculation. Spectral analysis shows that bond dilution creates motif-induced degeneracies and reorganizes the eigenstates connecting the root to the outermost layer. A comparison with dephased and classical transport shows that the non-monotonic landscape is not a purely geometrical percolation effect, but a coherent architecture-dependent phenomenon. These results provide a design principle for coherent transport in disordered photonic and quantum-network architectures.

The practical implementation of quantum algorithms on noisy intermediate-scale quantum devices encounters operational limitations due to decoherence and other sources of noise inherent in real hardware. To mitigate these errors while preserving the original functionality of the algorithm, shorter quantum circuits are therefore preferred. This motivates the development of effective quantum circuit optimization algorithms. Learning-based approaches have emerged as a leading candidate, yet existing autonomous agents remain inefficient, spending most of their training capacity rediscovering elementary reductions that deterministic rule-based methods already handle reliably. To address this challenge, we propose a reinforcement learning framework that embeds a deterministic Commutation-and-Reduction (CR) algorithm directly into the training environment. After every agent action, the CR algorithm automatically resolves elementary commutations and cancellations, enabling the agent to focus its learning capacity on the non-trivial optimizations where reinforcement learning adds real value. Empirical evaluation across two gate sets, the universal Clifford+T basis and the CNOT+Pauli basis, shows that RL+CR produces shorter circuits than a standard RL agent at all tested scales. We demonstrate that RL trained on smaller quantum circuits can be applied to larger quantum circuits. On 20-qubit Clifford+T circuits, five times larger than the training circuits, RL+CR removes twice as many gates as standard RL. This work provides a robust approach that could accelerate the compilation and optimization processes for future fault-tolerant and utility-scale quantum systems.

Quantum magic, or nonstabilizerness, is a quantum resource associated with computational advantage in quantum systems. In high energy collisions, Quantum Electrodynamics (QED) is inefficient at generating magic while the weak mixing angle, a fundamental constant of nature, sits near a value that minimizes magic production in charged-lepton scattering. These observations were made in the laboratory (lab) basis, in which spin is projected along the incoming beam axis. An alternative choice is the helicity basis, in which spin is projected along the direction of motion of each particle. The transformation between these two bases is, in general, not a Clifford operation and therefore can change the amount of magic. We present a detailed study of magic production in both bases for QED and electroweak processes, and compare these results with the basis-invariant non-local magic. In the ultra-relativistic limit, magic production is generally smaller in the helicity basis due to helicity selection rules, while the lab basis generally yields less magic in the non-relativistic regime. We provide circuit realizations of the ultra-relativistic Bhabha amplitudes using linear combinations of unitaries and show that the lab basis construction contains a larger $T$-gate count at generic scattering angles. Interestingly, in both bases the physical weak mixing angle lies close to the value that minimizes magic production.

Calderbank-Shor-Steane (CSS) codes, constructed from nested classical codes $C_2 \subseteq C_1$, are typically optimized for good code parameters. However, practical quantum computing equally demands fault-tolerant logical gates. In this work, we characterize nested pairs $(C_1, C_2)$ whose resulting CSS codes realize a target logical diagonal gate via transversal physical $Z$-rotations. In doing so, we recover a result of Camps-Moreno et al. that CSS codes can realize only logical single-qubit $Z$-rotations and multi-qubit controlled-$Z$ rotations via transversal physical $Z$-rotations. Building on our characterization, we develop the ''appending construction'', that takes as input an $[[n',k']]$ CSS code $Q'$ and a target logical $Z$-rotation (single-qubit or multi-controlled) $U_L$, and extends $Q'$ by systematically appending $n''$ physical qubits to obtain an $[[n,k]]$ CSS code $Q$ with $n = n'+n''$ and $k=k'$. The target logical gate $U_L$ is realized in $Q$ by applying a well-chosen physical transversal $Z$-rotation to the $n''$ appended physical qubits. The CSS code $Q$ may incur a loss in minimum distance, but the loss can be controlled through the parameter choices made in the construction. By repeatedly applying the appending construction, we can extend any CSS code $Q'$ to obtain a CSS code $Q$ that supports fault-tolerant implementations of multiple desired logical $Z$-rotations. The cost to be paid for this is the increased physical qubit overhead as the number of target logical gates grows.

Non-local search-to-decision asks whether two noncommunicating parties, given the two shares of a bipartite encoding of a uniformly random string $x\in \mathbb{F}_2^n$, can both predict the same random parity $\langle r,x\rangle$ without there also being local measurements with which both parties recover $x$. We prove that if their optimal probability of both recovering $x$ by local measurements is $p$, then their probability of both answering a common parity challenge correctly is at most $\min\{1,\frac{1}{2}+5p^{1/22}\}$. The result is motivated by applications to unclonable encryption and quantum copy-protection. The proof is information-theoretic and does not provide an efficient extractor. The proof and the exposition were developed with assistance from ChatGPT using GPT-5.6 Sol Pro and Codex in the Ultra reasoning mode.

We identify different regimes of quantum state transfer in long-range coupled spin-$\frac{1}{2}$ systems, where naturally occurring power-law interactions enable rapid, high-fidelity transfer with minimal engineering. Across a broad range of interaction profiles, from effectively nearest-neighbour coupling to Coulomb interactions, we show how long-range connectivity fundamentally reshapes the mechanisms underlying information propagation within such systems. For effectively short-range interactions, transfer follows familiar ballistic transfer dynamics: an initially localised excitation spreads across many eigenmodes concentrated within the approximately linear region of the spectrum, enabling robust wavepacket motion. In contrast, increasing long-distance interactions via lowering the power-law exponent $α$ ($α=1-2$) drives a striking transformation, where the initial state becomes confined to progressively fewer eigenmodes, ultimately reducing the dynamics to the coherent participation of only a few states corresponding to the highest eigenenergies. This spectral localization gives rise to emergent long-range oscillations between distant sites, revealing a distinct -- and faster -- transfer mechanism arising from the intrinsic structure of long-range quantum interactions rather than from full-system engineering pathways.

We introduce Bernstein-Vazirani Networks (BVNs), a non-variational quantum machine learning framework that leverages quantum interference for supervised learning, demonstrated on vision and representation learning tasks. In their standard form, BVNs follow the principle of quantum Fourier sampling: labelled data are placed in superposition and interfered in the Fourier basis to extract globally informative features. We then define generalised BVNs that enable interference in problem-adapted bases, yielding more expressive models under the same measurement budget as in the standard setting. BVNs achieve universal function approximation through (over)complete interference bases, while training of BVNs is gradient-free. Experiments on synthetic and real-world classification tasks, as well as implicit image representation, show strong generalisation capabilities and competitive performance with classical and quantum baselines.

Machine-learned exchange--correlation (XC) functionals offer a route to improve Kohn--Sham density-functional theory without incurring the cost of explicitly correlated electronic-structure methods. Their use in production simulation codes, however, requires a well-defined mapping between the learned model and the host-code density representation. We formulate and implement a Skala-1.1 interface in CP2K through the external GauXC library. CP2K supplies the geometry, Gaussian basis, spin-resolved atomic-orbital density matrix, and communicator, while GauXC evaluates the XC energy, atomic-orbital potential matrix, and available nuclear derivatives. The interface accepts both all-electron and valence-only density matrices. The latter may arise from separable dual-space pseudopotentials or molecular effective-core potentials. Implementation errors are isolated from functional differences by comparing the Perdew--Burke--Ernzerhof (PBE) functional evaluated through GauXC with native CP2K PBE. The resulting interface gives consistent energies, forces validated against finite-difference total-energy checks, and force-based molecular-virial diagnostics for representative molecular cases. The dietGMTKN55 benchmark suite is evaluated with an all-electron Gaussian augmented plane-wave treatment for elements up to bromine and def2 effective-core potentials for the heavier elements. The resulting aggregate mean absolute deviation of 1.255 kcal/mol is within 0.020 kcal/mol of the corresponding Skala reference value of 1.235 kcal/mol. This work establishes a validated molecular implementation of Skala in CP2K through GauXC.

We show that entanglement-generation speed across a fixed network interface is governed by two distinct resources: the entangling capacity of the interface itself and the ability of the surrounding architecture to replenish it with fresh degrees of freedom. For fermionic Gaussian dynamics, we derive the coefficient-sharp bound $\sum_k|\dotθ_k|\leq\frac12\|K_{AB}\|_*$ on the collective speed of the canonical entanglement angles. Explicit Ising-chain rematching trajectories saturate this bound, thereby certifying exact minimum interaction times under the stated control model. Beyond the Gaussian setting, exhaustive optimization of the complete $N=8$ tree--tree family shows that, at fixed interface capacity, first-layer entanglement, connectedness, and edge budget, the saturation depth is exactly classified by rooted architecture. With higher-resolution $x$-only control, variational entanglement-enhancing-field (VEEF) optimization reaches the numerically resolved fast-$X$ optimum in a two-channel benchmark. Across all 21 symmetry-reduced rooted orbits, a pre-specified two-time VEEF growth diagnostic recovers the complete replenishment partition directly from optimized dynamics. Interface capacity therefore sets how much entangling flux is available, whereas architecture determines whether fresh degrees of freedom can continually replenish the interface and sustain repeated use of that capacity.

High-refractive-index particles have recently attracted a growing interest in optical levitation experiments, offering the ability to further engineer optical forces through electromagnetic Mie resonances. Unlike standard silica particles, which are predominantly trapped in the dipole regime and exhibit trap frequencies mainly determined by material density, resonant meta-atoms formed by high-index particles enable qualitatively new trapping behaviors. In this work, we experimentally investigate the trapping of resonant silicon particles in an optical standing wave. A direct comparison of silicon and silica highlights the fundamental differences in their optical force scaling and trapping dynamics. Beyond conventional trapping at intensity-maxima, we demonstrate deterministic and stable three-dimensional trapping of silicon nanoparticles in optical intensity minima, a regime that remains inaccessible for silica particles. Drawing a mesoscopic analogy with blue-detuned atom trapping, our results establish meta-atoms as a versatile approach to further extend the optical manipulation tool box towards accessing novel trapping regimes e.g. in close proximity to a surface.

Practical fault-tolerant quantum computing (FTQC) requires efficient lattice surgery (LS), so that large algorithms fit on resource-constrained quantum chips. Existing approaches, however, are rigid: qubits, routing space, and resource states are allocated ahead of execution, which prevents running on small chips, leaves statically scheduled executions with large time overheads, and fixes each design at a single area of the space-time trade-off. We present dynamic LS, which enables efficient reconfiguration of the ancilla space, just-in-time allocation of resource states, and dynamic rotations of logical qubits, thereby spanning the entire space-time trade-off with a single, unified approach. We realize dynamic LS with RushHour through a hardware-compiler co-design: the RushHour ISA formalizes and programs our dynamic lattice model, the Lattice Management Unit abstracts dynamic lattice management and performs efficient lattice reconfiguration, and the RushHour Compiler compiles logical circuits for physical chips into optimized ISA programs while pipelining instructions. We evaluate RushHour against six state-of-the-art compilers and two resource models. On the smallest chips, 86% of benchmarks run only with RushHour, while existing approaches require 1.2-3.5$\times$ larger chips. On space-constrained early-FTQC chips, RushHour runs a median 2.0-7.2$\times$ faster than the best feasible alternative, while achieving results comparable to the state of the art on very large chips. RushHour's constructive results run 4.8$\times$ from an idealized-machine resource limit.

In the simplest approximation, the reduced dynamics of a quantum system $S$ interacting with its environment $E$ is considered to be given by a completely positive map. But, in general, this is not the case. In fact, the reduced dynamics of the system in not even linear, in general. Whether the reduced dynamics is linear or not is determined by two factors: the set of possible initial states of the system-environment $\mathcal{S}=\left\lbrace ρ_{SE} \right\rbrace $, and the joint system-environment unitary evolution $U$. When $U$ is factorisable as $U=U_S\otimes U_E$, then we can choose $\mathcal{S}=\mathcal{D}$, where $\mathcal{D}$ is the set of all system-environment density operators. In other words, when $U$ is factorisable, the reduced dynamics of the system $S$ is linear (in fact unitary) for arbitrary initial state of the system-environment $ρ_{SE}$. We show that this result cannot be generalized to any non-factorisable $U$: For any non-factorisable unitary evolution of the whole system-environment $U$, the set $\mathcal{S}$ must be chosen as a proper subset of $\mathcal{D}$ to achieve linear reduced dynamics. As a byproduct, considering a convex set of possible initial states of the system-environment $\mathcal{S}$ such that $\mathrm{Tr}_{E} \ \mathcal{S}=\mathrm{Tr}_{E} \ \mathcal{D}$, we show that when the reduced dynamics of the system, for one system-environment unitary evolution $U_1$, is positive, but not completely positive, this implies that reduced dynamics is not linear for another $U_2$.

Constructing new quantum codes and understanding their error resilience are central challenges in the development of robust quantum memories. Topological codes are particularly promising due to their favorable error-correcting properties and their connections to phases of matter in many-body physics. In this thesis, we explore the interplay between classical Ising models and quantum error correction through subsystem symmetries, fracton topological order, and Kramers-Wannier-type duality. We study two three-dimensional classical self-dual Ising models with subsystem symmetries, the Tetrahedral Ising model and the Fractal Ising model, investigating their thermal behavior, their relation to fracton phases through subsystem-symmetry gauging, and the properties of the resulting fracton codes. Using a statistical-mechanical mapping, we determine the optimal code-capacity threshold of the Checkerboard code to be $0.107(3)$, which saturates the theoretical limit for CSS codes and represents the highest optimal error threshold among known three-dimensional codes. We relate this saturation to a generalized entropy relation for classical spin models satisfying a Kramers-Wannier-type duality, and argue how this prediction extends to CSS codes with zero encoding rate whose $X$- and $Z$-noise models map to classically dual spin models. These findings establish fracton codes as highly resilient candidates for quantum memories and demonstrate the power of the statistical-mechanical framework, together with its duality predictions, in analyzing and constructing robust quantum error-correcting codes.

Hybrid quantum photonics seeks to combine the complementary advantages of continuous- and discrete-variable quantum optics. This typically entails photon-counting measurements on entangled states generated by interfering many single-mode squeezed-vacuum (SMSV) states. However, because conventional photon-counting schemes are mode-insensitive, it is critical that the SMSV states occupy a single, well-defined mode. Achieving this requires careful engineering of the process, which determines both the spatial and spectro-temporal properties of the generated state. In addition, the ideal source must be massively scalable, capable of efficiently generating strong squeezing, and remain compatible with existing detection schemes and fiber networks. Although many platforms address one or more of these requirements, satisfying all of them simultaneously remains challenging. Here, we present a source that meets all of these requirements: a single-pass, periodically poled, Type-II potassium titanyl phosphate (KTP) waveguide optimized for scalable hybrid quantum-photonic architectures. The SMSV state produced by the source has a measured effective mode number of 1.24. Furthermore, the source is extremely bright (producing up to 40 000 photons per pulse) and operates at a central wavelength of 1546nm, optimized for fiber-network compatibility and which, in combination with picosecond duration, also enables intrinsic photon-number resolution in superconducting nanowire single-photon detectors. Although this source constitutes an ideal source in a simplified picture, the ultimate limitations of any source will be governed by complex dynamics that arise when the system is driven at high-gain or due to unavoidable loss during state generation. We have therefore developed a complete theoretical framework that enables a comprehensive photon-counting-based characterization of the source.

Clifford circuits play a foundational role in quantum computing, particularly due to their importance in quantum error correction and fault-tolerant logical synthesis. While these circuits can be efficiently simulated and represented as symplectic matrices, standard synthesis methods-such as the Aaronson-Gottesman algorithm-often yield sub-optimal circuits with excessively high gate counts. In this work, we introduce AlphaClifford, a model-based Reinforcement Learning framework powered by Monte Carlo Tree Search, designed to efficiently synthesize Clifford circuits from the fundamental gate set composed of H, S, and CNOT. By modeling the state space through the algebraic properties of the symplectic group, AlphaClifford effectively explores this combinatorial space to minimize overall circuit cost. For unconstrained Clifford optimization, our approach achieves a consistent reduction in both total and two-qubit (CNOT) gate counts compared to state-of-the-art synthesis heuristics, despite operating with a strictly less expressive gate set. Furthermore, we demonstrate the broad applicability of our framework on two additional tasks: hardware-constrained Clifford transpilation, where we outperform existing RL-based compilers, and as a post-synthesis optimization component within a full Clifford+T logical synthesis pipeline. Our results underscore that model-based RL is highly effective at addressing the combinatorial complexities of quantum compilation, offering a scalable pathway to mitigate hardware constraints in both near-term and future fault-tolerant quantum devices.

The sensitivity of quantum sensors is fundamentally constrained by the standard quantum limit (SQL) arising from intrinsic quantum fluctuations. While non-classical resources like squeezing or entanglement can surpass this limit, their utility is often restricted by the extreme fragility of entangled states and the complexity of their preparation. Quantum criticality offers a compelling alternative by harnessing divergent susceptibility to amplify signals without requiring fragile non-classical resources. However, the practical benefit of this approach has remained controversial due to the potential for the simultaneous amplification of quantum noise. Here, we demonstrate a universal protocol for noiseless critical sensing by engineering a light-driven atomic ensemble near a dynamical critical point. Analogous to a Kapitza pendulum near its inverted orientation, the spin system enters a non-equilibrium regime where the signal susceptibility diverges while the quantum noise periodically recedes to its coherent baseline. We exploit this ``noise ebbing'' to create a built-in noiseless amplifier, demonstrating a 3.3 dB metrological gain over the SQL in an atomic magnetometer. Our implementation exhibits intrinsic robustness against common experimental imperfections such as detection losses, establishing non-equilibrium critical dynamics as a practical and versatile paradigm for surpassing the fundamental limits of quantum sensing.

The real classical shadows protocol of West et al. replaces the unitary (Clifford) ensemble of the Huang--Kueng--Preskill scheme by the orthogonal (real Clifford) ensemble, and for symmetric observables achieves strictly smaller estimator variances: a factor approaching two for global evolution and an exponential factor $(3/2)^k$ for $k$-local real Pauli observables. Real hardware, however, never implements the ideal evolution. Building on the noisy classical shadows framework of Koh and Grewal, we give a complete theory of the real classical shadows protocol in the presence of a known completely positive trace-preserving noise channel acting after the orthogonal evolution. We derive the noisy global and local orthogonal shadow channels from first principles using the Weingarten calculus of the orthogonal group, prove that each is a depolarizing channel acting on the symmetric (respectively locally symmetric) component of its input, and derive from it the exact single-shot variance in closed form, together with the associated shadow seminorm, two-sided bounds on it, and the resulting sample-complexity guarantees. We prove that the noiseless sample-complexity advantages survive intact under noise. Because the variances are exact rather than bounded, the ratio is controlled by a single dimensionless parameter, which gives a closed-form criterion for when the factor of two is attainable: both the second-moment and the variance ratio reach it exactly when the observable's norm profile grows, and the noise enters that limit only through a factor lying within $2/(d+2)$ of two, so the advantage is uniform in the noise. For rank-one targets it is provably unattainable, saturating strictly below two. The local real-Pauli advantage remains $(3/2)^k$. We treat complex measurement bases through a reality parameter and a transposed-noise scalar, recovering unitary shadows in the appropriate limit.

Tensor Networks are a relatively new machine learning approach. The architectures proposed initially are inspired by approaches from quantum many-body physics simulations. One common layout is the matrix product state (MPS) also known as a tensor train optimized with gradient descent techniques. We introduce a global normalization condition, so that the MPS represents a quantum state. We investigate two optimization methods that find the locally optimal tensors and compare them regarding their effectiveness. One is based on gradient descent and the other on an adaptation of DMRG.

For local hidden-variable accounts of the CHSH experiment that are faithful -- reproducing the observed singles and coincidence rates and unbiased marginals of a polarization singlet with symmetric detector efficiency $η_{\rm eff}$ -- I determine the minimal measurement dependence $M$ (Hall's variational measure) needed to achieve a CHSH value $S$. Linear programming over all local strategies yields, to machine precision at 32 grid points, $M(S,η_{\rm eff})=\max\{0,η_{\rm eff}((S+2)η_{\rm eff}-4)/6\}$, whose edges reproduce Hall's tight bound at $η_{\rm eff}=1$, the Garg-Mermin detection threshold, and the postselection ceiling $S=4/η_{\rm eff}-2$. The quantum point is certified exactly: $M(2\sqrt{2},9/10)=(27\sqrt{2}-33)/100$, with primal and dual certificates in $\mathbb{Q}(\sqrt{2})$ arithmetic. I solve the unique detection profile $D(m)=\sqrt{m}\,h(m)$ under which a deterministic sign model reproduces the singlet exactly, derive the $\sqrt{m}$ edge law, and prove exact quantum correlations and angle-independent coincidence rates jointly impossible for any pure-detection model of this class. Surviving local accounts trade off measurement dependence against a $\cos 4(a-b)$ modulation of the fourfold coincidence sum, of relative amplitude up to 12.4%, which vanishes identically at the CHSH angles and appears never to have been bounded below 1%. A settings-torus protocol reaches $5σ$ sensitivity at 0.1% within hours: a flat result forces $M\gtrsim 95\%$ of Hall's floor; a fringe would contradict the flat-rate prediction of quantum mechanics. Finally I exhibit a local mechanism -- moire phase locking -- with deterministic phase evolution and all randomness quenched in frozen lattice offsets and flight times, which attains the certified floor exactly at $η_{\rm eff}=1$ (10% uniform fidelity); its softening of the correlation extremes is a falsifiable fingerprint.

The threat quantum computers pose to classical public-key cryptography motivates the deployment of quantum-safe communication for critical infrastructure such as healthcare, finance, and energy systems. Quantum key distribution (QKD) and post-quantum cryptography (PQC) offer complementary security guarantees, information-theoretic key exchange and quantum-resistant end-to-end authentication that can be combined in a layered architecture. Here, we demonstrate a field-deployed quantum-secure network integrating entanglement-based QKD with end-to-end PQC over 140 km of installed fiber in Thuringia, Germany, connecting a rural health kiosk to a university hospital via a trusted-node architecture comprising heterogeneous underground and aerial fiber links. Unlike conventional deployments that rely on a dedicated key management system to forward keys to applications, our architecture injects QKD keys directly into standard Linux-based VPN tunnels between adjacent nodes, while PQC secures the communication end-to-end, remaining fully compatible with existing infrastructure and software. Polarization-entangled photon pairs were generated at 810 nm and 1550 nm, with the telecom photon transmitted over deployed fiber. Active polarization stabilization and dispersion compensation preserve the entanglement and enable 22 days of continuous, fully autonomous operation, further underscoring the technological maturity of entanglement-based QKD approaches in a real-world fiber environment. Although the two deployed links were operated during separate rather than concurrent periods, the predominantly aerial link exhibited markedly greater instability, with QBER variations most strongly correlated with wind speed. The generated keys secured a telemedicine proof-of-concept without modifying existing medical systems, demonstrating a practical framework for quantum-safe critical infrastructures.

Quantum simulation based on ultra cold atomic lattice gases is one of the most promising platforms to investigate high-$T_c$ superconductivity beyond the limited capabilities of quantum many body numerics on classical computers. Yet, despite enormous progress since the field's inception, realizing a high-$T_c$ superconducting state still remains out of reach. The present work lays the groundwork to purpose the recently proposed, and already partly realized, mixed-dimensional (mixD) models, towards this end. These systems offer the proven capability to realize very high pairing energies while retaining appreciable mobility of pairs. We specifically investigate the potential of 2D mixD-models with anisotropic tunneling, using the matrix product state plus mean field theory (MPS+MF) for fermions, and show that these models may enter a high-$T_c$ superconducting phase. These simulations in turn are based on a comprehensive characterization of the 1D mixD-systems, which are the sub-units of which the 2D system is comprized. In this, we cover the range of currently experimentally relevant system sizes, and establish practical heuristics to determine when finite\hyp size effects preclude the use of a 1D mixD-system to build the 2D ones.

Copy-protection encodes a functionality in a reusable quantum state that cannot be split into two states (freeloader adversaries) which remain simultaneously useful. Prior plain-model results handle only independently sampled challenges; the more natural identical-challenge notion, also tied to unclonable bits and copy-protection of point functions, has remained open. We strengthen these definitions and prove plain-model security for our new stronger notions. For single-decryptor encryption (SDE) we define correlated challenge security, show it implies all previous SDE notions including identical-challenge security, and prove that the construction of Kitagawa and Yamakawa (TCC'25) achieves it assuming iO and one-way functions. We also nearly fully characterize the relations among prior SDE notions. For general functionalities we define correlated challenge unclonable puncturable obfuscation (UPO), allowing arbitrary correlations among challenge points and puncturing bits plus auxiliary information before and after splitting, and requiring only conditionally uniform bits and $λ^c$ average conditional min-entropy in each point separately (thus, in particular, the points may be identical). Assuming post-quantum iO and quantum-hard LWE, we construct correlated UPO for polynomial-size keyed circuits with input length at least $λ^c$, answering an open question of Ananth, Behera, Huang, Kitagawa, Yamakawa (EUROCRYPT'26) and of Cakan-Goyal (EUROCRYPT'26). We also obtain the first plain-model copy protection for point functions, $k$-point functions, and compute-and-compare programs, and identical-challenge copy protection for general puncturable functionalities.

We consider a fundamental problem of \emph{mixedness testing}: Given $n$ copies of an $N$-qubit state $ρ$, determine whether $ρ= \mathbb{I}_d/d$ or $\|ρ-\mathbb{I}_d/d\|_1 \geq \varepsilon$ with high probability, where $d = 2^N$. In particular, we focus on performing this task in the practical setting of single-qubit measurements, where measurements are prepared independently on each qubit. We provide a nearly complete picture of single-qubit mixedness tesing by showing $n = \widetildeΘ\left(\sqrt{10}^N/\varepsilon^2\right)$. To establish our lower bound, we introduce a new measurement-dependent lower bound framework for adaptive single-copy state certification. For the upper bound, we present a randomized Pauli basis measurement protocol, which relies on a new primitive for computationally efficient uniformity testing of correlation-concentrated distributions on the Boolean hypercube.

Spatially graded nonreciprocity can move skin weight away from a boundary, but it does not generally preserve a real commensurate spectrum or analytically controlled dynamics. We study a finite open Krawtchouk network with oppositely graded directed hoppings. For a broad intermediate range of asymmetries, their local imaginary gauge field changes sign in the bulk, and its accumulated coordinate generates a positive diagonal similarity map whose normalized squared entries form a biased-binomial envelope. The same map converts the open chain into the spin-rotation generator \(2gJ_x\), so the focus and equally spaced spectrum follow from one grading. In this focusing regime, exact right, left, and biorthogonal eigenvectors show that the envelope width and participation number both scale as \(\sqrt N\), identifying a subextensive interior focus. In the physical node basis, spin rotation produces perfect mirror inversion with direction-selective amplification and attenuation whose gains are mutually inverse. The directional Green functions share their poles, while their residues differ by the same similarity ratio. Closing the chain exposes a gauge-invariant imaginary flux, and either exact one-way limit yields an exceptional point of order \(N\). Onsite disorder preserves the directional resolvent ratio, whereas independent hopping disorder breaks the clean analytic Krawtchouk map and degrades commensurability and transfer. The model therefore provides an exactly solvable finite-network framework linking localization geometry and eigenvector nonorthogonality to commensurate spectra and node-resolved directional response.

Achieving fast, high-fidelity state transfer is fundamental to scalable integrated photonics and quantum information processing. While adiabatic evolution provides inherent robustness against control and fabrication imperfections, its requirement for slow driving leads to impractically long propagation distances in photonic circuits. Existing acceleration strategies, such as shortcuts to adiabaticity (STA), can dramatically shorten evolution times but generally rely on non-native auxiliary couplings or delicate Hamiltonian engineering that are difficult to implement in practice. Here we introduce evolution-pause synthesis (EPS), an interference engineered shortcut protocol that achieves fast, near-perfect state transfer strictly within the native system Hamiltonian. It achieves this by treating transient excitations as coherent resources and canceling their accumulated amplitudes via strategically interleaved pauses. By decoupling relative dynamical phase accumulation from parameter variations, EPS steers open transition trajectories into a closed loop in complex amplitude space, enabling perfect state transfer without auxiliary fields or complex parameter detours. We demonstrate this mechanism in Landau-Zener dynamics and extend it to a multilevel STIRAP process, achieving an 11.8-fold acceleration over the adiabatic baseline. Further, we experimentally validate EPS on a silicon photonic platform, realizing high-fidelity state transfer in a $16\,μ\mathrm{m}$ footprint, a nearly tenfold reduction in device length compared with a $150\,μ\mathrm{m}$ adiabatic reference. EPS offers a general hardware-compatible framework for fast, practical coherent control across wave and quantum platforms.

We present a total function with a polylogarithmic two-message quantum protocol, whereas every randomised protocol, even with arbitrarily many rounds, requires polynomial communication.

Quantum metrology faces major challenges in noisy environments, where decoherence rapidly degrades useful quantum resources. We investigate the dynamics of the precision limits given by the quantum Fisher information (QFI) for phase estimation under spatially correlated dephasing. We characterize the dynamics of the QFI by the sensitivity and degradation indicators that can be obtained as analytical expressions derived using perturbative theory treatment. These short-time and weak-noise formulas yield analytic insight into how collective-spin moments govern both (i) the noiseless sensitivity and (ii) the leading noise-induced degradation of metrological usefulness. We identify a trade-off that is intrinsic to our commuting encoding-noise structure. We analyze the QFI dynamics for the Gaussian spin state (GSS) superpositions, encompassing spin coherent state (SCS), Dicke state superpositions, spin-squeezed states, and GHZ-like states. Predictions from indicators of the QFI dynamics are compared to both the quantum Cramér--Rao bound and the measurement-specific sensitivity bounds for an optimal parameter and interrogation time under a finite total time resource. When possible, we analytically derive the measurement-specific sensitivity bounds for spin-projection and parity-based measurements.

We demonstrate Fourier-domain optical coherence tomography (FD-OCT) based on a seeded SU(1,1) interferometer. Multilayer objects are probed with broadband light centered at 1550nm, while depth-resolved 3D images are reconstructed from photon flux measurements centered at 810nm. We show that, in the low parametric-gain regime, seeding increases the photon flux, enabling volumetric imaging with a spectrometer rather than single-photon detectors. Our analysis further shows that, under the conditions considered, seeding provides a more effective route to sensitivity enhancement than increasing the parametric gain.

We present the technical proposal for the Atom Interferometer CERN Experiment (AICE), a $\mathcal{O}(100)$ m vertical atom interferometer to be installed against the wall of the PX46 access shaft to the LHC. AICE is conceived as a versatile and flexible long-baseline atom-interferometry facility whose primary scientific goal is probing for bosonic ultralight dark matter (ULDM) in a mass range inaccessible to other experiments, with a secondary goal of pioneering the exploration of gravitational waves (GWs) with frequencies in the range ${\sim}$0.03-3 Hz as a pathfinder for future longer-baseline detectors. The initial configuration employs ultracold $^{87}$Sr atoms in a single-photon 698-nm interferometer with three shaft-based atom sources in a multi-source gradiometer geometry, supported by one surface reference source for laser stabilisation and diagnostics, to target scalar ULDM. Operation with $^{88}$Sr will give sensitivity to axion-like particles (ALPs), vector ULDM with $B-L$ couplings and violation of the principle of equivalence, while a $^{171}$Yb upgrade will improve the sensitivity to $B-L$ couplings and equivalence violations. Probing the Einstein equivalence principle (EP) and measuring $α$ will proceed in parallel with the ULDM searches. A conceptual feasibility study and a detailed technical implementation study have established that PX46 is a uniquely mature and implementation-ready site, with no technical showstoppers. Completing site preparation works during LS3 would enable the subsequent installation and operation of AICE without impacting HL-LHC operations. The detector design builds on the VLBAI and MAGIS experiments and the AION-10 Technical Design Report, scaling the strontium gradiometer architecture to the $\sim$100 m baseline. AICE is endorsed by the TVLBAI Proto-Collaboration, comprising 57 institutions in 22 countries.

Recent studies have explored whether physical constants and symmetries can be selected by extremizing bipartite entanglement entropy. We extend this approach to a three-particle setting. Specifically, we consider a $2+1$-particle system in which particles $B$ and $C$ are initially entangled, and then particles $A$ and $B$ scatter without the direct participation of particle $C$ for both gluon-gluon and graviton-graviton scatterings. Using angular expansions around the forward and backward scattering limits, we analyze bipartite entanglement in the corresponding two-particle system of $A$ and $B$ and two measures of genuine tripartite entanglement (GTE), the concurrence fill and the generalized geometric measure (GGM), in the three-particle system. As is already known, the bipartite entanglement provides no universal criterion for selecting the symmetry-preserving theory: depending on the initial helicities, it may either maximize or minimize the entanglement entropy. By contrast, we find that the GTE-based analysis uniquely identifies the gauge-invariant and diffeomorphism-invariant theories as those that suppress the GTE in gluon-gluon and graviton-graviton scatterings, respectively. This result suggests a nontrivial connection between tripartite entanglement and the gauge and diffeomorphism symmetries of fundamental interactions.

Machine-learned models are replacing first-principles calculations across materials discovery, and physical symmetry is the central guarantee built into them. The debate over how much symmetry to hard-wire rather than learn has run on rotations, where a symmetry error is an approximation error. Some constraints are exact: symmetry forces certain property tensors to exactly zero, so a nonzero prediction is physically impossible rather than inaccurate. Here we show that whether a model can make such predictions is decided before training by one rarely reported design bit, whether its features carry parity labels, and derive a criterion, the parity gap, that computes from group theory alone which properties and crystals are exposed. Across matched architecture pairs differing only in that bit, evaluated on two thousand centrosymmetric crystals whose piezoelectric tensor must vanish, parity-labelled arms sit at the floating-point floor while rotation-only arms predict forbidden responses on 90-96% of crystals, six orders of magnitude apart, at no accuracy cost. Training on explicit zeros does not recover exactness, and a head on a frozen universal potential inherits its backbone's symmetry group. One reflection at random initialization verifies the label in seconds.

Rapid thermal cycling is a central bottleneck in the development of superconducting quantum devices: conventional dilution refrigerators require cooldowns of a day or more and substantial cryogenic infrastructure, which throttles the fabricate-measure-redesign loop. We present an ultracompact dilution refrigerator (3 kg in mass and 100 mm in diameter) that completes a full cooldown-warm-up cycle to a base temperature of 70 mK in 1.2 hours when unloaded, and in 2.1 hours when fully equipped with the microwave wiring required for qubit measurements, while delivering 20 microW of cooling power at 100 mK. We validate the platform through a complete characterization of a two-fluxonium device: we extract the full circuit Hamiltonian by two-tone spectroscopy, measure energy-relaxation and coherence times, and benchmark single-qubit control. Although the relaxation time is limited by the base temperature of the system, we reach a single-qubit gate fidelity of up to 99%, at the coherence limit set by our operating temperature. These results demonstrate that compact, fast-cycling dilution refrigeration can support state-of-the-art quantum-device characterization without sacrificing measurement quality, offering a practical route to high-throughput quantum-hardware development.

Optically pumped room temperature masers are a promising platform for driven dissipative spin photon physics beyond steady state emission. Here we observe a sequence of dynamical thresholds in a room temperature nitrogen vacancy diamond maser as the optical pump is increased above the conventional masing threshold. The first threshold yields narrow-line continuous wave emission, while a second threshold produces a periodic train of microwave pulses whose repetition rate generates a frequency comb spectrum. At higher pump power, a third threshold gives rise to pulses with an oscillatory, frequency chirped decay. Time-resolved measurements link the comb directly to self-pulsing dynamics and Fourier analysis of individual bursts reveals a broad distribution of frequencies consistent with collective spin-resonator dynamics in an inhomogeneously broadened ensemble. These results establish the diamond maser as a room temperature platform for nonlinear nonequilibrium light matter dynamics and microwave comb generation.

Boosting the communication rate of quantum networks is a central challenge in quantum information science. Recently, an efficient entanglement distribution scheme employing quasi-deterministic Bell-pair sources based on time-frequency multiplexing, referred to as zero-added-loss multiplexing~(ZALM), has been proposed. Its implementation, however, requires high-fidelity entanglement swapping across densely multiplexed time-frequency modes, which has remained an experimental challenge. Here we demonstrate entanglement swapping across 16 parallel frequency modes with a high average fidelity of 93.9$\pm$\SI{1.4}{\%}. Notably, polarization-entangled photon pairs in each frequency mode are spectrally single-mode using only off-the-shelf 50-GHz dense wavelength-division multiplexing~(DWDM) filters, eliminating the need for additional narrowband filtering. Furthermore, in order to fully exploit the temporal degree of freedom, the pump pulse is operated with a repetition frequency of \SI{3.0}{GHz}. By combining the frequency and time multiplexing, the total swapping rate reaches 5.38$\pm$0.17\,\si{pairs\,s^{-1}}, which corresponds to the ZALM Bell-pair rate of \SI{8.2e2}{pairs\,s^{-1}}. Our results establish the key experimental capabilities required for ZALM and demonstrate a scalable route toward practical high-rate quantum repeaters and long-haul quantum networks.

Tsetlin Machines (TMs) learn interpretable Boolean clauses using finite-state automata. We introduce the Quantum-Logic Tsetlin Machine (QL-TM), which replaces Boolean literals with quantum propositions represented by projectors while retaining classical include/exclude automata. Clauses are restricted to commuting measurement contexts and activate through the Born probability of their joint projector. We prove an exact reduction to ordinary Boolean TM clauses in diagonal computational-basis contexts and connect Pauli-projector clauses to stabilizer and syndrome semantics. Controlled experiments on Bell states, phase-flip syndromes, randomized 16-class stabilizer tasks, mixed literal pools, context-budget ablations, and finite-shot noise show that correct non-diagonal contexts recover physically meaningful clauses, while diagonal or wrong contexts lose the relevant phase/syndrome information. The context-budget results closely follow the predicted separability ladder 2^(b-k) as true stabilizer generators are removed. The contribution is a controlled bridge between Tsetlin clause learning and quantum logic, not a claim of quantum advantage.

We construct $n$-qubit approximate unitary $k$-designs in 1D systems, achieving circuit depth $O(\log(n/\varepsilon) + k\log k)$ with relative error $\varepsilon$ and requiring $O(nk\log k)$ magic gates. This matches existing lower bounds $Ω(\log(n/\varepsilon) + k)$ for circuit depth, and $\widetildeΩ(nk)$ for the required number of $T$ gates, up to a $\log k$ factor, achieving simultaneous near-optimality in all parameters. Our construction is based on a combination and refinement of two existing results. We reduce the required magic block size for breaking Clifford symmetries in the magic-augmented circuit construction of Zhang et al. from $O(k\log k)$ to $O(\log k)$. We also improve the breakthrough construction of Chen et al. to construct a generating set of 1D local constant-depth circuits for the unitary group with a constant spectral gap, making $O(\log k)$-local random unitaries realizable in depth $O(k\log k)$. As a by-product, we provide a constant-size 1D-local generating set for the Clifford group, which we expect to be of independent interest. Combining the two results with the gluing lemma, we prove the final result.

It is sometimes said that a reason to prefer Everettian quantum mechanics is that it allows one to avoid the kind of spooky action at a distance that is a consequence of quantum entanglement according to other approaches. There is a straightforward argument to show EQM has this virtue, however some advocates argue that this requires we see branching as a local causal process. I explain this reasoning and then show why, given the way Everettians standardly conceive of worlds and branching as emergent phenomena, branching need not be viewed as a causal process for EQM to be relativistically local. Forthcoming in Local Quantum Mechanics, OUP 2026.

The periodic non-Hermitian Baxter-Fendley $Z_N$ clock chain has lacked a complete finite-size spectral solution, whereas its open-chain counterpart admits a solution in terms of independent quasienergies. For the periodic model we show that the operator-valued matching polynomial associated with its cyclic Weyl algebra simultaneously generates a set of conserved quantities, including the Hamiltonian, and realizes a cyclic $τ^{(2)}$ Yang-Baxter transfer matrix. Root-of-unity closure yields a finite system of polynomial spectral equations in each charge sector, which reproduces the complete finite-size energy spectrum counted with algebraic multiplicity. As a first application of this result, we show that Newton continuation of these equations provides a practical numerical route to the periodic ground-state energy without enumerating the full spectrum. For homogeneous chains the thermodynamic seam response yields a criterion for boundary-induced criticality; for $N=3$ it predicts two reciprocal critical couplings with singular ground-state curvature, in contrast to the single self-dual open boundary critical point.

Given a certain specific, $M$ by $M$ matrix form of the Feshbach's effective (i.e., energy-dependent) Hamiltonian $H^{(M)}_{e\!f\!f}(E)$, the inverse-problem reconstruction of the full-space, $N$ by $N$ matrix Hamiltonian $H^{(N)}$ is considered and reduced to the solution of a coupled set of polynomial algebraic equations. Using computer-assisted symbolic manipulations, an explicit algebraic reconstruction of $H^{(N)}$ is found feasible at not too large $K = N-M$.

The advancement of quantum hardware and the intricacies of quantum computing make well-designed quantum software increasingly necessary. Due to the interdisciplinarity of the field, it is crucial to understand the perspectives and specific needs of involved stakeholders, for example, to balance the desired level of abstraction with the exposition of (hardware)-specific details. In this work, we conduct a stakeholder-based analysis to identify personas of quantum software as a means of creating meaningful, user-tailored quantum software. We conducted an expert focus group at a Dagstuhl seminar in 2024 and qualitative interviews with practitioners at conference IEEE QCE in 2025, from which we derive eleven personas of potential users and stakeholders for quantum software. We discuss these personas regarding their use cases, interests, constraints and abstraction level.

Fault-tolerant quantum computation hinges on the requirement for low physical error rates. Reaching below threshold regime requires the accounting of circuit dependent noise, that is inherent to the execution context in which a quantum gate is usually embedded. Direct fidelity estimation is a technique that offers natural context preservation as it solely requires the insertion of local Pauli preparation and measurement fiducials around the window of interest. However, each sampled input-output Pauli pair demands its own preparation and measurement setting, an overhead that grows rapidly once the target gate is no longer Clifford. We introduce joint fiducial grouping, which partitions Pauli pairs into sets with commuting input and output operators, allowing several Pauli-transfer coefficients to be estimated within the same preparation-measurement setting. We derive an unbiased grouped estimator and finite-sample guarantees showing that grouping always reduces the number of distinct input-output settings and can also reduce the required channel uses when the target weight is concentrated within compatible groups. We characterize these gains for the parametric two-qubit gate $\mathrm{fSim}(θ,\varphi)$, and use the grouped estimator as a context-sensitive reward for reinforcement-learning-based gate calibration. Our results provide a practical route to lower-overhead, context-preserving fidelity estimation for continuously parameterized quantum gates.

Encoding quantum information with low circuit overhead is a fundamental challenge in fault-tolerant quantum computation. Random circuits provide a natural mechanism for rapidly spreading logical information through simple gates applied in parallel. Brown and Fawzi showed that random Clifford circuits on two-qubit Clifford gates provide such encoders that achieve the quantum Gilbert-Varshamov rate-distance tradeoff with depth $O(\log^3 n)$. We show that the same asymptotic tradeoff is attained in optimal $O(\log n)$ depth under a gate distribution with a more restricted support. For every fixed $δ>0$ and sufficiently large $n$, if $\frac kn < 1 - H(\frac{d}{n}) - \frac{d}{n}\log_2 3 - δ$, we can construct random circuits of depth $O(\log n)$ which define, with high probability, an $[n,k]$ stabilizer code of distance at least $d+1$, which matches the $Ω(\log n)$ light-cone lower bound for linear distance encoders. Our ensemble employs a random matching circuit architecture consisting of $T$ independent permutation-invariant layers. In each layer, the qubits are paired up by a uniformly random perfect matching, and a random independent two-qubit Clifford gate is applied to each pair. The gate distribution need not be uniform over, or even have full support on, the two-qubit Clifford group; rather, we allow for very general distributions on Clifford gates satisfying three regularity conditions. In particular, the construction can be implemented using $n/2$ CNOT gates on randomly matched pairs in each layer, with parallel one-qubit Clifford twirls. These regularity conditions allow us to reduce the second-moment dynamics of our random circuits to a reversible Markov chain on binary support strings. We establish logarithmic hitting-time bounds for this Markov chain and comparisons of its stationary distribution to prove the coding properties of the circuits.

Topological orders (TOs) are widely used as quantum error-correcting codes, with anyon excitations serving as error syndromes. For certain Abelian TOs, decoding can be performed by independently matching particle-antiparticle pairs of each species. However, matching-based decoders cannot handle more general fusion rules in either Abelian or non-Abelian TOs, nor account for noise that correlates different anyon species. While clustering decoders are more broadly applicable, they typically neglect anyon data and fusion properties, leading to poor performance in practice. In this work, we introduce a fundamentally different decoder for arbitrary TOs based on integer linear programming (ILP). The ILP formulation linearizes the error-correction problem through the introduction of auxiliary variables and encodes fusion rules as linear constraints. Classical optimization then identifies the minimum-weight error configuration. As concrete examples, we determine error-correction thresholds for three TOs: the Abelian $\mathbb{Z}_2$ TO under depolarizing noise, where charge and flux errors are correlated; the Abelian $\mathbb{Z}_3$ TO, which does not admit a pairwise matching decoder; and the non-Abelian $D_4$ TO under noise channels that generate all anyon species. We demonstrate the versatility of the ILP decoder by showing a clear performance advantage over most existing decoders in all three cases. We further extend the method to incorporate noisy syndrome measurements and propose a just-in-time variant for continuous error correction. Our results establish ILP as a natural framework for handling correlated errors and general anyon fusion rules, and as a powerful and flexible general-purpose decoder for incoherent anyon noise in arbitrary TOs, with applications to fault-tolerant quantum computation.

Projected entangled pair states (PEPS) provide an efficient variational ansatz for two-dimensional quantum phases, but computing observables remains challenging because PEPS contraction is generally costly. Here, we parameterize two-dimensional quantum states using variational PEPS subject to isometric constraints and map the resulting ansatz onto monitored quantum circuits, replacing tensor-network contraction with circuit sampling. For infinite cylinders, the transfer matrix defines a quantum channel on the virtual boundary. We use a fixed-point treatment and a monitored-circuit unraveling of this channel to evaluate observables efficiently. Using a constant number of variational parameters and a number of qubits that scales only with the cylinder width, our method yields a phase diagram for the $J_1$-$J_2$ model in qualitative agreement with DMRG results. Because the monitored circuits are compatible with near-term quantum hardware, this approach provides a hybrid quantum-classical framework for simulating two-dimensional quantum many-body systems.

Two-dimensional (2D) electron/hole gases confined in semiconductor heterostructures suffer from weak Rashba spin-orbit coupling (SOC) for manipulating spin degreee of freedom via an electric rather than a magnetic field. Here, we show that complementary metal-oxide-semiconductor technology-accessible strain could substantially enhance the linear Rashba SOC of the top hole subband in Ge/SiGe quantum wells (QWs) to a level comparable to that of 2D Rashba materials through enhancing the mixture of the light-hole and heavy-hole bands. We further show that strongly enhanced Rashba SOC boosts the Rabi frequency of hole spin qubits confined in Ge/SiGe QWs by two orders of magnitude to an unprecedented 40 GHz, more than one order of magnitude faster than other qubit platforms. We also demonstrate that the hole spin rotation with Rabi frequency > 25 GHz enters a new regime being immune to gate control-induced electric noise, opening a new avenue to simultaneously improve the gate speed and gate fidelity. Our findings provide a new routine to substantially enhance the Rashba SOC in 2D semiconductor hole gases to a level that is great for spintronic applications.

We present \textsc{TDSE-Z}, a high-performance open-source framework for strong-field quantum dynamics in atomic, molecular, and semiconductor effective-mass systems. The core engine implements a weak-form Galerkin discretisation of the Hermitian BenDaniel-Duke operator, $\hat{T}_{\mathrm{BDD}} = -\frac{1}{2}\nabla\cdot(m^{-1}(\mathbf{r})\nabla)$, on geometry-adapted B-spline meshes, supporting arbitrary potentials and customisable laser configurations in one to three dimensions. We validate the static position-dependent-mass (PDM) eigensolver through two stringent benchmarks: a comparison to the analytical Quesne PDM model and a $\text{GaAs/Al}_{0.3}\text{Ga}_{0.7}\text{As}$ double quantum well, where the exponential decay of computed tunnel splittings follows Wentzel-Kramers-Brillouin (WKB) theory at the sub-percent level. We further demonstrate the time-propagation engine on constant-mass systems, accurately reproducing high-harmonic generation (HHG) spectra in atomic benchmarks and confirming the importance of dimensionality in fully capturing the strong light-matter interaction. Our implementation demonstrates robust strong-scaling efficiency, maintaining performance across hundreds of CPU cores. While the static eigensolver currently supports optional GPU offloading, the time-propagation engine is CPU-optimised, providing a modular architecture for future expansion toward exascale quantum dynamics.

Programmable arrays of ultracold atoms are a leading platform for quantum computation and simulation, enabling state-of-the-art implementations of quantum error correction, and analog simulations of Hubbard models that address open problems in condensed matter physics. In these systems, all local control is mediated through precisely shaped optical fields, and so the challenge of managing many-body quantum states becomes an exercise in optical design. In particular, one wishes for fast, flexible control with low disorder and heating, and access to large arrays with many atoms. An ideal optical system therefore must generate arbitrary patterns with high spatial resolution and low disorder, and alter these patterns on a timescale that is faster than the relevant atomic dynamics. Here, we present an optical system that is comparable to previous approaches in scale, while advancing all other axes. We demonstrate arbitrary pattern generation with $10^{-3}$ intensity resolution, a frame rate of $>84$ MFPS (megaframes per second), and a spatial resolution of $83 \times 52$ beam waists (with $11 \times 52$ waists accessible via a single $40$ GHz electro-optic modulator). These capabilities unlock a new class of experiments. We develop and numerically validate a scheme for fully programmable Hubbard models, with time-dependent control over local chemical potentials, tunneling amplitudes, on-site interactions, and patterns of artificial magnetic flux. The same architecture performs fast, arbitrary permutations of tweezers in 2D, decoupling optical constraints from the design of high-rate error-correcting codes.

In this paper, we provide estimators for quantum Rényi and Tsallis entropies with nearly optimal sample complexity. Specifically, for order $α$, dimension $d$, and additive error $\varepsilon$, 1. For $0 < α< 1$, the sample complexity is $O(d^{1+1/α}/\varepsilon^{1/α} + d^{1/α-1}/\varepsilon^{2})$ for Rényi entropy and $O(d^{1+1/α}/\varepsilon^{1/α} + d^{2-2α}/\varepsilon^2)$ for Tsallis entropy. In particular, for $0 < α\leq 1/2$, the sample complexity for both entropies is $O(d^{1+1/α}/\varepsilon^{1/α})$. 2. For non-integer $α> 1$, the sample complexity is $O(d^2/\varepsilon^{1/α} + d^{1-1/α}/\varepsilon^2)$ for Rényi entropy. Our upper bounds improve the quantum Rényi entropy estimators due to Acharya, Issa, Shende, and Wagner (2017) and the quantum Tsallis entropy estimators due to Chen, Liu, and Wang (2026), and match the lower bounds recently established by Wang (2026).

Neural Quantum States (NQS) provide a powerful neural network-based variational framework for representing many-body wave functions and solving for ground states. Recurrent Neural Networks (RNNs) are particularly promising owing to their relatively low computational cost and their autoregressive property, which enables perfect sampling. Recently, RNNs have been reported to be unstable under curvature-based optimizers such as the minimum-step stochastic reconfiguration (minSR) method. In this paper, we address this perceived limitation and show that minSR can be stabilized through simple regularization techniques, enabling robust training of RNN-based NQS with only a few samples. Our approach outperforms the Adam optimizer on the one-dimensional transverse-field Ising model and the one-dimensional cluster state, and provides competitive results on the two-dimensional Heisenberg and $J_1-J_2$ models. This work offers a promising pathway for using modern optimization techniques with autoregressive NQS to address open questions in quantum simulation.

Complex Hadamard matrices encode perfectly balanced unitary transformations. They underlie mutually unbiased quantum measurements and multiphoton interferometry. Their classification is complete through order five, but order six -- the first dimension in which several continuous families coexist with an isolated solution -- has remained open for decades. Here, we give a complete and exact finite-incidence classification of order-six complex Hadamard matrices up to standard equivalence. We first prove that every such matrix can be constructed from an initial dephased $3 \times 3$ corner by a finite, branch-complete procedure. This supplies the global step missing from Szöllősi's dilation method and proves his conjecture: up to standard equivalence, every class outside Karlsson's three-parameter family and Tao's isolated matrix is recovered algebraically from a suitable corner. We then describe the geometry of the reconstruction from four initial phases and show that, except for Tao's isolated matrix and a single explicit Karlsson matrix, every class admits a representative obtained by solving one quadratic and one cubic equation in both the horizontal and vertical directions. Our work resolves the classification problem and provides a rigorous framework for further investigating order-six Hadamards, with applications to balanced six-mode interferometers and the study of mutually unbiased bases.

Real-time simulations of interacting nanostructures coupled to fermionic reservoirs can require a growing number of environmental degrees of freedom to retain long-lived correlations. We introduce tape-recorder coarse graining, which reorganizes each noninteracting lead into incoming, active, and outgoing modes. The device is propagated with the active modes, while outgoing modes are stochastically sampled and removed once their remaining integrated coupling falls below a prescribed threshold. For each outgoing-mode truncation, we derive a nonperturbative upper bound on the infidelity between the exact and truncated full device--reservoir states over any prescribed finite interval. The bound depends on the mode's remaining coupling weight and finite-interval response factors. Numerically, the active-mode count saturates in time at fixed relative threshold and grows logarithmically as the threshold is reduced. We benchmark the method on a two-site quantum point contact at zero temperature and maximal bias. For Lorentzian reservoirs, the dynamics agrees with converged HEOM calculations and the steady-state current with the Landauer--Büttiker result. For flat-band reservoirs with algebraically decaying correlations, it agrees with direct Schrödinger evolution before finite-size recurrences and reproduces the Landauer--Büttiker stationary current, while finite exponential HEOM decompositions remain unconverged. For interacting contacts, the method yields Coulomb-blockade peak splitting. In the noninteracting driven limit, it agrees with an exact Floquet Green-function calculation and reproduces coherent current suppression under periodic driving, which persists at finite Coulomb repulsion. Together, these benchmarks show that tape-recorder coarse graining enables practical long-time simulations of the full device--reservoir state in interacting fermionic transport.

As quantum processors scale to hundreds of qubits, execution speed is a critical performance dimension alongside scale and quality. While substantial progress has been made in benchmarking circuit fidelity, existing speed metrics often fail to reflect the sustained, end-to-end throughput experienced by users running utility-scale workloads. This shortfall is especially pronounced for layered, parameterized circuits executed repeatedly within classical-quantum workflows, such as variational algorithms and error-mitigated simulations. In this work, we formalize CLOPS_h (Circuit Layer Operations Per Second) as a holistic speed benchmark defined over layered, hardware-aware circuits. CLOPS_h measures the sustained rate at which the system executes physical layers, parallel slices of qubit-disjoint two-qubit gates separated by synchronization barriers. Because each such layer is one time slice of an N-qubit circuit, this rate maps directly to the execution rate of layered $N$-qubit circuits, connecting CLOPS_h to published device capability claims, and to the device-level throughput ceiling we formalize as Max Circuits Per Second (MCPS). CLOPS_h is obtained under layer-fidelity operating conditions, binding the speed measurement to an independently verified quality envelope, and it shares its layer decomposition with scalable layer-fidelity (LF) quality benchmarks, enabling coherent interpretation of speed and quality without conflating the two.

We study the dissipative dynamics of a Majorana tetron qubit in the presence of extrinsic quasiparticle poisoning due to the coupling to external leads. From the Bloch-Redfield equation describing a finite-size topological superconductor hosting four Majorana zero modes, we recover analytical expressions for the steady state, the parity leakage rate, and the decoherence rate of a Majorana qubit at arbitrary values of the charging energy. The analysis shows that the exponential suppression of the dephasing rate is gradually removed by the energy splitting of the qubit states. These results can be useful to understand time-domain experimental data in Majorana qubit prototypes.

The familiar Bethe-Heitler process on the proton target $e+p\to e+p+γ$ is transformed into a laboratory for studying multiparticle entanglement. We discuss how bipartite and genuine tripartite entanglement between the final state electron, proton and photon are built up by successive $1\to 2$ and $2\to 2$ elementary interactions. We validate our argument by simulating events. Below 5 GeV center-of-mass energy, we identify more than 900 Greenberger-Horne-Zeilinger (GHZ) states and 1200 W states, each with a fidelty exceeding 99%.

Gisin has provided an argument for the conclusion that no covariant nonlocal model can reproduce the operational statistics observed in Bell experiments. Gisin's argument applies only to deterministic models and we argue that proposed generalizations of the argument beyond determinism based solely on statistical notions are unconvincing, as they lack the resources to formulate a satisfactory notion of no-retrocausality. We introduce the framework of frame-indexed causal models in order to extend Gisin's argument to the genuinely probabilistic case. Frame-indexed causal models associate potentially different causal models with different reference frames while requiring corresponding operational variables to agree runwise. Within this framework, we establish two no-go results based on Gisin's argument. First, we show that no empirically adequate frame-indexed causal model can jointly satisfy Independent Settings, No-Retrocausality, and Causal Lorentz Invariance. Second, it is established that this result continues to hold when Causal Lorentz Invariance is weakened to Lorentz Invariance of Causal Connections, which requires only the skeleton of the causal structure to remain invariant, thereby allowing the direction of causal influence to depend on the choice of reference frame. These results are discussed in the context of relativistic interpretations of quantum theory and nonclassical causal inference.

We present a detailed account of the design choices required for planar Penning traps that feature a highly harmonic confining potential. High harmonicity is indispensable for a number of applications, particularly for confinement of single electrons as qubits in quantum-information processing. The present work extends previous studies [D. Goldmann and G. Gabrielse, Phys. Rev. A 81, 052335 (2010)] by a fully analytic treatment of finite electrode gaps and their relevance for small traps on the millimetre size scale and below, when relative gap sizes are non-negligible. We derive the overall trap potential with a particular focus on different models of finite-gap potentials and show how to find the optimum trap geometry and electrode voltages to minimize anharmonicities. The analytic calculations are compared with detailed finite-element simulations.

We study one- and two-magnon dynamics in a spin-$1/2$ XX chain coupled to a tunable Bose-Hubbard bath. The XX Hamiltonian transports the magnons, while the bath dresses their motion and mediates an effective attraction. A single magnon forms a mobile polaron whose retarded bosonic cloud reduces its velocity below the static Lang-Firsov prediction and generates magnon-boson entanglement. In the weak-dressing, off-resonant mobile regime, the residual velocity deficit and entanglement are governed by the excitation weight of the cloud, as captured by perturbation theory and tensor network-based real-time simulations. Transport therefore provides a model-calibrated proxy for entanglement without joint-state reconstruction. When two clouds overlap, the bath mediates a finite-range attraction, yielding finite-size evidence for a compact two-magnon bound state and a transient post-scattering signature. On-site bath interactions suppress local boson number fluctuations and stiffen the bath response, reducing entanglement and weakening ground-state binding. Bath deformability thus emerges as a common control parameter for magnon transport, entanglement, and bath-mediated pairing.

Anderson localization and the mobility edge (ME) have been extensively studied in isolated aperiodic systems. Conventional theory suggests that dephasing and decoherence should disrupt localization and facilitate transport. In this work, we investigate localization behaviors in a dimerized off-diagonal Aubry-Andre-Harper (AAH) quasicrystal subject to on-site pure dephasing. In the strong-dephasing limit, we apply adiabatic elimination within the Lindblad master equation framework to derive an effective classical Markov transition matrix that governs the dissipative relaxation dynamics. Counterintuitively, we demonstrate that pure dephasing can induce distinct MEs, including both conventional MEs separating extended and localized states and anomalous MEs separating multifractal critical states from localized states, even when all eigenstates of the original closed coherent system are delocalized or multifractal. Using fractal dimension finite-size scaling, wave-packet spreading dynamics, and energy spectrum statistics, we numerically verify the coexistence of fully extended, multifractal critical, and localized regions within the relaxation spectrum of the dissipative system, and construct the global dissipative phase diagram. These findings reveal that dephasing can see as a powerful mechanism for controlling localization transitions, thus enhancing our understanding of dissipative quasicrystal systems.

Neutral-atom arrays are emerging as a leading platform for scalable quantum error correction (QEC). Qubits are routed and reused across the array, while detected loss is reported to the decoder as erasure information. Existing neutral-atom compilers optimize this movement, including routing, shuttling, and reuse, and often model loss through scalar exposure costs. Yet total exposure is an incomplete statistic for erasure-corrected QEC. It captures how much loss occurs, but not where it lands on the code, which we call its deposition. Under the same expected atom-loss budget, different deposition patterns over a code patch induce substantially different logical error rates (LER). We formalize this as decoder-aware risk deposition and present CAST, a compiler-side optimization pass that overlays a code-topology sensitivity map on a role-indexed exposure ledger and minimizes a decoder-weighted harm objective under a comparable-exposure constraint, using only local route, role, and seam-cooling actions. Across surface-code memory, physical-scale architecture models, lattice surgery, and decoder-mismatch checks, CAST lowers LER relative to topology-blind exposure minimization, improving on it in 35 of 48 physical-scale settings and by as much as 5.3x where exposure is heterogeneous and routing has slack. The largest gains occur when high exposure and high decoder sensitivity are initially misaligned, giving CAST room to redirect risk toward lower-impact code roles. CAST shows that decoder-aware atom-loss risk deposition can be optimized as a compiler-side pass in neutral-atom QEC.

In fault-tolerant quantum computing systems with biased noise, Clifford deformation can substantially reduce the logical error rate (LER) without additional physical hardware overhead, such as extra qubits, syndrome extraction rounds, or code distance. Although Google Willow calibration data shows that $43\%$ of qubits exhibit strong $X/Z$ bias, existing calibration-aware deformation techniques remain impractical: (1) global searches over the $6^n$ deformation choices rely on computing-intensive simulations, and (2) local heuristics often underperform undeformed baselines. We present Chameleon, a fast, high-performance, and code-agnostic Clifford deformation compiler. We utilize our approximation to tackle a deformation problem based on an analytical bound on the LER. By minimizing this surrogate, Chameleon finds an optimized deformation that empirically reduces the LER with substantially lower computational overhead. In our evaluation, using calibration models derived from real superconducting devices, Chameleon demonstrates that improvements in our surrogate are strongly correlated with actual LER reductions, with an average rank correlation of $ρ=0.8$ and $ρ=0.89$-$0.94$ on the most strongly biased system. It also reduces classical computational time from $1.2$ days to $3.1$ minutes for the BB72 code. Chameleon achieves maximum LER reductions of $19\%$ ($13\%$ on average) for surface codes, $16\%$ ($7\%$) for color codes, and $10\%$ ($4\%$) for bivariate bicycle codes relative to competing baselines. The maximum gains for all code families are observed on the most strongly biased system.

High-harmonic generation (HHG) is conventionally understood to produce attosecond pulse trains only when the emitted harmonics are mutually phase-locked, in accordance with the classical theory of mode-locking. Such locking is necessary for pulse synthesis when the harmonic field is in a separable multimode quantum state. This requirement, however, can be circumvented entirely for harmonic combs exhibiting intermodal entanglement. We introduce a novel family of multimode quantum states, termed attoquants: states associated with highly structured pulse trains that are inherently insensitive to relative phases. As a concrete example, we analyse the coherent permanent state, constructed as a completely symmetric superposition of products of coherent states over all permutations of a fixed parameter set. It is shown analytically that its electric-field expectation value is a locked Fourier superposition of the driving-field harmonics, yielding an attosecond pulse train without requiring mode-locking. We further calculate the photon statistics, the Wigner function, and the logarithmic negativity of this state, confirming it to be genuinely nonclassical and entangled. Finally, we offer a phenomenological interpretation for the generation of such entangled states during HHG, as a consequence of multi-atom effects. Since the coherence volume of the driving field greatly exceeds that of its harmonics, a collectively-driven cluster of atoms can radiate the individual harmonics as spatially resolved, but fundamentally indistinguishable sources. This can generate the permutation-symmetric entanglement structure of an attoquant.

Synthesizing arbitrary $n$-qubit unitaries using as few non-Clifford gates as possible is a central problem in fault-tolerant quantum compilation. We present a Clifford+$T$ quantum circuit construction that approximately implements any classically specified unitary to within error $ε$ and achieves a worst-case $T$-count with leading exponential scaling of $2^{5n/4}$ whenever $\log(1/ε)=\operatorname{poly}(n)$. This improves upon the best previous $2^{4n/3}$ scaling. The key innovation lies in treating the target unitary as a single block-encoded object rather than a long product of simpler operations. A technique of block flattening controls the normalization while preserving an efficient implementation of the block encoding; subsequently, quantum singular value transformation maps its common singular value to one, thereby recovering the target unitary.

We formulate a non-Abelian theory of structural consistency for systems in which dynamical transformations reside on the links of a simplicial network. Gauge covariance follows from freedom to choose local representation frames, while plaquette holonomies quantify the incompatibility of alternative paths. For an SU(2) model on the complete simplicial $2$-complex with quenched random plaquette couplings, parallel-tempering simulations reveal a continuous disorder-driven loss of global compatibility. In the high-disorder phase, the uniform compatibility $M_P$ decreases with system size, the integrated adjacent correlation weight $\mathcal I_{\mathrm{adj}}$ remains finite value. Moreover, the connected replica-overlap width approaches the numerical noise floor and its distribution narrows, providing no evidence for thermodynamic replica-symmetry breaking. Dense frustration therefore produces a non-glassy correlated gauge liquid in which individual pair correlations are geometrically diluted while a finite integrated correlation weight survives.

Resonant cavity-quantum system interactions are well understood in the pulsed coherent and continuous-wave steady-state limits, but not much in between. We investigate the intermediate regime, where pulse duration, coupling, decoherences, and decays occur on comparable timescales, and pulse bandwidth matches cavity splitting and detunings. We reveal an interplay of cavity-enhanced excitation and Purcell-enhanced emission leading to warped chevron patterns. We develop a quantum master-equation model that efficiently treats the excitation-light coherent states in photon number space and reproduces the experimental data. Using these results we identify how polarization-split cavities can optimize single-photon purity and emission probability.

Energy shifting is usually trivial in imaginary-time evolution because it changes only the normalization of the evolved state. On a quantum computer, however, imaginary-time evolution can be implemented as a coherent or sampled superposition of real-time evolutions, in which energy shifts generate relative phases that can interfere. Here we introduce multi-shift quantum imaginary-time evolution (MS-QITE), which uses a distribution of energy shifts to engineer interference and optimize different implementations. In a Monte Carlo realization, multi-shift reshapes the sampling distribution and concentrates it within a shorter real-time window, thereby reducing the required Hamiltonian-evolution time and improving the stability of ground-state-energy estimation. In a continuous-variable-assisted realization, it permits postselection over a finite quadrature interval rather than near a single quadrature value, substantially reducing resource consumption while retaining accurate thermal-state preparation. Numerical results for transverse-field Ising models demonstrate that energy shifts provide a useful interference-based approach for optimizing quantum imaginary-time evolution.

Understanding collective phases of strongly correlated quantum magnets relies on theoretically tractable model systems with precise microscopic control. Antiferromagnetic spin ladders provide such a setting, hosting field-tunable gapped and gapless phases at half filling and unconventional pairing tendencies upon doping. Here, we realize a programmable Heisenberg spin ladder in a half-filled germanium quantum dot array featuring site-resolved, continuously tunable exchange interactions. Under a fixed magnetic field, we vary the rung and leg coupling to map the rung-singlet, canted antiferromagnetic, and fully polarized phases. Hamiltonian-learning protocols combining equilibrium and dynamical measurements quantitatively characterize the ladder, incorporating spin-orbit interactions to reproduce the observed crossover behavior. Measurements of higher-order spin correlators -- including four-point correlations inaccessible to conventional bulk probes -- reveal signatures of the underlying phase structure despite the finite size. Our results establish germanium quantum dot arrays as a controllable platform for quantum magnetism, opening routes to investigate unconventional superconductivity in doped ladders.

We study the quantum evolution induced by graph-indexed Ising Hamiltonians as a source of structural signal for graph learning. Graph automorphisms preserve symmetries of the Hamiltonian, and these symmetries constrain the quantum evolution in a way that turns time-dependent local measurements into informative probes of graph structure. Leveraging this idea, we introduce QDAGer, a quantum-inspired graph-pair Transformer that injects quantum-dynamical features from time series of node occupations and connected two-point correlators directly into the attention mechanism. We apply QDAGer to learning Graph Edit Distance (GED), an NP-hard similarity measure, using either a direct permutation-invariant embedding discrepancy or an alignment-based surrogate loss. Experiments on multiple GED benchmarks under different edit cost settings show that the proposed dynamical features provide a stronger inductive bias than classical structural alternatives under the same training protocol. In addition, we report ablations where the dynamical signal is replaced by standard random-walk and heat-kernel features while keeping the architecture fixed, highlighting that the gain comes from the injected dynamics rather than model capacity alone.

The quantum approximate optimization algorithm (QAOA) targets NP-hard maximum-likelihood (ML) detection in multiple-input multiple-output (MIMO) systems. Existing $M$-ary quadrature amplitude modulation (M-QAM) detectors design angles by expected Ising energy: online per instance, warm-started, or ramped, while train-once designs remain B/QPSK-only or block-local, leaving M-QAM without a size-scalable benchmark. Their infinite-size spin-glass theory assumes independent disorder, matching the retained covariances at B/QPSK but not M-QAM's correlated couplings and fields. We develop a correlated infinite-size multi-species spin-glass framework whose covariance-matched evaluators make that energy an offline objective with a size-scalable benchmark. In addition, the ML rate, the exponential rate of sampling the ML string, is for the first time exploited for QAOA angle design in MIMO detection. The energy evaluator is $q$-free at $O(p\,4^p)$ cost while the ML rate transfers angles from a fixed $q_{\rm ref}$-qubit reference. Tests reach 4096-QAM, 128 antennas, $p=30$ and per-symbol SNR 0-45 dB. In simulations, ML rates fall as a power law $r_0\,p^{-α}$, with larger exponents for the sampling design, which tracks exact ML at $5\times5$ 16-QAM (0-20 dB) and $3\times3$ 64-QAM (8-28 dB) while its bit-error rate (BER) advantage widens with SNR to two orders of magnitude. The approach points toward near-optimum decoding on deeper noiseless fault-tolerant quantum (FTQ) circuits.

Long-wavelength neutron interferometry using discrete optical elements is notoriously challenging due to stringent alignment and stability requirements. Here, we introduce a monolithic double-Laue neutron interferometer fabricated from a stack of commercial Bayfol HX photopolymer films. By recording holographic gratings simultaneously in multiple layers, we create a robust device that is inherently aligned, bypassing traditional stability problems. We demonstrate the device's function by observing the characteristic interference fringes in the diffracted intensity of both light and very cold neutrons. The interferometer is then used to perform in-situ characterization of the neutron beam's spectral profile, demonstrating its utility as a compact spectrometer. Our work establishes stacked holographic gratings as a simple, versatile, and powerful platform for matter-wave interferometry and metrology.

We argue for the universality of quantum theory using a dynamical consistency argument, within a specific Hamiltonian setting. We analyse two different types of coupling between simple quantum harmonic oscillators. Each illustrates an aspect of the free and interacting quantum fields and shows the inadequacy of semiclassical models. In particular, we establish that requiring the canonical algebra to be preserved under joint unitary dynamics rules out specific hybrid classical-quantum models. We apply our reasoning to the gravitational field in the linear regime, coupled to the quantised electromagnetic field and, separately, to quantised matter. We conclude with a comparison to DeWitt's analysis of quantum measurement, in which the apparatus, if classical, must be at least stochastic to preserve the Heisenberg Uncertainty Principle. We also note that stochastic models are inconsistent with the strict version of conservation principles, even if they comply with a probabilistic (on average) conservation.

Using supersonic expansion, we create a time-gated, directional beam of Xe atoms with a narrow momentum distribution and detect their collisions with a levitated nanosphere cooled to its quantum ground state. We observe individual momentum kicks below 50 keV/c with 96% confidence and distinguish directional momentum transfer from the atomic beam against the background of thermal collisions. Our experiments constitute a first step toward the exploration of distance-dependent short-range interactions between atoms and levitated systems, as well as toward the use of levitated platforms for impulsive force sensing in previously unexplored parameter regimes.

We develop a quantum algorithm for slow analytic Hamiltonians $\widetilde H(t)=H(t/T)$ with $\|H(s)\|\leqα$ that achieves nearly additive query complexity and low gate overhead. Our main technical contribution is a periodic Gevrey extension of $H(s)$, together with Fourier component decay and truncation bounds that enable an efficient finite-dimensional simulation. Combined with Floquet embedding and optimal time-independent Hamiltonian simulation technique, this gives query complexity $\widetilde{\mathcal O}\!\left(αT+\log(1/\varepsilon)\right)$ and additional gate complexity $\widetilde{\mathcal O}\!\left((αT+\log(1/\varepsilon))^2\log(1/\varepsilon)\right)$, assuming coherent access to $H'(s)$ and endpoint derivatives. For slow analytic control Hamiltonians, only block encodings of the time-independent control operators are required, with the same query complexity and lower gate overhead. Our method also extends to Gevrey Hamiltonians and improves the precision dependence for simulating slow analytic semi-dissipative linear differential equations.

Singular kicked rotors have long been compared with power-law random banded matrices (PRBM) because their momentum-space Floquet matrix elements decay algebraically. However, it has remained unclear whether the deterministic correlations of the rotor become irrelevant at long distances and, consequently, under what conditions the two systems share the same infrared theory. To address this question, we derive a nonlocal supersymmetric nonlinear sigma model directly from a quantum kicked rotor with a power-law or logarithmic singularity. By carrying out the renormalization-group analysis up to two-loop order, we show that, after matching the symmetry class and coupling convention, the rotor reproduces the long-range Anderson transition of the corresponding PRBM, including its localized, critical, and extended infrared regimes.

Goldreich-Levin reductions are ubiquitous in cryptography: they convert an algorithm capable of guessing $\langle r, m \rangle$ (mod $2$) for a hidden string $m$ and a random challenge $r$, to one that is capable of extracting the entirety of $m$. Here, we describe a "simultaneous" Goldreich-Levin reduction for two entangled parties who are capable of guessing $\langle r, m \rangle$ given uniformly random identical challenges $r$. This allows to upgrade any unclonable encryption scheme satisfying "search" security to one satisfying the gold standard of unclonable "indistinguishability". As a corollary, we show that the simplest candidate unclonable encryption scheme from BB84 states satisfies unclonable indistinguishability. This result was discovered by GPT-5.6 Ultra after a few interactions. Our prompts included recent results on unclonable encryption by Ananth and Sahai, and Ragavan.

The aim of this paper is to provide the reader with a review and current state of the art of the fabrication of high T2 coherence diamond, optimised by the use of double electron-electron resonance (DEER) spectroscopy. Using DEER, we study the formation, transformation, and annealing of paramagnetic defects in as-grown CVD diamond and after post-processing. Electron irradiation leads to the formation of an additional S = 1/2 resonance in the DEER spectrum, which we consider to be a composite X ensemble. By tracking the concentrations of X and P1 point defects during annealing from 650C to 1200C, we find that the X ensemble initially consists of a mixture of V- spins and interstitial spins, which disappear at about 650C. Vacancies migrate during annealing, forming clusters that persist to 1000C and disappear upon annealing at 1200C, contributing to the X ensemble signal. We have developed a model of the influence of the mixed spin bath on the coherence of NV centers, which includes independent couplings with P1 centers, V-, divacancies, and interstitials. Detailed DEER studies allowed us to reveal and resolve a weak signal from two additional S = 1/2 species associated with hydrogen: NVH- and consistent with a substitutional hydrogen defect, which overlaps the vacancy spectral line. Taken together, these results show that the NV-DEER method is a powerful tool for investigating paramagnetic defects in diamond with high precision and nanoscale resolution, essential for material optimisation. The achieved high T2 coherence time is consistent with the spin bath model, and the crystals reach the quality required for advanced quantum sensing applications.

We make progress towards the impossibility of imperfectly complete quantum-computation, classical-communication (QCCC) key agreement by constructing the first unconditional attacks on quantum key agreement in the following restricted settings. In the two-message setting, we assume that Alice makes only classical queries to the oracle in the first round and that her message to Bob is classical, but otherwise both parties may perform arbitrary quantum computation, make quantum queries, and send a quantum state in the second round. Our attack and analysis are based on the heavy-query learning techniques from Austrin et al. (CRYPTO 2022) and the reprogramming techniques of Katz and Sela (arXiv 2401.14319). In the round-independent setting, we show that the attack of Barak and Mahmoody (CRYPTO 2009; J. Cryptology 2017) can be extended to multiple rounds when Alice and Bob share classical communication and make only classical queries in all but the final round. In both settings, the attacker is computationally unbounded and makes $poly(λ)$ queries to recover the key whenever each honest query bound is at most $poly(λ)$ and the valid agreement probability is inverse-polynomial. As a consequence, we rule out imperfectly correct quantum public-key encryption for classical messages whose length is bounded by a polynomial in $λ$ in the QROM when key generation has classical oracle access, even if encryption, decryption, and the ciphertext are quantum. In particular, the one-bit case applies to the imperfectly correct PKE obtained from two-round OSP by Bartusek and Khurana (CRYPTO 2025) whenever the classical OSP sender makes only classical random-oracle queries.

Noisy Bell mixtures may carry entanglement, standard teleportation usefulness, projective-measurement steerability, and optimized Cavalcanti-Jones-Wiseman-Reid (CJWR) and Clauser-Horne-Shimony-Holt (CHSH) violations. If the noise already has an ability, the mixture may lose and later recover it at distinct boundary crossings as the Bell weight decreases. We characterize ability-absence intervals and definitive thresholds for mixtures of $|Φ^+\rangle$ with arbitrary complex two-qubit $X$ noise. A closed-form singular-value flow of the Pauli correlation tensor gives the exact teleportation-useless, CJWR-satisfying, and CHSH-local intervals, while the positive partial transpose criterion gives the exact separable interval. At fixed populations and coherence magnitudes, these intervals widen as the relative phase between the $Φ$-block coherence of the noise and the Bell coherence increases from $0$ to $π$. The definitive thresholds form a universal chain from entanglement through teleportation usefulness and the three-setting CJWR witness to the common two-setting CJWR witness and CHSH-nonlocal threshold. Replacing teleportation usefulness by steerability gives a second chain, although their thresholds are not mutually ordered. For arbitrary pure two-qubit noise, the steerability thresholds in both directions for projective measurements and arbitrary positive operator-valued measures equal the entanglement threshold. For arbitrary product noise, an effective $X$-state singular-value flow gives the teleportation usefulness, CJWR witness, and CHSH-nonlocal thresholds. If a local noise factor is pure, the entanglement threshold and all four steerability thresholds are zero. For generic full-rank mixed $X$ noise, finite-setting semidefinite programs give upper bounds on the unknown directional projective-measurement steerability thresholds.

Variational quantum sensing offers a promising route to high-precision parameter estimation, but its performance depends strongly on the circuit architectures used for probe preparation and measurement. Existing approaches typically optimize continuous parameters within predefined ansätze, restricting the accessible design space and limiting adaptation to sensing tasks and hardware constraints. Here, we introduce \textsc{AutoQSense}, a reinforcement-learning framework that searches circuit architectures using Fisher-information-based objectives. For few-qubit systems, a single agent sequentially constructs preparation and measurement circuits. For larger systems, a distributed formulation assigns local circuit design to subsystem agents and inter-block entanglement to a budgeted agent. Numerical results show that the learned architectures recover known benchmark strategies, adapt to dephasing noise, and outperform fixed hardware-efficient ansätze while using fewer entangling gates. These results establish \textsc{AutoQSense} as a resource-aware approach to adaptive and hardware-compatible quantum sensing.

Textbook quantum superposition refers to the feature that certain linear combinations of Hilbert space rays, each representing a valid quantum state, are themselves valid states. This notion is not operational, and it relies on the underlying Hilbert space formalism. Recent proposals for experimental tests of indefinite causal order, as well as tests probing the non-classicality of gravity, pivot on superposition, thereby calling for a theory-independent, operational formalisation of the concept. Here, we define superposition within the framework of Generalised Probabilistic Theories, based on observed statistics in prepare-and-measure experiments. Using this, we formulate three superposition principles to investigate which structural features of quantum theory carry over to other theories. We study conditions under which these principles carry over from subsystems to their compositions; to this end, we show that the quantum tensor product emerges as the largest composition rule for quantum systems respecting all three principles. Furthermore, we show how non-classical features such as entanglement and preparational uncertainty can be viewed as special forms of superposition.

We investigate quantum thermometry in a driven--dissipative Kerr cavity coupled to a thermal reservoir. The system exhibits a finite-size precursor of a dissipative phase transition, characterized by a pronounced minimum of the Liouvillian gap and a sharp jump in the steady-state physical observables such as average photon number at the critical driving strength. We show that this regime leads to strong enhancement of the quantum Fisher information (QFI) for temperature estimation. Using an effective two-branch description, we show that the enhancement originates from temperature-induced redistribution of the weight factors in photon number distribution between low- and high-photon-number branches, which is described by an effective binary Fisher information. By optimizing the coherent drive, the enhanced response persists over an extended low-temperature, low-thermal-occupation regime and yields a favorable relative temperature-uncertainty bound. These results identify finite-size precursors of dissipative phase transitions in Kerr-cavity platforms as useful resources for tunable nonequilibrium quantum thermometry. We further show that the predicted thermometric enhancement is accessible in a parameter regime compatible with circuit quantum electrodynamics (circuit-QED) platforms.

Spin defects in silicon carbide (SiC) are promising candidates for integrated quantum photonics, offering long-lived spin states and near-infrared emission suitable for low-loss photonic integration and fibre-based quantum communication. However, light extraction from these defects remains challenging due the relatively high refractive index of SiC. Metalenses offer a compact approach to enhance light collection by engineering the wavefront directly at the material interface. Here, we design and fabricate monolithic metalenses from SiC bulk material that simultaneously operate at 860 and 1240 nm, matching with emission from the nitrogen vacancy and silicon vacancy colour centers. By independently engineering the phase response at both wavelengths, the metalens enables collection and polarization manipulation of the emitted light. We further employ the metalenses to demonstrate optically detected magnetic resonance of both defects simultaneously. These multifunctional metalenses provide a compact optical interface for scalable integrated SiC photonic devices.

We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.

Gate-level noise degrades the classification accuracy of Quantum Support Vector Machines (QSVMs) on Noisy Intermediate-Scale Quantum (NISQ) hardware, and the degree of degradation depends on how classical data is encoded into quantum states. We tested Z, ZZ, a Pauli, and an amplitude-inspired feature maps under depolarizing, bit-flip, and phase-flip noise channels in $52$ controlled experiments with error probabilities $p =0.01, 0.05, 0.10$, and $0.50$. The amplitude-inspired feature map had $100$\% test accuracy up to $p = 0.10$ across all three noise channels, while other feature maps fell to $65$-$90$\% under the same noise level and type. The Z feature map was found to be immune to phase-flip noise to a significantly high error rate, a consequence of the commutation relation $[R_Z, Z] = 0$. Entangled circuit variants produced generalization gaps in train-test sets of up to $17.5$\% under noise, whereas the amplitude variants maintained zero gap throughout. These results give practitioners data-driven criteria for a feature map on near-term quantum hardware.

Achiral molecules can be prepared in superposition states that are chiral. Here, we propose angular momentum orientation in the molecular frame to achieve the required symmetry breaking, exerting rotational control without the need for laboratory frame orientation. We derive the conditions for chiral rotational dynamics from the requirement to simultaneously break the continuous spatial rotational symmetry and the molecular point group symmetry. This can be achieved by three microwave pulses as well as two non-resonant optical pulses in combination with a THz pulse or three THz pulses, all with mutually orthogonal polarization directions, and the ensuing dynamics can be probed by photoelectron circular dichroism. Our results open the way for distinguishing structural from dynamical enantioselectivity and investigating time-odd chiroptical phenomena in randomly oriented molecules.

Recent discussions of QBism have turned increasingly toward the question of its ontology. I argue that key insights into QBism's ontology of agency can be identified by reconstructing its response to Wigner's friend paradox. I clarify the relation between two formulations of that response: one grounded in the claim that quantum states are agents' personal probability assignments, and another grounded in the injunction to treat all users of quantum theory as agents on equal footing. Once disambiguated, these formulations reveal an implicit commitment to a mutually recognitive conception of agency, according to which the agential status of a user of quantum theory depends constitutively on the acknowledgement of other agents. This analysis clarifies what is at stake in recent QBist engagements with phenomenology - namely, the search for a more philosophically robust account of this conception of agency. I show how Merleau-Ponty's account of intersubjectivity underpins the recognitive structure implicated in QBism before tracing these themes to Hegel's account of mutual recognition. By locating QBism within a longstanding tradition of mutual recognition, I claim that we not only illuminate its theoretical structure but also open up novel conceptual resources for the rigorous articulation and justification of its ontology.

Quantum repeaters are essential for overcoming the exponential photon loss that limits entanglement generation over long distances in quantum networks. An absorption-emission-based quantum repeater exploits the fundamental light-matter interactions of a diamond nitrogen-vacancy (NV) center---photon absorption and photon emission---to transfer a quantum state from an absorbed photon to an emitted photon, offering a scalable architecture that operates without photon interference between remote nodes. Here we demonstrate an absorption-emission-based quantum repeater node using a single NV center, realizing the complete single-node operation in which heralded photon-to-memory quantum state transfer, repeat-until-success (RUS) emission of a spin-entangled photon, and quantum teleportation of the memory state onto the emitted photon constitute the essential repeater operation. By characterizing the complete repeater operation as a quantum channel from the absorbed photon to the emitted photon via quantum process tomography, we obtain a process fidelity of 78%. This demonstration establishes the absorption-emission approach as a fundamental building block for scalable quantum repeater architectures and paves the way toward practical long-distance quantum networks.

We consider a Su-Schrieffer-Heeger(SSH)-type trimer model with next-nearest-neighbor(NNN) interaction and balanced loss-gain(BLG) to study the combined effect of lattice symmetries, topology, non-hermiticity and general boundary conditions(GBC)on the existence of flat band and the nature of Bulk-Boundary correspondence(BBC). We derive the necessary and sufficient conditions for the existence of an entirely real spectrum under the periodic boundary condition(PBC). The exact expressions for the compact localized states(CLS) and energy eigenvalues corresponding to flat bands are derived analytically under the PBC. We establish topological phase transitions(TPT) for PT-symmetry and pseudo-chiral symmetry through the computation of the Zak phase and sub-lattice Zak phase, respectively. The Hamiltonian under the open boundary condition(OBC) is studied numerically, and edge states are observed in the topologically non-trivial phase, thereby establishing the non-hermitian BBC. The CLS exists in both bulk and the boundary for systems having only pseudo-chiral symmetry, and an additional PT-symmetry destroys the CLS at the boundary. We generalize a known formalism to study the same Hamiltonian under GBC, and derive analytic expressions for the energy and eigenstates for a class of boundary conditions in parametric ranges which admit flat band under the PBC. The edge states for these boundary conditions, including the OBC, are obtained analytically in the topologically non-trivial phase, thereby establishing BBC. The non-hermitian skin effect(NHSE) is seen in the model with reciprocal bulk interaction and strongly non-reciprocal boundary terms. The winding number based on spectral topology is computed analytically.

When can one interpret the outcomes of a quantum measurement as revealing a pre-existing objective property? Using the recently developed formalism of quantum measurement retrodiction, we provide a quantitative treatment of this question: for any POVM and faithful prior state, we construct a positive semidefinite bilinear form that quantifies the non-objectivity of every real-valued outcome feature through the disagreement between its predictive value and its retrodictive counterpart. We show that this form decomposes exactly into the sum of two positive semidefinite bilinear forms: an unsharpness form and an asymmetry form given by Wigner--Yanase skew information. The total form vanishes precisely on those outcome features that can be interpreted, relative to the prior, as revealing pre-existing properties; in particular, it vanishes identically if and only if the POVM is sharp and commutes with the prior. Finally, under maps that preserve the prior and are covariant under its modular group, asymmetry cannot increase, and any loss of asymmetry is offset by at least as much unsharpness, so that total non-objectivity cannot decrease.

A measurement of a single-qubit quantum sensor reveals at most 1 bit of information about the signal that was sensed. To perform a classification task on the signal, the conventional approach is to repeat a sensing protocol many times, averaging the measurement results to obtain a high-precision estimate of the sensed signal, and then to apply classical postprocessing. Quantum computational sensing (QCS) is an alternative approach that breaks with the paradigm of first obtaining a classical estimate of the signal and then computing a function of the estimated signal in postprocessing. QCS instead combines quantum sensing with quantum computing to concentrate information about the signal relevant to the task into the solitary bit revealed by each measurement. Here, we report on the experimental demonstration of QCS where sensing and computing were both performed by the same single superconducting transmon qubit. We consider various binary classification tasks based on static and oscillating magnetic fields induced by current through a flux line. The fields were sensed through a double-junction superconducting quantum interference device (SQUID) loop that was part of the qubit. We used a protocol based on quantum signal processing to preprocess the sensed signals in the quantum domain prior to measurement. For tasks on static magnetic fields, our protocol outperformed the conventional baseline of Ramsey-based phase estimation by as much as 15 percentage points. For tasks on oscillating magnetic fields, we classified signal amplitude and frequency with up to 20 and 15 percentage points higher accuracy, respectively, compared to the conventional baseline of optimized dynamical-decoupling protocols. Our results illustrate how quantum computing can enhance quantum sensing even with a minimally sized quantum system subject to the practical limitations of decoherence and error-prone operations.

Cubitt, Harrow, Leung, Montanaro, and Winter (CHLMW) exhibited an explicit pair of quantum channels whose minimum output Rényi entropy is nonadditive at order zero, and reported numerical violations at positive orders close to zero. Their paper states that a semidefinite-programming argument yields a rigorous positive-order interval for the same example, without printing the endpoint or a verifiable certificate; a recent paper by Leung, Lovitz, and Wu records that for this pair "no rigorous endpoint was obtained". We close that gap for the trace-preserving normalization of the printed pair fixed in Section 2. Small rational witness matrices prove that every output of either channel has all eigenvalues between $301/100000$ and $2/3$; a single explicit entangled input has an exact rational joint output spectrum of rank eight; and two independent elementary interval arguments turn these three facts into a proof of strict additivity violation, $S_p^{\min}(\mathrm{N}_R\otimes\mathrm{N}_{\bar S}) < S_p^{\min}(\mathrm{N}_R)+S_p^{\min}(\mathrm{N}_{\bar S}),$ for every real order $0<p\le 1/22$. Every step of the verification reduces to comparisons of integers, and the complete certificate is a few small rational matrices that a reader can check with a short program -- or, for any single order, by hand. To our knowledge, consistent with the assessment of Leung, Lovitz, and Wu, this is the first printed, computer-verifiable certified positive-order endpoint for this explicit pair. We claim no novelty for the phenomenon or for the eigenvalue-floor mechanism, both due to CHLMW, and no optimality of the endpoint.

Recently, a set of coupled singlet-octet universal Lindblad equations (ULEs) was derived within the framework of non-relativistic QCD (NRQCD) to describe quarkonium dynamics in the quark-gluon plasma (QGP). These equations provide a unified quantum description spanning the quantum Brownian and quantum optical regimes. In this work, we further develop this framework and establish its connection with semiclassical transport. We first derive the universal Lindblad equations within the potential non-relativistic QCD (pNRQCD) effective field theory and show that they coincide with the small-dipole limit of the NRQCD ULEs. We then derive the semiclassical limit of the NRQCD ULEs, obtaining a set of coupled singlet-octet Boltzmann equations. To our knowledge, this is the first derivation of Boltzmann transport equations directly from the universal Lindblad framework. The resulting equations are valid beyond the small-dipole approximation, allowing the evolution of heavy-quark pairs from compact to widely separated configurations. Taking their small-dipole limit allows a direct comparison with the Boltzmann equations of Yao et al. [Phys. Rev. D 99, 096028 (2019)], which were derived within pNRQCD from the Davies secular equation, relying on the rotating-wave approximation (RWA). While the singlet equations are found to be in near-complete agreement, the octet equation contains an additional collision term describing transitions within the continuum of octet scattering states, which is absent from the RWA-based derivation. Finally, we derive the leading quantum correction to the singlet Boltzmann equation. Our results establish a more general and systematic theoretical foundation for the semiclassical transport description of quarkonium in the QGP.

Neutral-atom processors rely on spatially arranged qubit arrays and parallel Rydberg entangling gates for scalable execution. Their compilers enforce geometric spacing rules for simultaneous gates, yet legal separation does not make residual van der Waals coupling disappear. This paper studies that gap between geometric legality and residual noise by treating entangling-zone spacing as a cross-layer reliability-parallelism variable anchored to experimental neutral-atom geometry. We combine fixed-schedule residual replay, surface-code simulation with matched correlated decoding, and fresh recompilation to connect spacing to physical residual exposure, logical reliability, and makespan cost. The results show that near-floor spacing can produce structured correlated exposure that is visible both at the physical layer and, in the tightest case, after quantum error correction (QEC). Modest geometric slack strongly suppresses this residual contribution, but the timing cost of looser spacing is mediated by placement and scheduling rather than by a simple monotonic slowdown. These findings distinguish hardware legality from residual-noise safety and motivate spacing-aware compiler evaluations that report physical geometry, QEC absorption, and scheduling cost together.

We propose a Z-transform framework for the analysis and synthesis of finite range lattice momentum operators in quantum field theory. In this formulation, translation-invariant lattice operators are represented as functions of the complex variable $z$ in the unit circle, allowing their spectral properties to be analyzed using tools from digital signal processing and rational approximation theory. Within this framework, the fermion doubling problem is reinterpreted as the appearance of unwanted zeros of the discrete momentum operator on the unit circle --- an aliasing phenomenon in the sense of the Nyquist sampling theorem --- and the conditions for ghost suppression are expressed as precise constraints on the zero structure of the operator's transfer function. It is proven that no rational function can satisfy all required conditions simultaneously, motivating the finite impulse response approach developed here. This reframing naturally suggests a class of finite-range momentum operators, constructed by solving a least-squares approximation problem in the frequency domain. The resulting finite impulse response (FIR) operator approximates the continuum derivative across the full Brillouin zone, with ghost suppression achieved through the accuracy of the spectral approximation rather than through the addition of a symmetry-breaking Wilson term or the infinite-range nonlocal SLAC derivative. Numerical investigation confirms that near $θ= π$ only plane waves propagate coherently, and these exhibit group velocities far exceeding the speed of light, further distinguishing them from physical low-energy excitations. No ghost wave packet solutions exist near $θ= π$.

We investigate whether the second-order purity-corrected stabilizer Rényi entropy (SRE) of reduced two-qubit density matrices can serve as a reliable local indicator of quantum phase transitions (QPTs) in frustrated quantum spin systems. We consider the one-dimensional isotropic \(J_1-J_2\) Heisenberg model, the one-dimensional XXZ \(J_1-J_2\) model, and the two-dimensional \(J_1-J_2\) Heisenberg model on a \(4\times4\) square lattice. Unlike several previously studied quantum information measures, which fail to detect QPTs in the ground state of these frustrated systems, the reduced ground-state purity-corrected SRE successfully identifies most transitions. For the remaining cases, we consider a low temperature subjacent state, modeled as a statistical mixture of the ground and first excited states with a Maxwell--Boltzmann-type occupation probability. For the 1D isotropic model, the subjacent-state SRE shows a discontinuity at the critical point, yielding \(α_c(\infty)=0.24116\), in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding \(α_c(\infty)=0.2681\). For the 1D XXZ model, the subjacent-state SRE reproduces the full anisotropy dependent phase diagram, while the ground-state SRE captures transitions only at low anisotropy. For the 2D model, the subjacent-state SRE detects two transitions, at \(α_c(4\times4)=0.40781\) and \(0.6208\), while the ground-state SRE identifies the second at \(0.6230\). Compared with conventional two-qubit entanglement, purity-corrected SRE shows a clear advantage in revealing otherwise-invisible phase transitions, establishing it as a robust, efficient, local probe of frustrated quantum criticality.

The value of a multiqubit geometric phase at a single operating point does not reveal whether it was generated directly or through a connected sequence of lower-body interactions. For analytic, gapped, nondegenerate Abelian holonomies, we jointly resolve logical support and independently calibrated coupling support. Every nonzero connected response must involve an active set that connects and covers the target and must contain one factor of each active coupling, yielding the sharp onset bound $ν_S \geq τ_E(S)$. The same selection law applies locally to projected Berry curvature. Conversely, an unrestricted finite-dimensional construction realizes all responses allowed by the connected-cover condition simultaneously, making the condition necessary and sufficient within this theorem class. Operationally, simultaneous confidence bands certify detected mixed responses while controlling false positives; a factor-of-two separation condition additionally recovers exact library-relative response minima. In a complete dictionary, nontriviality of every minimal-cover response is generically necessary and sufficient for these minima to coincide with the minimal calibrated mechanisms. Three-qubit Wilson calculations distinguish direct and pair-mediated routes with the same endpoint phase, and a synthetic Ramsey audit locates the finite-resolution boundary.

We study the von Neumann entanglement entropy generated by a Haar distributed passive interferometer acting on $n$ equally squeezed input modes with fixed nonzero squeezing strength $s$. Previous work established proportional weak typicality for integer R'enyi orders $α\geq 2$ and stated a sublinear von Neumann result, while the proportional von Neumann case remained open. For a subsystem of $k_n$ modes satisfying $k_n/n\to r\in(0,1)$, we prove that, for every $\varepsilon>0$ and all sufficiently large $n$, $\mathbb{P}\left(\left|\frac{S_{1,n}}{\mathbb{E}S_{1,n}}-1\right|\geq\varepsilon\right)\leq2\exp\left[-\frac{c_{s,r}\varepsilon^2n^2}{\log^2(en)}\right].$ The proof represents the entropy as a singular value statistic of a principal block of $UU^{\mathsf T}$, where $U$ denotes the unitary interferometer. It regularizes the logarithmic singularity at the endpoint corresponding to a pure Gaussian mode and applies concentration on the unitary group. The result establishes proportional von Neumann weak typicality and further implies almost sure convergence of $S_{1,n}/\mathbb{E}S_{1,n}$ to $1$, a typical volume law, and the variance bound $\mathrm{Var}(S_{1,n})=O_s(\log^2 n)$. An accompanying Lean 4 development verifies the proof chain.

We show how to compile an arbitrary classical circuit into a fault-tolerant circuit, which performs the desired computation even when an almost-linear number of bits are adversarially chosen and corrupted in each timestep. Using a variant of this fault-tolerance scheme that only detects (rather than corrects) corruptions, we give a new construction of probabilistically checkable proofs (PCPs) for NP with polylogarithmic query complexity. This PCP construction from fault-tolerance presents a promising candidate for quantization by the work of Anshu, Breuckmann, and Nguyen (STOC'24), who provided a roadmap for constructing quantum PCPs via fault-tolerance.

We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on $\bar{N}$ logical qudits of depth $\bar{T}$, we construct a fault-tolerant circuit on $N=\text{poly}(\bar{N})$ physical qudits of depth $\bar{T}\cdot\bar{N}^{o(1)}$, which is robust against an adversary who may arbitrarily choose and corrupt an almost-linear number $N^{1-o(1)}$ of physical qudits at each time step. This robustness significantly improves upon prior fault-tolerance theorems, which assumed corruptions were either local and stochastic, or else only act on a polynomially vanishing fraction of qudits. Our fault-tolerance scheme addresses a key bottleneck towards constructing quantum PCPs via the circuit-to-Hamiltonian mapping of Anshu, Breuckmann, and Nguyen (STOC'24). More fundamentally, our result demonstrates that fault-tolerant quantum computation remains possible under noise models that are global, worst-case, and non-Markovian over the full duration of the computation, directly countering concerns that correlated noise could fundamentally undermine quantum fault tolerance. Our construction is based on a new family of subsystem product codes we develop, which have large dimension and distance along with low-weight parity-checks, and which support transversal non-Clifford gates. We show how to perform single-shot fault-tolerant error correction on these codes using a Floquet-like procedure based on the local testability of classical tensor codes. We then obtain a universal fault-tolerance scheme using repeated code switching in a hypercubic qudit architecture. Finally, we recursively compose our scheme with itself to reduce an initially exponential qudit dimension down to a constant.

We determine the distribution of fidelity susceptibility for chaotic eigenstates at the spectral edge of Gaussian random-matrix ensembles. Previous work showed that, in the unitary class, the characteristic susceptibility scale of edge states grows as $D^{1/3}$, rather than proportionally to $D$ as in the spectral bulk, reflecting Airy-edge level rigidity. Extending a determinant-based framework introduced for bulk states, we derive the universal edge distributions for both the orthogonal and unitary ensembles. The two symmetry classes share the scaling variable $g/D^{1/3}$ and exhibit a symmetry-dependent cubic suppression of small susceptibilities, while their algebraic large-$g$ tails reflect the corresponding symmetry-dependent level repulsion. Although eigenvector statistics retain their random-matrix form throughout the spectrum, edge rigidity makes low-lying chaotic states parametrically less sensitive to generic perturbations than bulk states. Our results establish universal, symmetry-dependent spectral-edge fidelity-susceptibility statistics in systems whose chaotic dynamics extends down to the ground state.

We determine the exact worst-direction Fisher-information cost of using a parameter-independent readout to estimate an unknown qubit direction at known Bloch-vector length $η$. Every fixed-local architecture, including recorded classical randomization, heterogeneous single-copy measurements, and arbitrary outcome spaces, reduces exactly to a zero-barycenter probability measure on the Bloch ball. For every full-rank qubit and every trace-balanced spectral Fisher loss, the resulting minimax problem is rigid: the unique optimal aggregate design is the spin-coherent Haar positive-operator-valued measure (POVM). For $N$ copies, inverse-Fisher $A$ loss has the exact value $2/[Nf(η)]$, where $ f(η)= \frac{2η-(1-η^2)\log[(1+η)/(1-η)]}{4η}$. This uniqueness has an immediate finite-readout consequence. No finite-support measurement attains the unrestricted mixed-state optimum, while at the smallest globally regular support the tetrahedral symmetric informationally complete (SIC) measurement is uniquely $A$- and $D$-minimax, with exact worst-direction values. Relaxing the fixed-readout constraint separates the asymptotic resources: one-way local operations and classical communication (LOCC), unrestricted LOCC, and separable measurements have $A$-loss coefficient $4/η^2$, whereas collective measurements attain $2(1+η)/η^2$. We further classify the rigidity conditions for unequal contrasts and show that Haar uniqueness survives at the nonregular pure-state endpoint.

A classical-limit formula is derived for matrix elements between bound states of distinct one-dimensional potentials. We leave open the physical interpretation of the potentials, but generally envision them to be Born-Oppenheimer-type potentials with the position variable $x$ identifying with a slowly evolving degree of freedom of the system. For instance, $x$ could represent the internuclear separation in a diatomic molecule, with the potentials being potential energy curves for different electronic states. In this scenario, the matrix elements could be, e.g., conventional Franck-Condon factors. To test the derived formula, we assume functional forms for the potentials and operator that afford analytical solutions for the matrix elements. As the classical limit is approached, the computed matrix elements exhibit a clear tendency towards the classical-limit formula, providing strong validation for the formula. In future work, we anticipate using the formula to model inhomogeneous excitation spectra of atoms in one-dimensional optical lattices, with an eye towards improved optical lattice clock performance.

Neutral-atom quantum processors have rapidly advanced in scale and coherence, yet their practical performance remains constrained by limited quantum circuit iteration rates (qCIRs) and information throughput. Here we experimentally demonstrate a high-throughput neutral-atom system based on non-destructive readout and atom reuse. By integrating a chip-based photonic interface with a 10-qubit array, we implement non-destructive readout with a retention probability of 99.7%, and further achieve a raw qCIR of 101Hz and a post-selected qCIR of 74.8Hz. More importantly, we verify a general throughput optimization methodology and obtain a normalized Fisher information rate of 57.7Hz, improving the achievable throughput by more than one order of magnitude compared with conventional methods. Our results establish a practical route toward high-throughput neutral-atom quantum processors.

We study quantum simulation of SU(3) non-Abelian gauge theory dynamically coupled with fundamental fermions in $3+1$ dimensions by employing the lattice Hamiltonian in axial gauge that avoids Gauss's law constraints. The temporal component of the gauge field is analytically solved in terms of independent field degrees of freedom and a lattice regulated Green's function. The axial gauge condition is trivially maintained in time evolution, even under Trotterization. The gauge field degrees of freedom are expressed in the local field basis and can be efficiently transformed into the canonical conjugate momentum basis by local quantum Fourier transforms. We prove the number of qubits needed for describing all states up to an energy $E$ with an accuracy $ε$ on a lattice of volume $V$ at bare coupling $g$ is bounded as $16n_A V + 12n_f V$, where $n_A \approx \log_2 (\frac{64 E' V^{4/3}}{π^2ε} + \frac{32\sqrt{2}g n_f E'^{1/2} V^{7/6}}{\sqrt{3}π^3ε^{1/2}} ) $ is the number of qubits needed for each independent gauge field per site with a shifted energy $E'$, and $n_f$ denotes the number of fermion flavors. We then analyze a quantum algorithm for time evolution that is based on Trotterization, quantum Fourier transform, and Jordan-Wigner transformation, for which quantum circuits can be explicitly constructed under arbitrary gauge field truncation and digitization. We find the numbers of CNOT and single-qubit rotation gates both scale as $O(n_A^4 V^{4/3}) + O(V^{5/3})$ per Trotter step for fixed $n_f\leq 6$. We conclude that quantum resources needed for simulating real-time dynamics of lattice QCD scale polynomially with volume, energy, time, accuracy, and bare Hamiltonian parameters.

In timeless formulations of quantum theory, the Page-Wootters proposal (PW) recovers time and dynamics as relative clock-and-world states. By interpreting the total timeless system as a clock entangled with the world, the states having a definite clock reading appear to recover the temporal states of the world as relative states, and dynamics emerges. But an entangled state admits infinitely many decompositions as a superposition of product states, each decomposition corresponding to a different but equally valid time operator of the same clock system. Different valid choices of the time operator for the same clock system lead to different physical histories, where the world states in a history are superpositions of the world states from another history. Fixing one operator as "the" clock time would import the temporal meaning that the Page-Wootters proposal is meant to explain in the first place. Therefore, the interpretation of PW that the world state is passively conditioned on the clock state cannot hold. The timeless state is resolved into time-dependent states by the intrinsic pointer observables of the world, without having to outsource the role of the time operator to a separate clock. Fortunately, the formalism of PW remains valid, provided that it is interpreted in terms of intrinsic pointer observables of the world itself.

The mobility ring (MR), a critical boundary in the complex energy plane separating extended and localized states, is fundamental to understanding the Anderson transition in non-Hermitian (NH) disordered systems. While MRs have been extensively studied in one-dimensional (1D) NH quasiperiodic models, rigorous analytical frameworks beyond 1D remain critically scarce. Here, we investigate a class of two-dimensional (2D) quasiperiodically decorated Lieb lattices (QDLLs) featuring complex incommensurate potentials selectively applied to the lattice vertices. By exactly mapping these 2D structures onto NH generalized Aubry-Andr{é}-Harper (AAH) models and leveraging extended-localized transition point, we analytically derive the Lyapunov exponents and obtain exact expressions for the MRs. These exact theoretical boundaries are strongly corroborated by numerical computations of wavefunction fractal dimensions and real-space probability distributions. Furthermore, we reveal distinct evolutionary behaviors of the MRs driven by the quasiperiodic potential strength: systems characterized by $κ=2$ possess a single MR, whereas systems with $κ=3$ undergo a dynamic sequential evolution from a single integrated ring into two independent rings. We hope that our exact results of MRs in 2D will benefit the study of Anderson localizations and MRs in high-dimensional NH systems.

Germanium hole spin qubits are a promising and versatile platform for quantum computation and simulation. In this system, strong spin-orbit interaction (SOI) renders the single-qubit $g$-tensor anisotropic and electrically tunable, enabling operational sweet spots with reduced noise sensitivity. SOI also transforms the isotropic two-qubit exchange coupling into an anisotropic tensor whose geometry is inherited from the single-qubit $g$-tensors and spin-flip tunnelling. Here, using two hole spin qubits in a strained-germanium quantum well and full vector control of the magnetic field, we map this exchange tensor, separate it into longitudinal and transverse components, and show that they govern controlled-phase and SWAP-like dynamics, respectively. We find that the longitudinal exchange can be tuned via the magnetic field orientation from a conventional positive value, through zero, to an effectively negative one, as measured by inverted exchange-split spin transitions. The magnetic field direction thus provides continuous control over the interaction Hamiltonian: at a point of purely transverse exchange, we engineer a single-pulse baseband iSWAP, unattainable under isotropic exchange. Linking $g$-tensor geometry to exchange anisotropy establishes native Hamiltonian engineering, enabling spin-based quantum simulation and gate sets selected by the global field orientation alone.

We determine the optimal quantum manipulation protocols for implementing high-fidelity, fast single-qubit gates. We demonstrate that the time-optimal pulse sequence is a ``bang-bang'' sequence: discrete pulses of either positive or negative maximum amplitude or zero. The non-adiabatic bang-bang pulse sequence minimizes gate duration providing a speedup for low-frequency architectures. We first derive the protocol for a transversally driven two-level system, extracting exact analytic expressions for minimum gate times. We then extend this framework to general multilevel architectures, identifying conditions that enable the coherent suppression of leakage errors. Using the fluxonium circuit as a representative case study, we optimize $X/2$ and $Y/2$ gates through a combination of discrete bang sequences and continuous waveform smoothing. This approach preserves near-optimal execution speeds while mitigating transitions outside the computational subspace. Open-system simulations demonstrate that these sequences outperform commensurate and resonant pulse schemes across different fluxonium regimes, achieving low-error manipulation significantly faster than standard resonant control, even in the presence of $1/f$ flux noise and dissipation.

The process-matrix formalism describes quantum processes without assuming a fixed global causal order, but the physical meaning of indefinite causal order remains open. We address this question within histories theory, where temporal ordering and dynamical evolution are distinct structures. We show that the decoherence functional admits coherent superpositions of dynamics. In measurement settings, under suitable factorization conditions, these generate process matrices. Thus, we identify process-matrix indefinite causal order as an operationally restricted realization of the more general phenomenon of superposition of dynamics. Histories theory also admits a distinct kinematical notion of indefinite order, in which the ordering of physical events is itself a history observable. The resulting distinction between event order and intervention order clarifies the relation between indefinite causal order, quantum dynamics, and spacetime structure.

We demonstrate a static, disorder-free spin chain Hamiltonian which, by tuning the coupling to an auxiliary qubit, realizes a crossover between super-ballistic, ancilla-accelerated scrambling and sub-ballistic operator confinement. Our minimal model is the mixed-field Ising chain with a spin-1/2 ancilla coupled to its longitudinal magnetization. The ancilla mediates an effective all-to-all interaction which accelerates operator spreading and entanglement growth when weakly coupled, but rapidly saturates its entanglement and projects spin chain operators into effectively frozen subspaces when the ancilla coupling is strong. We locate this crossover independently through both a divergent peak in the mutual-information saturation time near $λ_c N/h \approx 8$ and an exponential suppression of the late-time OTOC growth rate, $\logα\propto 1/λ$. Through a Feshbach-Fano projection and Schrieffer-Wolff transformation, we reveal an effective hidden symmetry on the chain which confines operators on the chain for a time exponential in the coupling strength. This reconciles the fast, $\log(N)$ scrambling reported for random-unitary-circuit realizations of the star geometry with the confinement previously found in its time-independent Hamiltonian analog, showing both emerge from a single Hamiltonian family as a function of one dimensionless parameter.

The sensitivity of miniaturized optically pumped magnetometers (OPMs) is limited by weak atom-light coupling, which an optical cavity can enhance. In this work, we model the photon-shot-noise-limited sensitivity of cavity-enhanced OPMs in the regime of strongly collisionally broadened optical transitions, characteristic of buffer-gas-filled miniaturized vapor cells. The cavity enhancement is benchmarked against a single-pass free-induction-decay OPM employing Faraday-rotation readout, with the probe power and detuning jointly optimized using the Cramér-Rao lower bound as a figure of merit. For a Fabry-Pérot cavity, we compare side-of-fringe, homodyne, Pound-Drever-Hall, and Faraday-rotation readout. All four yield an optimal sensitivity enhancement scaling as $α\sqrt{2\mathcal{F}/π}$, where $\mathcal{F}$ is the cavity finesse and $0.5\leq α\leq 1$ is a readout-dependent prefactor. The enhancement is maximized at critical coupling, and we quantify its degradation away from this point. We further show that, despite spin-dependent absorption associated with the ensemble's vector polarizability, near-critical coupling can be maintained throughout spin precession at arbitrary finesse by exceeding a derived probe-power threshold and increasing the atomic detuning with finesse. We also establish a limit to the maximum cavity enhancement set by vector light-shift noise.

Atomistic descriptions of hydrogen diffusion and trapping at defects are essential for understanding hydrogen embrittlement. As the lightest solute in metals, hydrogen exhibits nuclear quantum effects that alter these processes even at room temperature. Explicit treatment of such effects is computationally demanding, limiting large-scale simulations of complex environments. Here, we use an Fe-H machine-learning interatomic potential (MLIP) based on the performant implementation of the atomic cluster expansion (PACE), covering diverse Fe-H environments, and relabel the training configurations underpinning its transferability with quantum mean forces from centroid-constrained path-integral molecular dynamics at 300 K. This yields a nuclear-quantum-corrected PACE (NQC-PACE) without additional density functional theory calculations. At parent PACE, NQC-PACE describes nuclear quantum effects on hydrogen trapping at vacancies, dislocations, surfaces and general grain boundaries, H-H interactions, and diffusion in alpha-Fe. Grand-canonical Monte Carlo/molecular dynamics simulations show nuclear quantum effects markedly enhance hydrogen segregation at general grain boundaries and trapping behaviour in closer agreement with experimental trends. This enhancement arises from selective quantum stabilisation of open, anisotropically soft local environments. Our framework uses finite-temperature quantum mean forces to relabel the configurational space covered by an MLIP, enabling large-scale analysis of complex materials where light-element quantum effects matter.

In this paper, we analytically compute the quench dynamics of simple product states that evolve under a spin-1/2 XY-model with power-law interactions in a staggered magnetic field. We use linear spin-wave theory as well as a low-energy theory that accounts for strong phase fluctuations. This allows us to provide an analytic expression for the dynamics of phase-type correlations with short-range interactions, where the linear spin-wave theory is known to fail. For density-type correlations the low-energy theory and the linear spin-wave theory give the same result. Our analysis is valid for arbitrary magnetic field strength and in particular provides an analytical understanding of the quench dynamics near criticality. Our results can thus provide useful tools for the experimental observation of excitation gaps and critical behavior.

While the impossibility of perfectly identifying non-orthogonal states is a cornerstone of quantum information science, their probabilistic discrimination is nonetheless permissible. Here, we propose a two-reservoir quantum machine driven by this mechanism to map its functional boundaries across the parameter space of the state overlap $μ$ and the Carnot efficiency $η_C$. Within this $η_C$-$μ$ plane, the machine exhibits phase-transition-like functional switching among a pure heat-engine phase, a mixed phase, and a dissipative phase. We identify critical thresholds governing these transitions: strong thermal driving ($η_C \ge 0.5$) unconditionally guarantees positive work extraction, whereas weak driving ($η_C \lesssim 0.13$) induces an anomalous reentrant transition, where increasing $μ$ unexpectedly restores engine functionality after a purely dissipative regime. Our results explicitly demonstrate how quantum mechanics and thermodynamics jointly constrain information-to-energy conversion.

The corrections to Casimir pressure (force) on two plates of real metal described by the dielectric constant of the Drude, Drude-Lorentz, Drude-Smith and plasma models at the finite temperature and conductivity are considered. We consider the contour integral lost in the Lifshitz formula and discuss inconsistencies for the corrections to the Casimir force given in the literature. Numerical and analytical results in the near and far zones are presented. The two first-order correction obtained due to the actual dielectric constant of the metal coincided with the literature data.

We investigate the emergence of a scarred discrete time crystal (SDTC) phase in a periodically driven dimerized spin chain. While generic interacting Floquet systems are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), we demonstrate that this system hosts quantum many-body scars (QMBS) that induce a regime of weak ergodicity breaking. Through an analysis of Floquet level statistics, entanglement entropy, and eigenstate fidelity, we identify a manifold of low-entanglement states characterized by semi-Poisson statistics embedded within an otherwise thermal spectrum. These scarred states support robust subharmonic oscillations with period doubling, signaling the spontaneous breaking of discrete time-translation symmetry. We show that the SDTC response is robust against a variety of initial state configurations, demonstrating its stability beyond fine-tuned conditions. A finite-size scaling analysis reveals that the time-crystalline lifetime grows with system size within the range accessible to our exact-diagonalization calculations. However, drawing on the general phenomenology of approximate many-body scars, we expect that hybridization between Floquet scars and the thermal continuum will eventually curtail this growth, causing the lifetime to saturate at system sizes beyond our current numerical reach. This characterizes the SDTC as a long-lived metastable dynamical regime rather than a strictly stable thermodynamic phase, providing a comprehensive framework for understanding the interplay between periodic driving and constrained many-body dynamics in disorder-free systems.

Quantum Feedback Network Theory (also known colloquially as the SLH-framework) is a powerful tool for modeling systems in quantum optics. This paper describes a method for discretising SLH-networks such that they can be implemented on a quantum computer. Building on a discretisation theorem for quantum stochastic differential equations, we establish strong convergence, uniformly on compact time intervals, of the discretised system to the continuous SLH-network as the discretisation mesh goes to zero.

Anyons obey fractional statistics that lie between bosonic and fermionic statistics, giving rise to a broad range of intriguing phenomena. However, how anyonic statistics govern quantum-state complexity is still largely unexplored. In this work, we investigate the interplay between the statistical phase and on-site interactions in the anyon-Hubbard model, identifying exact quantum many-body scar eigenstates and novel quench dynamics. The Krylov complexity exhibits perfect periodic revivals independent of the statistical phase in the scarred dynamics, whereas after a quench it depends on both the statistical phase and the interaction strength. In the strong-interaction regime, we find approximate scarred dynamics, while in the weak-interaction regime the state spreads over Krylov space and the complexity ultimately saturates. Moreover, for the bosonic initial state, the complexity of fermions exhibits the lowest saturation value, and vice versa. For fractional statistics, the saturation plateau is minimized when the post-quench statistical phase is close to that of the initial state. Our results demonstrate the central role of the statistical phase in governing many-body dynamics and provide new insights into Krylov complexity and quantum many-body scars.

Experiments have revealed that collective strong coupling in optical cavities can drastically alter the conductivity and dielectric properties of molecular ensembles, or even trigger abrupt phase transitions (in Rayleigh scattering or dispersion force driven conformational equilibrium). Until now, the underlying physical mechanism has remained unknown. A recently proposed theory attributes these collective effects to cavity-induced electron correlations that share properties of the known spherical Sherrington-Kirkpatrick model of a spin glass. As a consequence, entropic effects can trigger a phase transition in the inter-molecular electron correlations that could potentially explain the above experiments. In the following work, we derive analytic expressions for the correlation (free-)energy-induced polarizability changes, which reveal that under certain conditions collective strong coupling can even render our molecular ensemble metallic by entropically ionizing collectively degenerate molecular orbitals. Our results are a first major step towards a holistic theory of cavity-mediated electron correlation effects.

The predictive simulation of molecules and materials has had a broad and significant impact. It nevertheless remains constrained by the cost of accurately treating electronic correlation, excited states, and complex energy landscapes. Quantum computing offers a fundamentally different computational paradigm in which quantum states are encoded and manipulated directly rather than approximated on classical hardware. Here we discuss where this approach may provide a genuine scientific advantage in chemistry, materials science, and biochemistry. Promising directions include the high-accuracy treatment of correlated active spaces, improved excited-state simulations, and accelerated exploration of combinatorial structure spaces. The central challenge is therefore not qubit scaling alone, but demonstrably chemically meaningful gains in predictive reliability. We argue that near-term value is most likely to come from disciplined workflow integration rather than wholesale replacement of classical methods. Noisy physical devices, error-mitigated utility experiments, early fault-tolerant devices, and fully fault-tolerant quantum computers offer different scientific prospects, and claims of usefulness must be tied to the specific regime being discussed. Quantum computing will become scientifically valuable when it demonstrably reduces uncertainty in computed energies, rates, spectra, or materials stability after the full costs of state preparation, measurement, error handling, and coupling to classical simulation are included.

Based on the van Kampen-Schram method, a formula for the Casimir force between two plane-layered structures is obtained, which includes the sum of the Matsubara frequencies and a contour integral. It is shown that the contour integral is not taken into account in the Lifshitz formula. Taking it into account gives a small contribution at high temperatures when the Lifshitz formula is approximately correct. However, at low temperatures, its contribution is significant, and the Lifshitz formula for the finite temperature does not transform into the Lifshitz formula at zero temperature. An example of interaction of metal plates is considered.1

We identify a non-Hermitian counterpart of dynamical tunnelling induced by a localised absorbing region in a symmetric confining potential. The absorbing region, described by an imaginary potential barrier, induces an effective double-well structure with a pair of long-lived states that have little population in the barrier. In contrast to the periodic tunnel oscillations through a real barrier, the system slowly evolves towards equal population of the two sides, while the absorbing region remains only weakly populated. We demonstrate this generic mechanism in two continuous potentials, and capture its essence analytically in a minimal $3\times 3$ matrix model. We propose a realistic optical waveguide setup for the experimental observation of the effect.

Quantum permutations, or magic unitaries, have in recent years been explored in the context of identifying `genuinely quantum' isometries of graphs. Here, we import this tool in physics, showing that quantum permutations yield a generalisation of quantum reference frames in a discrete setting that is reminiscent of the passage from special to general relativity. We show that the typical quantum reference frames framework corresponds to quantum permutations classified as `classical' in the mathematical literature, and which we demonstrate are quantum controlled transformations (superpositions of classical coordinate maps). Genuinely quantum permutations (i) allow to construct \emph{non--commuting} quantum reference frames (ii) correspond to \emph{local}, as opposed to global, superpositions of transformations. Strikingly, we find that the non-commutativity of quantum fields, when used as reference systems, is exactly what implies that the change of frame is achieved through a genuine quantum permutation. We illustrate the above with several examples in both first and second quantization formalism, which demonstrate (a) simultaneous control on non--commuting variables, (b) the existence of bipartite states that can be localized with a genuine quantum permutation and cannot be localized with the usual quantum reference frame transformations (without introducing additional degrees of freedom), (c) extension of the Ising model symmetries to genuinely quantum permutations, and (d) extension of the symmetries of a scalar field action on curved spacetime to genuinely quantum permutations. While we have in mind applications in quantum gravity, we expect our formalism to be of interest in a wide range of topics in quantum information.

Two-photon bound states in the continuum provide a stringent setting in which quantum interference must suppress radiative decay despite photon--photon interactions. Here, we prove a no-go theorem showing that a single nonlinear mode linearly coupled to a noninteracting bosonic continuum cannot support an interaction-active two-photon bound state in the continuum, provided the local spectral density vanishes only at isolated energies. Apart from this regularity condition, the result is independent of the continuum dispersion and the frequency-dependent coupling. Although such an exact bound state is forbidden, long-lived two-photon quasi-bound states remain possible. For a giant Kerr cavity nonlocally coupled to a waveguide, we derive the asymptotic scaling of the two-photon decay rate with the coupling-point separation from weak nonlinearity to the hard-core limit. We further identify a regime in which the two-photon resonance is substantially longer lived than the single-photon excitation. Our work establishes the limits of exact multiphoton confinement while opening a route to engineering long-lived interacting few-photon states.

We establish spectral filtering as a control parameter for the conditional momentum and position correlations of SPDC biphotons used in quantum imaging. The conditional momentum uncertainty in spontaneous parametric down-conversion (SPDC) is strongly crystal-length and spectral-filter dependent along the walk-off axis; therefore, the effect is observed only in critically phase-matched (CPM) crystals such as $β$-barium borate (BBO) crystals, while quasi-phase-matched (QPM) crystals and the non-walk-off axis of BBO remain scaled strictly according to the standard pump waist size ($w_0$) dependent scaling law $1/w_0$-independent of the filter. In position space, the spectral-filter effect is universal and produces a flat-dip-rise (FDR) profile in every crystal class examined. Although this FDR profile was previously demonstrated in BBO only in the nondegenerate regime, our results establish its generality: the FDR dip is also present at exact degeneracy in QPM crystals, an unexpected feature that was previously thought to deliver a resolution advantage in the nondegenerate regime alone. Our treatment applies to all SPDC-based quantum-imaging regimes (including CPM and QPM crystals, walk-off and non-walk-off axes, degenerate and nondegenerate emission, and signal and idler filtering) and offers enhanced quantum-imaging resolution via the design rules presented-most prominently along the walk-off axis of CPM crystals (in far field) and across all transverse axes in the near field.

Higher-form symmetries generalize conventional global symmetries and act on lower-dimensional submanifolds of a quantum system. While Abelian topological phases can be organized by 1-form symmetries that form a group, non-Abelian topological phases based on finite groups require 1-form symmetry operators governed by non-invertible fusion algebras. In this work, we make this statement precise in quantum double lattice models $\mathcal D(G)$ for finite non-Abelian groups $G$. We construct the electric, magnetic, and dyonic 1-form operators directly at the lattice fixed point and show that together they form a complete nonlocal diagnostic algebra for the topological Hilbert space. Using these operators, we explicitly determine the cylinder and torus ground-state subspaces for arbitrary finite $G$. Furthermore, we calculate the microscopic fusion and gluing of the 1-form symmetries and show that their topological deformation properties emerge after projection to the defect-free topological subspace. Our results establish ground states of non-Abelian quantum double models as a concrete microscopic realization of spontaneous non-invertible 1-form symmetry breaking and provide an operator language that may be useful for characterizing such states in quantum processors.

We present MoMPy, an open-source Python package that provides a unified, declarative construction of moment matrices for semidefinite programming (SDP) hierarchies. The user declares operator labels together with a small set of structural relations, and MoMPy returns a matrix of SDP variable indices in which every implied identification has already been made, ready for CVXPY or any other modelling layer. Internally, the identification problem is recast as a word-rewriting problem on tuples of integers and solved with a memoised breadth-first closure coupled to a disjoint-set forest, so that each distinct monomial is processed exactly once per build, however many matrix entries it eventually labels. The central abstraction is independent of the physical scenario: the same construction handles tracial, state (NPA), and block-valued moments, with no notion of parties, settings or preparations. We demonstrate this generality on a tripartite Mermin inequality, the bipartite CHSH inequality, measurement compatibility in a steering scenario, state discrimination and dimension witnessing in prepare-and-measure scenarios, device-independent randomness certification, and certification of deterministic correlations from known ensembles. The construction is validated against an independent brute-force implementation and benchmarked across eight structurally distinct scenarios, spanning bipartite and tripartite Bell tests, heterogeneous-outcome, steering-type, jointly-measurable and network configurations.

Detector-based first-arrival models and operator-based arrival-time observables provide two conceptually distinct approaches to the quantum time-of-arrival problem. Here we connect these approaches by using the positive unidirectional first-arrival current of Marchewka and Schuss (MS) as the basis for constructing a family of positive arrival-time operators and, after normalization, an arrival-time POVM. The first-arrival character is inherited from the dynamics with a Dirichlet boundary, while the detector response is introduced at the amplitude level through a non-negative spectral function $λ(k)$. For a one-dimensional free particle, resolution of the identity uniquely selects $λ(k)=\fracπ{4k}$, yielding an arrival-time POVM. The normalized unidirectional current can therefore be interpreted as a generalized Born-rule probability density rather than as a hazard rate, as in the original MS formulation. We further show that the normalized one-sided MS amplitude coincides, up to an irrelevant phase, with the corresponding momentum-sector amplitude in Kijowski's arrival-time distribution. Consequently, the two directional contributions in Kijowski's distribution can be reproduced by two first-arrival problems defined on opposite sides of the boundary. This establishes an equivalence between the resulting arrival-time statistics while emphasizing the different physical interpretations: MS describes a first-arrival process with coherent momentum components, whereas Kijowski's POVM treats the two momentum sectors as separate directional contributions. Thus, the normalized unidirectional current provides a POVM description of first arrival at a point, combining detector-based dynamics with a positive-operator measurement structure.

Quantum position-verification is a cryptographic task wherein a verifier attempts to establish the location in space of a prover. Recent experiments have implemented a well-studied class of position-verification schemes, known as the $f$-BB84 scenario, but their security under realistic loss and imperfect state preparation remains incompletely understood. We give a new lower bound on any attack on this scheme, in particular proving nearly-linear quantum gate lower bounds on the attacker, even when allowing the attacker to declare a transmission loss of up to $50\%$, allowing for the challenges prepared by the referee to be imperfect, and allowing the quantum messages used in the protocol to be arbitrarily slow. Our results are applicable to recent and upcoming experimental implementations of $f$-BB84, and in particular establish their security under a bounded quantum gate assumption on the attacker. The key ingredient is a tight analytic tradeoff for a lossy BB84 monogamy-of-entanglement game, valid without requiring the attackers' outputs to agree, which replaces observations previously made numerically.

We determine the exact strong converse exponent of quantum soft covering under the sandwiched R{é}nyi divergence for all orders $α\in[\frac{1}{2},\infty)$. For $α\in[\frac{1}{2},1)$, the exponent is characterized by the two-parameter club-sandwiched mutual information, whereas for $α\in[1,\infty)$, it is characterized by the order-$α$ sandwiched R{é}nyi mutual information. We also determine the exact strong converse exponent of privacy amplification against quantum side information under the sandwiched R{é}nyi divergence for $α\in(2,\infty)$, expressed in terms of the corresponding order-$α$ sandwiched R{é}nyi conditional entropy. To the best of our knowledge, these results provide the first exact characterization of the strong converse exponent of quantum soft covering and the first precise operational interpretation of the two-parameter club-sandwiched mutual information in the quantum setting. The key ingredient is that we establish the exponential rate of the $K$-functional, which is instrumental in deriving the strong converse exponent of quantum soft covering for $α\in[\frac{1}{2},1)$.

We show that the maximum winning probability in the repeated CHSH game for classical strategies is at most $\left(\frac{1+\sqrt{5}}{4}\right)^n$. Together with a matching lower bound by Barak et al. (FOCS'2008), this determines the asymptotic value of the repeated CHSH game exactly. We also show that, if an XOR game has a gap between classical and quantum values, there is also a gap between the asymptotic values for the repeated game.

Sample-based quantum diagonalization (SQD) and quantum-selected configuration interaction (QSCI) are the electronic-structure methods with most hardware traction, yet their canonical target -- the ground-state energy -- is where classical methods have caught up. We move the target to dynamics and the resource question. From one bitstring-sampling primitive -- computational-basis measurements of a shallow real-time circuit, with no Hadamard or controlled unitaries -- we reconstruct, from sampled subspaces, the single-particle spectral functions $A(ω)$ and $A(k,ω)$ and the neutral-sector dynamical structure factors $S(q,ω)$ and $S^{zz}(q,ω)$, each built classically in the Lehmann representation from its own subspace. The reconstruction matches exact diagonalization on Hubbard chains and, for $A(ω)$, across nineteen molecules (FCI-verified to $<10^{-5}$ Ha), and runs on the IBM Heron processor. Second, we ask which resource controls the cost -- the determinant support $|\mathcal{S}|$ the sampler must populate. On number-conserving states the fermionic AntiFlatness collapses to one 1-RDM invariant, $\mathcal{F}_1 = 4\,\mathrm{tr}[γ(1-γ)] = 2N_u$. An orbital-rotation (Gaussian) invariant while $|\mathcal{S}|$ is basis dependent, $\mathcal{F}_1$ is provably decoupled from the cost; the cost is instead lower-bounded and tracked by the entanglement -- the minimal bond dimension $χ$ (Spearman $ρ= 0.90$). One-body magic is thus a faithful multireference diagnostic but an unreliable cost predictor; any genuine advantage lives in the non-Gaussianity of the higher-body cumulants. We prove moment exactness and a sampling bound polynomial in $|\mathcal{S}|$, independent of Hilbert-space dimension. Self-consistent configuration recovery improves the subspace under device noise, while a learned generative model does not beat that classical baseline.

The exact diagonalization of the nuclear shell model scales exponentially, leading to severe memory bottlenecks in classical high-performance computing (HPC). While hybrid quantum algorithms like the Variational Quantum Eigensolver (VQE) aim to overcome these limits, their deep quantum circuits and iterative feedback loops are susceptible to substantial noise inherent in the current Noisy Intermediate-Scale Quantum (NISQ) hardware. This noise renders several algorithms, such as the VQE, impractical for large-scale calculations despite sophisticated noise-mitigation techniques. As a pragmatic approach tolerant to these issues, we apply the Sample-based Quantum Diagonalization (SQD) framework to nuclear shell models for the first time. Using $^{38}\text{Ar}$ as a benchmark to confirm the numerical accuracy, we extend SQD to $^{32}\text{Mg}$, solving a nuclear shell-model Hamiltonian whose underlying Hilbert space cannot be directly diagonalized using conventional classical methods in a given HPC system. We present a systematic comparison of SQD with standard variational quantum schemes and exact classical solvers. By leveraging NISQ hardware connected via the cloud to classical HPC clusters, the SQD-based scheme could outperform conventional supercomputers in memory scaling and total execution time, enabling more rigorous large-scale shell model calculations.

The Virtual Quantum Subspace Expansion (VQSE) extends the Variational Quantum Eigensolver (VQE) by leveraging additional measurements on the reference state to capture the influence of excluded virtual orbitals. This makes VQSE attractive for chemical applications where accurate energy differences along potential energy surfaces are crucial for modeling reaction rates and kinetics. In this work, we analyze VQSE performance on H$_2$ dissociation including references that use Hartree--Fock molecular orbitals with broken spin symmetry. We identify two mechanisms which affect accuracy: overlap of the reference state with the exact full configuration interaction (FCI) wavefunction and operator pool expressivity. We show these mechanisms are strongly co-dependent. When operators are restricted to act only from the active to the virtual space, results become highly sensitive to the reference, and enlarging the active space does not guarantee improved accuracy. In this case, prioritizing reference overlap over energy minimization is therefore essential. Adding single excitations and number operators within the active space recovers the accuracy of MR-CISD (multi-reference configuration interaction singles and doubles) regardless of the reference. In our noisy hardware experiments, we achieve chemical accuracy by adding additional operators and using strict regularization. These findings motivate careful co-design of reference fidelity, pool expressivity, and hardware constraints for practical VQSE deployment.

The fluctuation theorem (FT) relates microscopic trajectory distributions to macroscopic averages. Using quasiprobability trajectories, this framework has recently been extended to quantum information dynamics. Despite sharing the form of conventional thermodynamic FTs, information FTs involve quasiprobabilities whose negativity and statistical properties remain poorly understood. We analytically determine the properties of negative distributions based on the two-qubit Bell-diagonal states evolving under local dephasing, depolarizing, and amplitude-damping channels. We show that the occurrence of negative quasiprobabilities is not determined by the entanglement or Bell nonlocality of the initial state. Instead, a diagonal-interference decomposition of the transition quasiprobability provides a sufficient condition for negativity. More importantly, we prove that quasiprobability distributions containing negative weights can violate Horváth's necessary and sufficient criterion for the Jensen-Steffensen inequality to hold for every continuous convex function, even though the specific exponential Jensen-like relation enforced by the FT and the quantum data-processing inequality remains valid. This trajectory-level contrast with classical stochastic descriptions reveals a distinctive feature of quantum information dynamics that is invisible when only the corresponding average-level information inequalities are considered.

Point-particle descriptions of electron-electron interaction omit the coherent longitudinal extent of a free-electron quantum wave packet (QEW). A relativistic two-electron wave-packet theory identifies the longitudinal QEW size as a direct control parameter for entanglement generated by mutual electromagnetic coupling. For two electrons in spatially separated paths, the quadratic interaction phase gives a dimensionless entangling parameter $\Gee$ and the logarithmic negativity $\EN=\operatorname{arsinh}(\Gee)/\ln2$. Full time-dependent Schrödinger equation calculations confirm the scaling for narrow QEWs and reveal higher-order Coulomb effects at larger spatial extent. Free drift increases the interaction-point QEW width while preserving the momentum probability distribution, thereby enhancing the subsequently generated entanglement. The results establish a direct connection between free-electron wave-particle duality and bipartite entanglement.

We investigate how nonequilibrium quantum initial states can reduce the finite-time thermodynamic cost of Landauer erasure. Considering a general finite-dimensional quantum memory coupled to a thermal reservoir via a Davies generator, we show that the dissipated heat at a fixed operational erasure fidelity is largely controlled by the overlap of the initial state with the slowest Liouvillian relaxation mode. We derive a modified finite-time Landauer bound in which the excess dissipation above the quasistatic limit scales quadratically with this slow mode projection, and we prove a sufficient Mpemba Landauer condition under which a hotter state can erase faster and dissipate less heat than a colder preparation, without violating Landauer's principle. A minimal qutrit model illustrates these quantum Mpemba speedups and reveals broad parameter regimes where coherence and Hamiltonian-induced modes conspire to suppress finite-time entropy production. We further identify practical control knobs, including temperature tuning, coherence engineering, and Hamiltonian shaping of Liouvillian spectra, which enable Mpemba-enhanced erasure to be directly tested on platforms such as superconducting circuits, trapped ions, semiconductor quantum dots, and solid-state spins.

Magnetically trapped type-I superconductors are promising candidates for precision experiments at the quantum-to-classical borderline, with applications in quantum sensing of forces and accelerations and fundamental tests of quantum physics. Here, we show how the rotational motion of micron-sized superconductors is strongly affected by (i) the diamagnetic torques due to the gradient of the trapping field and by (ii) the gyromagnetic coupling due to Einstein-de Haas and Barnett effects. We show that this allows the three-dimensional alignment of asperhical superconductors in the trap center, as required for future sensing applications and quantum experiments, and determine the resulting librational trapping frequencies. Finally, we propose an experiment to probe gyromagnetic coupling in levitated superconductors and we discuss how it can be used to control the particle rotation.

Fractionalizing a quantum two-level system is usually associated with encodings based on pairs of Majorana fermions---an operational fractionalization. We show an alternative algebraic fractionalization by embedding Székely's classical ``half-coin'' into a non-Hermitian Krein space. The coefficients of $(q+pz)^{1/2}$ define a signed sequence and a normalized, non-Hermitian biorthogonal operator describing a biorthogonal half-qubit. We prove that two such objects fuse into an arbitrary pure qubit through the signed Vandermonde convolution that the collective $N\ge2$ vectors are null in Krein space. $L_1$ norm of the half-qubit follows in closed form, $\lVert p\rVert_1 = 2\sqrt{q}-\sqrt{q-p}$. Its $L_1$ norm increases monotonically with the bias and attains its supremum $\sqrt{2}$ precisely at the unbiased point $p=q=1/2$. Interestingly, we identify two structural results as follows. First, number parity and the $η$-metric generate a distinguished commuting $\mathbb Z_2\times\mathbb Z_2$ subgroup. Second, we find the $η$-metric obstructs any local $η$-self-adjoint partner of the parity, so a half-qubit carries a $\mathbb{Z}_2$ observable but no local $SU(2)$. The full Pauli algebra emerges only upon fusion. We then show that the construction survives truncation of the Fock basis: the fused qubit is exact at every cutoff, and the Vandermonde cancellation is visible in sign-weighted photon-number statistics, and can be tested using existing cavity and trapped-ion state-synthesis methods. Finally, we generalize this algebraic fractionalization to a $1/n$-qubit, which can be achieved by replacing the square root with an $n$th root.

We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. Considering the initially excited qubit and field states described by multiphoton Fock-like states, we demonstrate that the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a multimode coherent state in a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.

Semiconductor quantum-device design still lacks an integrated Technology Computer-Aided Design (TCAD)-like environment that connects material geometry, quantum many-body simulation, and automated design. Here we introduce zenDot, a large-language model (LLM)-integrated quantum TCAD platform that links a material-labelled device state to a unified condensed-matter physics toolbox. The device and calculation components are integrated into a desktop workbench, Python API, and an embedded LLM agent, allowing electrostatics, charge and transport characterization, correlated-state calculations, and qubit modelling to be executed within one reproducible environment. We demonstrate zenDot on a Si/SiO2 double quantum dot, where a single device state reproduces the characterization workflow and supports hybrid, tunnel-charge, and singlet-triplet qubit analyses. A platform-level universal-control scan revises the singlet-triplet operating point and reduces the predicted worst-gate infidelity by nearly 30-fold. Beyond analysis, the LLM agent directly operates the same physics environment as human users, proposing design changes, executing registered simulations, and iterating on solver-returned metrics under physics-aware validation. Across three demonstration tasks it completes 18 validated design iterations, including geometry modification followed by a full re-solve from the material stack. zenDot establishes a machine-operable quantum TCAD workflow that connects device physics with LLM-driven design exploration.

Entanglement among particles is a defining feature of strongly correlated quantum materials, distinguishing them from conventional metals and semiconductors. The ability to certify intrinsic entanglement among interacting electrons in solid-state materials is important not only for classifying quantum states of matter, but also for developing material-based quantum technologies. Here, we introduce a transport-based protocol for witnessing multipartite entangled electronic states, based on the equilibrium noise spectrum as an experimentally accessible observable. The appropriately integrated, symmetrized, and projected current noise obeys an upper bound that can be derived from microscopic model parameters and is invariant with respect to the choice of electronic basis. We benchmark this framework in several paradigmatic systems, including twisted bilayer graphene, twisted bilayer MoTe$_2$, and Hubbard models, certifying entanglement in the fractional Chern insulating state. The method extends recently developed scattering-based entanglement witnesses to ultralow-temperature materials, where conventional spectroscopic probes are inaccessible but candidate entangled states are expected to arise.

In quantum optics, quantization of the electromagnetic field typically occurs in a finite volume - a cavity - which results in discrete frequency modes where photons are created, annihilated and exchanged between such modes. As a result, evolution of quantum optical states is periodic in the carrier wave of the field, measurement protocols return cycle-averaged information, and any sub-cycle evolution that is foundational to many light-matter interactions, especially at high field strengths, remains hidden. Adapting an attosecond technique, here we capture the electric-field evolution of a quantum optical state, femtosecond bright squeezed vacuum, with sub-cycle precision. We find that it consists of many stochastic, time-localized bursts within each pump pulse whose phase randomly switches between two values. We exploit the random phase flips to generate quantum random bit sequences with a generation rate that can reach petahertz frequencies. In addition, the sub-cycle resolution allows us to measure coherence functions of the waveforms between any two times, which we explain with a superposition of time-limited modes. These results bridge attosecond metrology and quantum optics and pave the way to measuring quantum light-matter interactions as they evolve on a few-femtosecond time scale, and integrate quantum randomness in petahertz electronics.

Electronic position controls how a crystal polarizes and responds to an external field. In crystals, it is usually described through local changes of electronic states in momentum space. This Berry framework has reshaped modern solid-state physics, but strong fields drive electrons across a finite momentum range, where coherence between different momenta becomes part of the response. Here we establish a first-principles theory of electronic position at finite momentum that retains this missing information. We show that unequal-momentum coherence can cancel under spatial averaging and still produce polarization, forming a coherence dipole. We obtain the matrix directly from material wave functions, without model bands or fitted transition elements. In Si, the finite-momentum geometry sets a material momentum scale. Comparing this scale with the momentum change driven by the field predicts when finite-momentum physics becomes active. Crossing the scale strongly reorganizes the fifth and higher harmonics, showing that momentum-space geometry, rather than emitted photon energy alone, controls the nonlinear response. HHG is the first demonstration, but the theory applies whenever driven electrons explore a finite momentum range. It therefore extends quantum geometry beyond the local Berry limit and provides a general basis for predicting field-driven phenomena in real materials.

The silicon T-center is a telecom-band spin-photon interface in a manufacturable photonics platform. In nanophotonic devices, however, its optical linewidth is broadened by a fluctuating charge environment, limiting photon indistinguishability for quantum networking. Here, we address this challenge through characterization and suppression of the local charge-noise of single T-centers in lateral p-i-n waveguides, demonstrating an unheralded method of T-center optical linewidth narrowing. Above-band illumination resets the charge environment, neutralizing the local field and suppressing spectral diffusion. Across 46 emitters this reset narrows the median linewidth 3.5-fold to 0.57(11) GHz, and an optimized emitter reaches 128(22) MHz, the narrowest unheralded linewidth reported for an integrated T-center. The narrowed transition supports coherent optical Rabi oscillations with a coherence time of 20(2) ns. Finally, we perform Stark-shift tuning using the p-i-n junction, and read out the local electric field and the charge-noise width at 15 mK. An analytical model of proximal surfaces, bulk, and junction field effects provides good agreement with our findings. Our multi-pronged characterization of the nanophotonic-integrated T-center charge environment enables future device optimization toward scalable quantum interconnects.

Demonstrating quantum advantage in a manner that can be independently verified by classical means remains one of the most pressing open problems in quantum computing. Here we propose a new heuristic approach for constructing quantum circuits that are hard to classically simulate yet whose output distributions can be efficiently verified classically. Our approach is based on Clifford circuit obfuscation. This obfuscation scheme hides the Clifford structure and injects a controlled and rapidly growing non-stabilizer resources that resist known classical attack strategies including reverse engineering and direct simulation. Our protocol is heuristic but is supported by both numerical and theoretical evidence. This work provides a new avenue toward classically verifiable quantum advantage that avoids the stringent implementation requirements of known approaches.

Quantum Annealers (QAs) are among the first commercially scaled quantum computing systems designed for large-scale optimization. Unlike digital systems that execute sequences of compiled instructions, QAs operate as analog single-instruction machines that directly evolve an Ising Hamiltonian toward low-energy solutions. To execute an application, the logical problem graph must first be mapped onto the hardware's sparse connectivity via embedding, where logical variables are represented by chains of connected physical qubits. As a result, embedding becomes the dominant system challenge in QAs, shaping whether and how workloads can execute on the machine. Despite its central role, embedding has largely been treated as a preprocessing step rather than a system bottleneck. In this work, we present ChainForge, the first systems and architecture characterization of embedding in QA workloads. Using diverse workload families and graph topologies on modern QA hardware, we characterize how embedding impacts effective hardware capacity, routing overheads, runtime variability, and solution quality. Our results show that embedding inflates physical resource usage, long chains degrade annealing fidelity and scalability, and heuristic embedders may fail even when valid embeddings exist. We further show that embedding latency can become a runtime bottleneck for dynamic workloads requiring frequent remapping, while nominal qubit counts significantly overestimate the usable capacity of QAs for realistic applications. Overall, our findings establish embedding as the defining workload bottleneck and systems abstraction of QAs, providing architectural insights for future hardware topologies, runtime systems, and workload-aware annealing platforms.