Quantum Physics Paper Analysis

Understanding and mitigating noise in two level quantum systems is essential for achieving high fidelity qubit control. Conventional frequency tracking techniques, such as Ramsey interferometry, are fundamentally limited by trade offs between sensitivity, bandwidth, and dynamic range. Here we introduce the adiabatic tangentially-modulated (ATM) pulse, a pulse derived from quantum adiabatic theory that maps qubit detuning onto a sigmoidal, near-binary response. Using numerical simulations supported by analytical modelling, we show that pulse sensitivity and detuning range can be independently engineered through simple design parameters. We derive scaling relations governing these quantities and demonstrate their agreement with simulation. A single shot ATM measurement achieves sensitivity comparable to that obtained from multi-shot Ramsey averaging, enabling tracking of substantially higher frequency noise components with a lower closed-loop white-noise floor. In addition, this pulse exhibits strong robustness to amplitude fluctuations compared with binary response pulses derived from the Shinnar-Le Roux formalism. Together, these properties establish the ATM pulse as a promising approach for robust qubit frequency tracking.

Squeezed light states have a special place in quantum optics with potentially profound applications in emerging quantum technologies. We present a numerically-exact matrix product states (MPS) approach to model quantum pulses of squeezed light, at the few-photon level, interacting with a two-level system in a waveguide environment. We represent the squeezed state as a coherent superposition of Fock states and explore the nonlinear population dynamics as well as multi-photon correlation functions that emerge. We show how the squeezed pulse can create quantum correlations that are unique to squeezed pulses, including $\langle b(t) b(t+t')\rangle$ for transmitted fields as well as $\langle b^\dagger(t) b^\dagger(t+t') b(t+t') b(t) \rangle$. We also demonstrate how $\langle b(t) b(t+t') \rangle$, a first-order correlation function, shows nonlinear photon correlations that are similar to those known and measured for two-photon scattering states. Finally, we also study the squeezed spectra of the pulse before and after interacting with the two-level system, and highlight the role of the spectral bandwidth of the incident pulse. The MPS theory allows the modeling of arbitrary bandwidth squeezing without making any Markov and Born approximations for the light-matter interaction processes, and can easily be extended to waveguide systems with multiple emitters and time-delayed feedback.

The quantum lattice Boltzmann (QLB) scheme of Succi and Dellar advances a four-component Dirac spinor on a lattice by a fixed sequence of local, exactly norm-preserving operations: a basis rotation, a collision, a streaming shift, and the inverse rotation. This unitarity is a structural property of the scheme, not an approximation, which suggests that a QLB time step should map onto a sequence of quantum gates. Here we make that mapping explicit. We give a gate-level construction of every operation of the three-dimensional Dirac QLB scheme: the fixed rotation gates, the collision gate, the streaming shift as a controlled increment on a position register, the position-dependent potential as a phase oracle, and periodic and reflecting (bounce-back) boundary conditions as unitary circuits. We then compose them into single-axis, two- and three-dimensional time steps. On a state-vector emulator the resulting circuits reproduce the classical QLB solver to machine precision (maximum density deviation between $3.7\times10^{-12}$ and $1.0\times10^{-17}$ across the one-, two-, and three-dimensional tests), so the circuits are the scheme rather than an approximation of it. The scope is narrow: we establish that the Succi-Dellar theory can be implemented on a (gate-model) quantum computer, and report the associated gate counts. We make no claim of computational advantage; state preparation, measurement, and asymptotic cost are discussed as open questions. All operators, circuits, tests, and figures are reproducible from the open-source quantumKineticMethods library.

The interplay between topology and correlation can give rise to exotic collective excitations. The integer and fractional quantum anomalous Hall (QAH) magnets recently discovered in two-dimensional (2D) flatband systems are predicted to host spin excitations distinct from those in conventional magnets. Experimentally, nevertheless, these new excitations remain largely unexplored. Here we investigate spin-valley excitations in a twisted MoTe2 moiré superlattice using resonant ultrafast pump-probe spectroscopy. We observe a metastable spin-valley excitation in the QAH magnet below T ~ 3.7 K that survives reverse magnetic field several times larger than the saturation field. The behavior of this excitation is sharply distinct from ordinary domain walls and magnons, indicating a new type of spin-valley textures unique to topological magnets. We propose that these textures are chiral domain walls with an in-plane winding of the pseudospin order parameter along the domain wall. Their metastability arises from the interplay between the topological winding in real space and the quantum geometry of the parent bands in momentum space through a universal mechanism. These chiral domain walls govern the nonequilibrium dynamics of QAH magnets and may play a central role in their stability. Our study highlights intrinsic quantum geometry effects on spin excitations in topological magnets; and provides key insights into the fundamental mechanism limiting stability of topological protection.

Non-Markovianity can be characterized by performing a series of successive measurements and analyzing departures of the corresponding outcome statistics from a Markovian probabilistic structure. Considering a system coupled with its environment via a dephasing interaction, we show that joint outcome probabilities can be written in terms of a set of two-time environment correlations. Their definition involves forward and backward propagators with different Hamiltonians, associated with a recently introduced generalization of standard Loschmidt echoes [Cormick and Budini, Phys. Lett. A 593, 132011 (2026)]. This result establishes a solid connection between quantum non-Markovianity defined in an operational (measurement-based) way and complex quantum dynamics studied through their sensitivity to dynamical perturbations. We find conditions that guarantee a Markovian (system) behavior and also determine how the generalized echoes can identify information exchanges between the system and its environment. We illustrate our ideas considering examples of spin environments that realize these different dynamical regimes.

Loschmidt echoes are a well-established method to characterize dynamical properties such as quantum chaos and sensitivity to perturbations. Here we present a straightforward generalization that identifies non-classical dynamical behavior. The generalized echoes involve four forward-backward time propagators. If these propagators do not commute, one can readily identify signatures of this property in the relations between echoes. As an example, detection of intrinsic non-commuting quantum features is analyzed in critical dynamics of a spin chain. Interestingly, this phenomenon is also observed for Gaussian dynamics and high temperature limits which are generally regarded as classical.

Spin waves are promising signal carriers for microwave control at the micrometer scale. However, realizing low-damping, tunable control of spin-wave propagation remains a central challenge. Here we use magnetic shielding by superconducting control elements to tune the local spin-wave dispersion and realize temperature-controlled refraction of spin waves in a thin-film magnetic insulator. Using magnetic imaging based on spins in diamond, we characterize the refractive index and demonstrate both positive and negative refraction as well as wavefront shaping by the superconductors. The observed refraction is explained by a geometrical analysis of the superconductivity-induced modification of the hyperbolic spin-wave dispersion. Our results demonstrate that superconductors enable tunable spin-wave optical elements, opening new opportunities for microwave control in classical or quantum information devices.

We investigate Bell correlations for a free real quantum scalar field on the noncommutative Moyal plane. Although the free field dynamics and the one-particle sector remain unchanged, the deformation enters through twisted multiparticle statistics and its Fock-space dressing representation. A classical external source coupled locally to the twist-dressed quantum field prepares coherent superpositions of momentum-pair configurations propagating toward two spacelike-separated laboratories. The momentum-dependent twist phases are generally nonfactorizable and generate entanglement between the corresponding wave-packet modes. We show that suitable local mode measurements lead to a violation of the CHSH Bell inequality. The resulting correlations provide an operational probe of the noncommutative structure encoded in the multiparticle sector of the quantum field.

\textit{Shadow tomography} is a fundamental problem in quantum information theory. Given multiple copies of an unknown $d$-dimensional quantum state $ρ$ and a known collection of observables ${E_1,\ldots,E_m}$, the goal is to estimate all expectation values $\{\Tr(ρE_i)\}_{i=1}^m$ to additive accuracy $\varepsilon$ with probability at least $1-δ$. An elusive open question from the seminal shadow tomography work of Aaronson (STOC'18) is whether this task admits a dimension-independent sample complexity with only polylogarithmic dependence on $m$, as suggested by the best-known lower bounds. In this work, we give a quantum protocol for shadow tomography with sample complexity \[ O\left( \frac{1}{\varepsilon^2} \frac{(\log (m/δ))^4} {(\log\log (m/δ))^3} \right), \] which is polylogarithmic in the number of observables and independent of the dimension of the unknown state thereby answering Aaronson's original question while also providing an exponential improvement in the prior best dimension independent sample complexity of shadow tomography from Sinha (STOC'25). Our approach first reduces the general shadow-tomography problem to a finite-ensemble estimation problem via a minimax argument. We then develop an observable-independent protocol that repeatedly applies the pretty-good measurement and updates the priori distribution over the finite ensemble according to the measurement outcomes. A refined tail analysis of the resulting estimation error yields simultaneous accuracy guarantees for all observables.

The geometry of quantum states has emerged as a key ingredient in understanding the linear and nonlinear responses of quantum materials. To date, however, the connection between geometry and nonlinear response is best understood for clean, noninteracting systems at zero temperature. In this work, we develop a theory of multi-state geometry for density matrices and use it to derive sum rules for second-order rectification, making no assumptions about the strength of disorder or interactions. We first show that perturbation theory for thermal density matrices gives rise to two dual information-theoretic connections and an almost complex structure. We introduce a complex, quantum generalization of the Amari-Chentsov tensor of classical information theory, the cQAC tensor, which captures the multi-state geometry of the perturbed density matrix. We derive a zero-temperature sum rule for the frequency-integrated DC rectification response of an insulator as a difference between a ground state third cumulant and the complex distortion tensor, a multi-state geometric quantity built from the cQAC tensor. This generalizes known single-particle sum rules for the shift and nonlinear Hall currents to many-body systems and general perturbations. Specializing to the shift current, we resolve the geometric contribution for multiband insulators into particle-like and hole-like terms. We verify the sum rule numerically in a generalized Kane-Mele model, finding that the geometric contribution can dominate the integrated response. Finally, we show that although the splitting of the sum rule into cumulant and geometric contributions does not survive at nonzero temperature, the measured sum rule for insulators differs from its zero-temperature form by corrections exponentially small in the gap, allowing low-temperature rectification measurements to probe the multi-state geometry of insulators.

Rare fluctuations in physical systems depend on the detailed microphysics responsible for the fluctuations. In classical statistical systems, the large deviation principle has elucidated the role of semi-classics in describing this regime, and has simultaneously provided a the mathematical foundation of statistical mechanics. Large deviation theory for quantum system is considerably less developed. As all physical systems are fundamentally quantum mechanical, this leaves a major gap in our understanding of rare fluctuations relevant to statistical physics, cosmology, and more. In this paper, we develop the practical aspects of the theory of large deviations relevant for calculating rare events in physical systems from quantum walks to cosmology. We first analyze the case of the anharmonic oscillator coupled to a bath, showing explicitly how the system evolves from dominantly statistical (e.g. thermal) to quantum fluctuations. We then generalize these results, showing that the dominant rare fluctuations minimize the measurement-induced relative entropy. This perspective provides a thermodynamic description of a wide range of open quantum systems. We apply these results to random walks that arise in cosmology through stochastic inflation. We show that the evolution of the density matrix of long wavelength fields on a fixed de Sitter background breaks the KMS symmetry, giving rise to a stationary density matrix that does not respect detailed balance.

As quantum computing continues to demonstrate promise and attract growing attention, there is an increasing need for more precise experiments to advance the development of quantum devices, as well as higher circuit throughput to validate more domain applications. However, this need is hindered by a memory bottleneck at the quantum control system layer, arising from limited on-chip BRAM capacity and the non-deterministic latency of DRAM. To break this bottleneck, we present Ant-Q, a memory hierarchy design that integrates DRAM with BRAM to support pipelined quantum circuit execution while ensuring deterministic inter-circuit timing. We evaluated Ant-Q using 26 real-world experimental and computing circuits. The results show that Ant-Q supports deep circuits for 1Q and 2Q Randomized Benchmarking and reduces the overhead of circuit loading and readout uplink relative to execution time from 22.90%-1417.05% to near zero. Ant-Q is being integrated into QubiC 3.0, with part of its functionalities already available.

Quantum data hiding asks how much distinguishing power can be lost when global measurements are restricted to local measurements and classical communication. In this work, we establish sharp results and improved bounds for several natural classes of restricted measurements. For bipartite systems on $\mathbb C^n\otimes\mathbb C^m$, we prove that the optimal data-hiding ratios against separable and LOCC measurements are both $\min\{n,m\}$. This result follows from a stronger result that, for every $2\le p\le\infty$, the largest centered Schatten $p$-ball whose associated binary measurements are implementable by finite-round LOCC has radius $\min\{n,m\}^{2/p-1}$. This strengthens the classic separable-ball theorems, while also providing an explicit finite-round LOCC implementation. For Alice-first one-way LOCC with Alice's local dimension equal to $n$, we prove that the optimal ratio is $(1+o(1))n$, with the upper bound obtained from a Gaussian rank-one POVM. For local operations without communication, we improve the universal upper bound to $(π\sqrt3/4+o(1))\min\{n,m\}$.

We apply time-reversal symmetry to quantum codes and show that it imposes parity selection rules on the physical error algebra. A time-reversal-invariant logical qubit on an odd number of spins is a Kramers doublet, forcing every even-weight Pauli to act as a scalar. Consequently, all even-weight Knill--Laflamme conditions hold automatically, so single-qubit error detection implies correction. We then reinterpret the Rains shadow enumerator through time reversal: each coefficient is a sum of error-resolved overlaps between a code and its time-reversed image.

The precision of transport observables can be bounded by the entropy production and the activity of the transport process via kinetic and thermokinetic uncertainty relations. In linear bosonic systems, such uncertainty relations can provide tight bounds when the activity is replaced by a local activity of the measurement contact of interest---even in the strong-coupling regime. How much nonlinearities (or interactions) impact the validity and predictiveness of these local bounds and how much this impact depends on the concrete definition of activity are open questions that we address for two experimentally relevant model systems, a harmonic oscillator network and the intrinsically nonlinear spin-boson model. We thereby provide experimentally testable predictions on how nonlinearities impact or even break local kinetic and thermokinetic precision bounds.

We develop a fully quantized theory of nonlinear Compton scattering driven by a single-mode quantum field. Exact quantum-Volkov states retain pump depletion, back-action, and final-state correlations through displaced or squeezed-displaced Fock-state ladders. A finite Fock-state pump produces discrete photon-transfer edges and a terminal spectral cutoff. In the bright, weakly depleted regime, the exact theory reduces to a Wigner-function weighted-average of scattering probabilities evaluated at fixed complex field amplitudes, with ordinary and generalized Bessel functions describing the harmonic structure for circular and linear polarization, respectively. For squeezed coherent light, the squeezing angle controls the high-energy emission through photon-number fluctuations.

Topologically ordered phases naturally realize quantum error correction through nonlocal encoding of quantum information. More recently, conformal field theories have been shown to realize approximate quantum error-correcting codes, but such constructions generally require fine tuning to criticality. Here we introduce a family of approximate quantum error-correcting codes realized by the chiral edges of two-dimensional topologically ordered phases. The proposed encoding combines the robustness of a gapped topological bulk with the flexibility of gapless edge conformal field theories. To characterize its robustness, we study coherent-information loss under local erasure. We derive an exact expression relating coherent-information loss to relative entropy, reducing the recoverability problem to universal properties of the edge theory. This leads to power-law scaling of coherent-information loss with the size of the erased region. We further show that, for geometrically local erasures near one edge, the two-dimensional chiral edge code is at least as robust as the dimensionally reduced CFT code, and is strictly more robust in several representative examples. For Abelian code subspaces, we further construct a power-law-range recovery map supported on the erased region together with a power-law-range buffer; this recovery map depends only on the code subspace, not on the unknown encoded state. We provide numerical calculations for lattice realizations of compact free boson and Ising CFT examples that support the theoretical predictions of the power-law exponents.

Syndrome-measurements timing is usually treated as a fixed clock cycle of a quantum error-correcting code. For quantum memories, however, the intra-measurement interval is itself an optimizable control parameter: measuring too rarely allows idling errors to accumulate, whereas measuring too often introduces measurement-induced faults. We propose a phenomenological logical-noise model for this trade-off and analytically show that the optimal syndrome-measurements interval scales inversely proportionally with the code distance and that this produces an exponential reduction of logical-error rates in the distance relative to constant-interval schedules. Furthermore, for time-dependent idling noise, we develop an adaptive timing strategy based on the measured syndrome activity that outperforms every fixed-interval protocol, with largest gains for short but strong noise bursts. Simulations of rotated surface-code memories with matching decoding validate the phenomenological model, the distance-dependent optimum, and the adaptive-strategy improvement. Moreover, with the experimental noise parameters reported by Google in Nature 638 (2025), our model predicts reductions in logical-error rates per unit time of up to $40\%$.

Non-Gaussian states can exhibit large quantum Fisher information (QFI) in quantum sensing. In optical systems, however, its generation is often probabilistic via the boson-sampling type conditional operation and thus its generation rate is limited. This probabilistic generation of non-Gaussian resource should be taken into account for evaluation of the sensing performance. Then a natural question arising is whether the use of heralded probabilistic non-Gaussian states is better than that of the original deterministic Gaussian states for quantum sensing. In this paper, we answer to this question for single-parameter phase-estimation. By using photon-number conservation in passive linear optical systems, we show that heralded state preparation before parameter encoding can be mapped to a postselection problem after parameter encoding for phase estimation. This mapping allows the success probability of heralding to be included naturally in the metrological performance. We introduce an effective quantum Fisher information (EQFI), defined as the success-probability-weighted QFI of the heralded outputs, and prove that it cannot exceed the QFI of the original Gaussian inputs. The result highlights the importance of resource counting in quantum sensing toward better understanding of the resource efficient advantage of optical quantum sensing.

To probe a bipartite quantum system, one may use arbitrary global operators or restrict to product operators acting separately on the two subsystems. We determine the sharp universal comparison between the resulting norms. For every $z\in M_n\otimes M_m$, we prove $\|z\|_1\leq\sqrt{2}\min\{n,m\}\|z\|_\varepsilon$, where $\|\cdot\|_1$ is the trace norm and $\|\cdot\|_\varepsilon$ is the injective tensor norm associated with the trace norms on $M_n$ and $M_m$. To prove the upper bound, we establish an $L_1$ noncommutative Khintchine inequality whose random coefficients are the entries of a Haar unitary. We also show that the coefficient $\sqrt{2}$ is sharp. As applications, we show that the same sharp constant governs the gap between bipartite correlation measured in trace norm and that measured by a correlation function, and obtain an improved universal upper bound for quantum data hiding. The upper bound has also been formalized and machine-checked in Lean.

Mobile impurities provide a powerful means of probing correlated and topological quantum matter, through their dressing by the surrounding medium and the practical probes granting access to the resulting composite object. Motivated by the recent observation of anyon-impurity composites in the solid state, as well as recent realizations of Laughlin-type states in engineered lattice systems, we investigate the formation of a bound state between a mobile impurity and a single pinned quasihole in the interacting Harper-Hofstadter model deep in the fractional Chern insulator regime. Combining analytical arguments with large-scale numerical simulations, we characterize the structure, energetics, and stability of hybrid anyon-impurity bound states, and show that their binding energy provides direct access to the fractional charge of the quasihole under conditions that we identify. We further demonstrate that the composite object can be coherently transported by externally steering the quasihole pinning potential. Our results establish a realistic pathway for controlled anyon-impurity manipulation in quantum-engineered platforms, enabling experimentally feasible protocols for braiding.

Quantum optimization has attracted growing interest as quantum hardware continues to improve, yet state-of-the-art classical solvers remain a formidable benchmark for practical utility. Rather than seeking a fully quantum replacement for classical optimization, we propose a hybrid strategy that uses quantum information to enhance leading classical heuristics. Specifically, we introduce a warm-start method based on local correlators obtained from the Quantum Approximate Optimization Algorithm (QAOA), and use this information to initialize the Burer-Monteiro (BM) rank-two relaxation. We demonstrate numerically that, compared to a random, multi-start initialization baseline (a standard strategy used for BM), this quantum-informed initialization offers a significant head start, i.e., high-quality solutions with very small number of iterations, for two problem classes -- random Erdős Rényi graphs with edge density of $10\%$ (ER-10) and fully-connected Sherrington Kirkpatrick (SK) spin glass models, at $n=500$ and $n=1000$ qubits. At the same time, given enough iterations, the random baseline often eventually catches up and slightly outperforms the warm-start strategy on average, an effect visibly stronger for $n=500$ than for $n=1000$. The results demonstrate an exploitation/exploration tradeoff of using WS to quickly arrive at very good solutions vs exploring slightly better solutions with a larger iterations budget via a standard strategy. Our results highlight how low-depth quantum circuits can provide useful structural information for classical optimization and suggest a promising route toward near-term quantum utility through quantum-assisted initialization.

We derive two quantum fluctuation relations for systems undergoing repeated projective measurements. These fluctuation relations characterize the work that can be extracted from a quantum device when a first-detection event triggers a mechanical operation leading to positive work production. The correction to the standard quantum Jarzynski equality depends logarithmically on the mean first-detection time for the time-reversed dynamics. Application of Jensen's inequality leads to fundamental limits on both the total work involved in the repeated measurements and final mechanical operation, and the extracted work alone. The general case of a device connected to an external environment is also considered.

We construct explicit error-detecting surgery gadgets---small systems of auxiliary qubits and checks---for the high-rate Iceberg codes $[[2N,2N-2,2]]$, to perform fault-detected measurements of logical Pauli products. The construction follows the perspective of surgery as the gauging of a logical operator, regarded as a symmetry of the code. We give a complete classification of logical Pauli operators under the permutation automorphism group of the Iceberg code, reducing the construction to one gadget per orbit, and we verify with circuit-level simulations that the gadgets are fault-detecting, with the expected post-selected logical error rate. The gadgets require reconfigurable long-range connectivity, available on platforms such as neutral-atom arrays, making an error-detected demonstration of Pauli-based computation a natural near-term experiment. The paper doubles as a self-contained introduction to gauging and code surgery, developed alongside a simple worked example.

Compact cesium beam clocks are major frequency references for deployable timing systems. However, further improvement of their short-term frequency stability is limited by the clock signal-to-noise ratio (SNR). Although two-laser optical pumping can increase the effective atomic utilization, the achievable clock SNR has long been limited by laser-induced frequency-to-amplitude noise conversion. Here, we demonstrate a compact dual-Faraday-laser-pumped (DFP) Cs beam clock enabled by a low-frequency-noise atom-referenced laser architecture. The intracavity Faraday anomalous dispersion optical filter provides inherent alignment to the Cs D$_2$ resonances, while modulation transfer spectroscopy offers suppressed frequency noise and drift. The resulting laser system supports robust turnkey operation with a Lorentzian linewidth of 2.12 kHz. The DFP Cs clock achieves a clock SNR of 46,365 in a 1-Hz bandwidth and a fractional Allan deviation of $7.7\times 10^{-13}/\sqrtτ$ , with Hadamard deviation reaching $7.7\times 10^{-15}$ at 10,000 s. This work pushes the fractional frequency stability of a compact Cs beam clock into the $10^{-13}/\sqrtτ$ regime, providing a pathway toward high-performance Cs frequency references for field-deployable precision timing, navigation, and synchronization.

Can one neural wave function describe both a Bose condensate and a chiral topological liquid? We introduce ChernFormer, which combines a fermionic transformer with a fixed Chern-Simons phase that attaches one statistical vortex to every particle pair. Each factor changes sign under exchange, so their product is exactly bosonic. The fixed phase changes statistics but not probability, making every bosonic learning problem equivalent to a fermionic one with the same approximation error and overlap. With enough capacity, ChernFormer can approximate any normalizable bosonic wave function on the plane at fixed particle number. A finite, smooth network still vanishes when particles meet, yet this contact hole can shrink while the wave function and condensate fraction approach those of a nodeless condensate. Following the needle-in-a-haystack target-reconstruction benchmark introduced in \cite{NazaryanGaggioliTengFu2025}, we test ChernFormer on the Kalmeyer--Laughlin ground state and its first two chiral edge states. The overlap curves stay close to unity through their largest sampled sizes, while independent amplitude and phase maps at $N=20$ for all three states recover both local Laughlin vortices and the collective edge vortex. By contrast, a continuous, nonzero product of identical particle-wise factors misses these elementary edge sectors. ChernFormer therefore provides one variational language for conventional bosonic order and chiral topological matter.

Solving the Vehicle Routing Problem (VRP) in Stochastic Transportation Networks (STNs), a core task in Intelligent Transportation Systems (ITS), introduces estimation challenges for stochastic path travel times and the resulting VRP objective function. These challenges have typically been addressed through computationally expensive sampling-based techniques such as Monte Carlo simulation, whose performance depends on sample size, the sampling strategy, and the underlying travel time distributions. To address these issues, this study proposes and validates a quantum computing technique, Quantum Amplitude Estimation (QAE) for path-level travel time estimation in STNs. Without relying on sampling or prior assumptions of the travel time distribution, the proposed framework encodes all feasible travel time realizations into a quantum superposition, enabling a theoretical quadratic speed-up over Monte Carlo simulation. Four QAE variants are implemented in IBM's Qiskit framework, namely Canonical AE (CAE), Iterative AE (IAE), Maximum Likelihood AE (MLAE), and Faster AE (FAE), together with four rotation-angle scaling strategies for handling different discrete travel time distributions. Experiments on a small-scale STN show that the choice of scaling method and rotation-angle range significantly affects estimation accuracy, while the four QAE variants produce comparable estimates across all tested conditions, with IAE exhibiting the most stable overall performance. The results provide practical guidance on parameter selection for future hybrid quantum-classical optimization frameworks in ITS applications.

Cold heavy molecules are promising systems for exploring nuclear $\mathcal{P}$- and $\mathcal{CP}$-violating phenomena in search of new physics beyond the Standard Model. However, most proposed experimental strategies and their early realizations to date have been limited to proof-of-principle molecular species with effectively spin-zero nuclei that are not sensitive to nuclear symmetry-violating phenomena. Here, we introduce a comprehensive experimental toolbox that integrates cooling, trapping, coherent state manipulation, and a complete precision-measurement protocol that is applicable to molecules carrying relevant nuclear spins. Using ${}^{137}$Ba${}^{19}$F and nuclear-spin-dependent parity violation (NSD-PV) as representative species and benchmark application, respectively, our approach achieves a projected statistical sensitivity roughly two orders of magnitude beyond comparable molecular beams by combining techniques already demonstrated individually in current experiments. This level of precision could provide realistic experimental access not only to the enhanced NSD-PV signals arising from the heavy ${}^{137}$Ba nucleus within this molecule but also to the contributions from the lighter ${}^{19}$F nucleus, bringing direct benchmarks of nuclear \textit{ab initio} theory within reach. We further identify a candidate magic wavelength as a route to second-scale rotational coherence in future experiments. The techniques developed here can be transferred to measurements of nuclear Schiff and magnetic quadrupole moments in molecules containing deformed nuclei, establishing a general platform for laboratory searches for nuclear symmetry violations.

We investigate the open quantum dynamics of a system of two masses interacting with an environment of linearized gravitational waves. We formulate the analysis in terms of the observable proper distance between the two masses, and show that the canonical variables obtained from the standard Lagrangian, expressed in terms of the Fermi normal coordinates, are not suitable for an effective description of the system. We resolve this issue through a unitary transformation that provides a physically meaningful system--environment decomposition and derive the master equation to leading order in $G$. Its dissipative sector reproduces the classical energy loss due to gravitational-wave emission, while the noisy contributions suppress coherences between states with different mass quadrupole, or effectively, different proper separations. In the regime where the proper distance can be described by considering small quantum fluctuations around an average distance $l_0$, the dynamics reduces to a Caldeira--Leggett-type equation, with a decoherence rate dependent on the baseline length $l_0$.

Dynamical decoupling sequences are essential for nanoscale quantum sensing, but the finite duration of microwave pulses generates spurious responses. While phase randomization (PR) protocol can suppress these artifacts, they rely on probabilistic averaging. This introduces an inherent statistical variance that demands excessive sequence lengths and stringent hardware capabilities for true random phase generation. Here, we propose Hadamard sensing channel (HSC), a deterministic phase-design framework based on Hadamard matrices. HSC completely eliminates the statistical variance of PR by exactly and deterministically canceling spurious signals using a finite set of orthogonal phase patterns. Simulations confirm that HSC matches the ideal suppression of PR but exhibits superior robustness against control errors. HSC offers a mathematically exact and hardware-friendly solution for reliable high-resolution nanoscale nuclear magnetic resonance.

A freely moving quantum Hall (QH) interface may end on a physical edge or topological boundary, but fixed-edge theory cannot determine what endpoint data make such a termination consistent. Here we formulate an open-worldsheet junction framework in which the embedding, material charge, anomaly flow, and topological boundary condition are organized together. The endpoint is specified by a geometric support and variational boundary data, together with condensable topological sectors and any outgoing channels required to absorb or continue the worldsheet flux. This construction extends the charge--shape relation to an interval and shows why a lone chiral Majorana cannot terminate on a finite-dimensional endpoint degree of freedom. It gives an operational definition of a QH brane and a systematic basis for endpoint and network theories of dynamical QH interfaces.

A Moore--Read interface carries a chiral Majorana mode on a boundary whose geometry may itself fluctuate. Fixed-edge theory does not determine how this neutral mode should be transported when the interface bends and moves, or how its dynamics couples to the fluctuating shape. Here we construct a spatially reparametrization-invariant Majorana theory on the nonrelativistic worldsheet of a freely moving interface. The changing line element fixes a universal half-density transport law, while additional curvature- and velocity-dependent couplings remain controlled by microscopic interface physics. The resulting framework identifies the Majorana stress tensor as the mediator between neutral and geometric dynamics and provides the neutral sector needed for effective theories of dynamical non-Abelian quantum Hall interfaces.

A freely moving quantum Hall interface is fundamentally different from an ordinary edge fixed by an external confining potential. Since a normal displacement changes the areas occupied by the adjacent incompressible phases, the interface geometry and charge dynamics cannot be treated as independent degrees of freedom. We formulate this problem for interfaces between Abelian quantum Hall phases using a spatially reparametrization-invariant worldsheet description, in which tangential motion is a relabeling of the interface while normal motion is physical. Starting from the two-sided Chern--Simons response, we derive the relation between normal charge transport and interface motion. We then introduce a relative-area construction, defined with respect to a material reference curve, that converts this velocity relation into an equal-time constraint linking the charged boundary sector to the interface shape. Combined with the folded $K$-matrix current algebra, this identifies the universal Hall kinematics of the moving interface while leaving its geometric energy and neutral dynamics dependent on microscopic interface physics. The resulting framework provides a systematic basis for effective theories of dynamical quantum Hall interfaces.

We give a query-optimal algorithm for simulating a general $n$-qubit time-dependent Hamiltonian $H(t)$ on $[0,T]$, assuming that $H$ is Lipschitz continuous and $\|H(t)\|\leqα$. In the standard $\mathrm{HAM\mbox{-}T}$ access model, the algorithm approximates the time-ordered propagator $U_H(T)$ to error $\varepsilon$ using $$ O\left( αT+\frac{\log(1/\varepsilon)} {\log(e+\log(1/\varepsilon)/(αT))} \right) $$ $\mathrm{HAM\mbox{-}T}$ queries. This matches the known query lower bound for time-independent Hamiltonians, showing that time dependence incurs no asymptotic query overhead. Our method first constructs a one-query transducer that, given an auxiliary state, implements an approximation to $U_H(T)$ and returns the state unchanged. A weighted combination of circuits that apply the transducer different numbers of times makes the error caused by omitting this state decay factorially, yielding the stated optimal precision dependence. For time-independent Hamiltonians, the same method also gives a query-optimal alternative to qubitization.

Mapping quantum programs to restricted physical chips requires SWAP operations, incurring depth and error penalties. In symmetric programs, this routing overhead breaks theoretical symmetry because identical logical roles experience unequal shuffling. While often attributed to hardware topology alone, we show this is a two-level phenomenon. A qubit patch's shape dictates if it can host a balanced assignment. When balance is possible, the actual imbalance is set by the logical-to-physical assignment, meaning a balanced assignment can distribute routing costs perfectly evenly at no extra depth. Through exhaustive search on a 57-qubit "heavy-hex" lattice, we prove these topological constraints. For a four-part ring, 108 of 124 connected patches admit a cost-free balanced assignment, with the 16 exceptions being star-shaped. For a six-part ring, cost-free balance is impossible on compact patches. For a fully connected four-part symmetry, balance is structurally impossible at any depth. Simulations using realistic error rates show that, relative to the worst-case concentrated assignment, balanced assignments reduce symmetry-breaking by 92.7% (95% CI [+89.8%, +95.3%]) for the raw metric and 87.0% (95% CI [+79.6%, +94.1%]) for the decoherence-corrected measure (p = 2.45 x 10^-32). Substrate error heterogeneity accounts for at most 10.8% of this effect. Notably, switching to the compiler's highest generic optimization level did not yield a statistically significant change in routing imbalance, highlighting the need for targeted symmetry-aware passes. When patch geometry permits, routing imbalance is a compiler choice rather than a hardware limitation. Thus, symmetry-aware assignment should be a primary objective for compiler optimization and chip design.

Graph representations of discrete events provide a natural foundation for machine-learning models of anomaly detection, yet they also suggest a deeper quantum description in which graph structure gives rise to interacting quantum degrees of freedom. We develop a quantum framework based on a directed participant graph whose edges represent events connecting pairs of source and destination vertices. A line-graph transformation maps each event to a node of a bidirectional event graph, whose edges inherit relational information from the participant graph. Since event datasets are naturally organized as collections of event records, their raw attributes align directly with the nodes of the event graph. A quantum harmonic oscillator (QHO) is assigned to every node of the participant graph, with the collective Hilbert space of these QHOs providing a complete basis for representing quantum states. Every directed edge of the participant graph thereby acquires a Schwinger isospin arising from the two endpoint oscillators. Under the line-graph transformation, event-graph nodes correspond to observable isospins whose interactions through bidirectional edges provide a natural substrate for learning from event datasets, while the quantum states associated with the underlying participant nodes remain latent and inaccessible to direct observation. Within this framework we formulate a compact U(1) lattice gauge theory (LGT) on the event graph that leads to a Kogut-Susskind Hamiltonian (KSH) in the form of an XY-type spin model governing the dynamics of sparse anomalous-event isospins immersed in a bath of many nominal events. The proposed framework establishes a mathematical foundation for quantum-inspired graph-based anomaly detection and provides a principled bridge between graph learning, LGT, and quantum information.

The Monte Carlo sampling of the stochastic differential equations (SDEs) based on the quasiprobability distribution function, such as the Glauber--Sudarshan P, Wigner, and Husimi Q functions provides a powerful framework for investigating bosonic open quantum many-body dynamics described by the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) equation, while considering the effects of quantum fluctuations beyond the mean-field approximation. However, the stochastic Monte Carlo simulation is possible only when the corresponding Fokker--Planck equation has a positive-semidefinite diffusion matrix, and the general conditions for the diffusion matrix to be positive semidefinite have remained unclear. In this work, starting from the path integral formulation, we first derive the sufficient conditions under which the diffusion matrix is positive semidefinite for an arbitrary Hamiltonian, jump operators, and choice of quasiprobability distribution functions. We also analytically derive the corresponding SDEs to be solved. We then investigate the dynamics of the GKSL equation in the thermodynamic limit and show that, depending on the form of the jump operators, the mean-field approximation may fail to describe the dynamics accurately, making stochastic Monte Carlo simulations indispensable. Furthermore, we derive the sufficient conditions under which the higher-order quantum fluctuation terms beyond the Fokker--Planck description vanish identically, even when the jump operators contain quadratic terms. Under these conditions, whenever the corresponding SDEs can be derived, the stochastic Monte Carlo simulation reproduces the exact dynamics. These results clarify the conditions under which the stochastic Monte Carlo simulations are both feasible and necessary for accurately describing the dynamics governed by the GKSL equation in phase space.

We develop an ODE/IM-based formulation for the thermal partition function and the spectral zeta function of the homogeneous Hermitian and PT-symmetric oscillators. For both classes of systems, the quantization condition can be expressed using the counting function $a(E)$, which can be solved via the Destri-de Vega equation of the integrable model. We then express the partition function and spectral zeta function as contour integrals involving the counting function, thereby providing a direct bridge between quantum spectral functions and integrable models.

We study the entanglement Hamiltonian of an infinite hopping chain in its ground state, after partial projective measurements in the occupation basis. For a segment separated by two measurement regions from the rest of the chain, we show that the reduced density matrix can be related to a grand-canonical state via a conformal mapping and a gauge transformation in the underlying field-theory description. The entanglement Hamiltonian is then described by a local inverse temperature that vanishes as a square root around the endpoints and is independent of the particular measurement outcome. In sharp contrast, the local chemical potential is shown to be related to the induced charge density in the segment. Hence the entanglement Hamiltonian of a post-selected state contains much more information on the measurement outcome than the respective entropy.

High-dimensional nuclear spins offer a hardware-efficient route to quantum error correction (QEC), with the spin cat code providing intrinsic robustness against phase errors -- the dominant noise channel in donor-in-silicon architectures. However, realizing the full potential of this encoding requires gate operations that preserve its error-correcting properties. In this work, we construct a universal logical gate set that is error-transparent (ET) to phase errors, and discuss its practical implementations and challenges. The ET gates ensure that phase errors occurring stochastically during gate operations are propagated in a systematically traceable manner and remain correctable in a subsequent QEC step. Among the universal gate set constructed, we identify the logical $X$ gate as the primary challenge and discuss potential realization schemes. In addition, to fully leverage the spin cat code's advantage over an unencoded qubit, multi-tone microwave driving of the logical $CZ$ gate is essential. Our simulations show that ET gates significantly outperform non-ET gates and may be necessary to surpass the break-even point. We further show how logical measurement and recovery can be constructed from ET operations, and explain why state-preparation cannot be made ET. In particular, ET measurement in the computational basis is realizable via spin parity measurement, and that error correction circuits constructed from ET operations achieve optimal error correction capacity. Our work charts a concrete path toward full fault-tolerant quantum computation with high-dimensional nuclear spin systems.

We study idealized levitated protocols that create spatial superpositions of massive test particles. For each protocol, we compare the dimensionless contrast-loss exponent of mass-proportional continuous spontaneous localization (CSL) with the Diósi--Penrose (DP) self-energy exponent $E_Gτ/\hbar$. We first prove that the point-particle CSL separation kernel has an exact random-unitary realization: Gaussian momentum kicks arriving at Poisson-distributed times produce the same unconditional decay of spatial coherence, although a pure state conditioned on the complete kick record remains pure. The separation kernel alone therefore specifies an operational decoherence law, not the occurrence of objective collapse. We then show that the ratio of the CSL and DP exponents is independent of particle mass and interrogation time. In the point-particle model it depends only on branch separation and an effective distance; for the standard GRW reference parameters, its resolved-superposition crossover is $x_*\approx1.91\,\mathrm{nm}$. For rigid spherical bodies with an arbitrary normalized radial mass profile, total mass, overall density scale, and interrogation time again cancel, leaving a dimensionless geometry factor. The results distinguish three requirements for a decisive experiment: detectable absolute effects, a controlled comparison of CSL and DP scales, and observables capable of discriminating physically different dynamics that share the same ensemble decoherence kernel.

Entanglement dynamics depend not only on how a quantum system is partitioned, but critically on how interactions across that partition are structured. For a spatial bipartition of a locally interacting system, entanglement is generated near the boundary and then propagates into the bulk. By contrast, when two extended quantum fields are coupled locally along their entire length, the interaction crosses the field-space partition everywhere, and this generates correlations throughout the system. Here, we study the entanglement dynamics between two gapless one-dimensional quantum many-body systems described by Luttinger liquid theory. The systems are initially decoupled and prepared at zero or finite temperature, after which a time-dependent tunneling interaction is activated uniformly along their length. Within a Gaussian approximation, we derive general analytical expressions for the logarithmic negativity, mutual information, and Rényi entropies under arbitrary coupling protocols. At zero temperature, entanglement displays an early-time power-law growth whose exponent is fixed solely by the first non-null derivative of the tunneling protocol. Once the coupling saturates, we obtain exact long-time averages of the information-theoretic quantities and characterise how the correlations scale with temperature and the final coupling strength. We also analyse how mutual information and logarithmic negativity approach the adiabatic limit for a very slow protocol with respect to intrinsic system timescale. This work extends the study of entanglement dynamics in nonequilibrium field theory to field-space partitions and mixed initial states.

We study dynamical phase transitions in the generalized dissipative Dicke model in an array of trapped Rydberg ions, where their density-density interactions compete with the collective spin-phonon coupling, laser driving and dissipation. This setting offers a versatile approach to study equilibrium as well as non-equilibrium many-body phenomena, as parameters, such as the Ising interaction, laser-ion and spin-phonon coupling can be tuned. Through analyzing the mean-field phase diagram, we find a variety of distinct phases and the emergence of a tricritical point that are sensitively dependent of the interaction between Rydberg ions. We then study the quantum dynamics for a finite system size and characterize parameter dependent dynamics using the spin average, entropy, and Loschmidt echo. Distinctive signatures of the dynamical phases, such as slow relaxation and metastability, arise near the phase transition. This analysis predicts rich quantum dynamics of the finite system that link to the non-equilibrium mean-field phases. Our study widens the exploration of collective and non-equilibrium phases in Dicke models, and reveals that the Rydberg ion interaction drastically affects the phase diagram and dynamics.

Entanglement is a key resource for quantum technologies. We show that protocols employing quantum Mpemba effects allow one to exponentially accelerate the generation of entanglement, or to slow down the decay thereof. Two entanglement Mpemba effects with different operational meaning are introduced, focusing either on the task of rapidly generating a certain threshold value for entanglement or on achieving the asymptotic steady-state value. We show that entanglement Mpemba effects depend on the chosen entanglement measure. Using cluster elimination methods, many-body quantum systems also benefit from the exponential speedup of entanglement generation, as we demonstrate for a dissipative long-range Ising chain.

Modern physics has achieved extraordinary empirical success while retaining much of the absolute, unobservable structure introduced by Newton, largely without questioning its necessity. We investigate how far this structure can be eliminated by adopting a relational ontology guided by Leibniz's principle of sufficient reason. Removing absolute position, orientation, time and, finally, scale leads naturally to a formulation of the gravitational $N$-body problem where only dimensionless ratios are physically meaningful. Within this framework, the scale-invariant variety $V$ becomes a central quantity, providing a measure of structure, a natural ordering of shapes, and an emergent gravitational arrow of time. We argue that the resulting formulation unifies classes of Newtonian solutions previously regarded as distinct, uncovering a possible new symmetry, suggests a notion of explanation based on timeless spatial correlations rather than temporal evolution, and points towards a more economical ontology. Although developed in the context of Newtonian gravity, the principles proposed here may also offer a new perspective on general relativity and quantum mechanics.

Reaching fault tolerance means scaling qubit counts by orders of magnitude, a jump that conventional superconducting architectures cannot sustain without solving the so-called `wiring problem'. Global control sidesteps this bottleneck, but implementing quantum error correction (QEC) on previously proposed global architectures incurs extremely steep overhead costs, due to the need for separate correction procedures for the computational and auxiliary qubits that comprise the global device. We resolve this by introducing the first globally-controlled architecture with zero qubit overhead. Every physical qubit is a computational qubit, and thus, every qubit is protected under a single error correcting scheme. We identify a class of cyclic stabilizer codes realizable through global iSWAP and single-qubit gates, yielding QEC thresholds nearly seven orders of magnitude larger than previous estimates for globally-controlled arrays. We further show these thresholds improve systematically as the global architecture is augmented with a limited amount of local measurement sites, demonstrating a trade-off between wiring simplicity and fault-tolerant performance.

Classical simulation remains essential for developing and validating quantum algorithms, but its cost grows rapidly with circuit size. Tensor-network contraction can reduce this cost by exploiting circuit structure, although its efficiency depends strongly on the chosen contraction plan. On GPUs, plans with similar theoretical complexity may perform very differently because execution also depends on parallelism, reduction structure, memory traffic, and contraction geometry. We present a learning-to-rank framework for selecting efficient contraction plans before executing them. Each plan is represented by structural features derived directly from its sequence of pairwise contractions, and gradient-boosted rankers are trained from GPU measurements using listwise and pairwise objectives. We evaluate the resulting models on diverse circuit families, using separate in-distribution and circuit-family-shift test sets, and compare them with random and MinFill-based baselines. The learned rankers generally identify better plans, with the listwise model providing the strongest overall decision quality. We also study backend shift by comparing empirical plan orderings on two GPU architectures and evaluating the source-trained models on the second device without retraining. The rankings remain substantially, though not perfectly, stable across GPUs, and the models retain useful decision quality. These results support Learning to Rank as a practical way to reduce contraction-plan search, while showing that performance remains partly backend dependent.

We construct Hermitian self-dual maximum-distance-separable codes with parameters $[12,6,7]_{25}$, $[18,9,10]_{121}$, and $[18,9,10]_{169}$. Through the nonbinary stabilizer construction these codes define $\text{AME}(12,5)$, $\text{AME}(18,11)$, and $AMD(18,13)$ states, and one-party projection gives $\text{AME}(17,11)$ and $\text{AME}(17,13)$. The $[12,6,7]_{25}$ code, which is not monomially equivalent to a generalized Reed-Solomon code, is obtained by a systematic search without prescribed coordinate symmetry; its monomial-semilinear automorphism group acts with a regular $\mathbb{Z}_3^2$ orbit on nine coordinates. Imposing that action on two nine-coordinate orbits reduces the length-eighteen search to a nine-element group algebra kernel, whose Hermitian character decomposition splits the invariant self-duality constraints into independent blocks with exact family counts; a norm-one coordinate scaling removes a factor $q+1=14$ at $q=13$. Hermitian self-duality and the MDS property are certified by exact field arithmetic and complete square-minor enumeration. Graph-state cut-rank computations, including all single-vertex deletions of the length-eighteen graphs, provide additional exact checks.

In one-round $f$-routing, Alice receives an $n$-bit string and an unknown qubit, while Bob receives another $n$-bit string. They exchange one simultaneous message each, and the value of $f$ determines which party must recover the qubit. Message lengths, local systems, and local operations are unrestricted. We charge only $E_{\dim}(ρ_{LR})=\log_2\min\{\operatorname{rank}ρ_L,\operatorname{rank}ρ_R\}$, the logarithm of the smaller marginal support dimension of the shared state prepared before the inputs arrive. The state may be arbitrary and mixed. For the inner product modulo $2$, we prove that every protocol with worst-case error at most $0.09$ in both routing cases, measured in the full, unhalved diamond norm, satisfies $d\log_2(2d)=Ω(n)$ for $d=\min\{\operatorname{rank}ρ_L,\operatorname{rank}ρ_R\}$. Thus $d=Ω(n/\log n)$ and $E_{\dim}(ρ_{LR})\ge\log_2 n-\log_2\log_2 n-O(1)$. The closest earlier growing Schmidt-rank lower bound for an explicit routing function assumes zero error in one routing case. Our proof converts correctness into a matrix whose entries have a constant gap between the two routing cases. It approximates this matrix by one whose rank depends on $d$, but not on the dimensions of messages or local systems. A sign-rank lower bound for the matrix of the inner product modulo $2$ completes the argument. A lower bound polynomial in $n$ on $E_{\dim}$ remains open.

We present QSCI-CMP, a quantum-classical hybrid algorithm for molecular ground-state calculations that reduces both the query count and the gate count of sample-based quantum diagonalization with amplitude amplification (SQD-AA). SQD-AA mitigates the measurement bottleneck of quantum-selected configuration interaction (QSCI) by amplifying the basis states that have not yet been measured. Its oracle, however, specifies the measured states by listing them one by one, so its gate count grows with the number of collected states. Moreover, the quantum resources are spent even on states whose importance is evident from chemical knowledge, such as low-order excitations from the Hartree-Fock reference, which could be collected classically at the outset. We therefore propose to fix such chemically trivial states in advance, include them in the diagonalization subspace from the start, and exclude them from the amplification target, using a low-cost oracle that recognizes them through the excitation level and the seniority number of each basis state. We numerically demonstrate that QSCI-CMP reduces the query count and the gate count required to reach chemical accuracy by up to approximately 68% and 72% relative to SQD-AA for 24-qubit systems. The chemically trivial subspace is freely tunable within the classical computational budget. A larger subspace shifts more work onto the classical solver and increases the reduction in quantum cost, and when it captures the ground state sufficiently well, no quantum sampling is needed at all. We also point out that a query-optimal iteration count known from the analysis of quantum search further reduces the query count of both methods by approximately 12%.

Spin ensembles are considered as potential candidates for quantum memory and quantum enhanced sensing applications. Here, we explore the controlled coupling of multiple superconducting microwave cavities to a spin ensemble, which shows signatures of strong coupling and, due to the multi-mode character, the formation of dark states. In particular, the latter are of interest, as they provide a potential pathway to enhance memory times and enable protected storage of non-classical states in spin ensembles due to the suppressed coupling to the circuit environment. We model the spin multi-cavity hybrid to reproduce the spectra and extract characteristic coupling strengths using the input-output formalism.

Quantum cryptographic primitives beyond key distribution remain a less well understood area of research. In classical cryptography, one-way functions underpin nearly all standard cryptographic protocols, motivating the search for meaningful quantum analogues and for a clear understanding of the physical and computational mechanisms that could enforce one-wayness. In this article, we review quantum one-way functions and a range of closely related quantum-state primitives, including one-way state generators, pseudorandom quantum states, and efficiently indistinguishable pairs of states. We discuss both computational and information-theoretic notions of quantum one-wayness, emphasizing the different adversarial models and security assumptions that underlie these constructions. We compare and contrast the various proposed primitives, and clarify their conceptual relationships. Particular emphasis is placed on questions of physical realizability, experimental feasibility, and robustness to noise. Finally, we outline open problems and future directions toward the development of practical quantum cryptographic primitives beyond key distribution, and the emergence of a broader quantum-cryptographic ecosystem.

Objective facts in quantum Darwinism are values recorded redundantly in many independently accessible fragments of the environment. Redundancy does not create additional logical information, so its thermodynamic meaning has remained unclear. We show that it creates an exact work asymmetry between controllers with different access architectures. For a record cloud $F$ and a partition $\mathcal{P}$ into blocks that cannot be jointly controlled, the reversible isothermal erasure penalty relative to a global controller is $k_{\mathrm{B}}T$ times the partition total correlation. If the source event $X$ is supplied as catalytic classical side information, subtracting the corresponding penalty gives the source-loss law $\mathcal{F}_{\mathcal{P}}^{T}=k_{\mathrm{B}}T\left[\sum_{B\in\mathcal{P}}I(X{:}F_B)-I(X{:}F)\right]$. We call this the thermodynamic factuality charge. It ranges from $-k_{\mathrm{B}}T H(X)$ for perfect secret sharing to $(|\mathcal{P}|-1)k_{\mathrm{B}}T H(X)$ for perfect broadcast objectivity. Its normalized form defines a thermodynamic record number between $0$ and $|\mathcal{P}|$. We derive Landauer--Darwin bounds, endpoint-rigidity certificates, exact growth and partition-refinement laws, spectrum-broadcast saturation, and closed formulas for noisy classical and quantum collision models. The theory does not modify quantum mechanics or posit objective collapse; it identifies the thermodynamic resource generated by redundant records under restricted control.

Programmable electron optics -- electronically controlled phase plates -- underpin proposals from dose-efficient phase imaging to shaped-electron X-ray sources, nearly all assuming a pure, fully coherent delivered wave whose purity has never been measured. Here we reconstruct the transverse density matrix of a microelectromechanical electrostatic spiral phase plate by mixed-state ptychography, from one four-dimensional STEM scan per state and without added hardware. The delivered beam is substantially mixed: its purity falls from approximately 0.47 to approximately 0.24 as the applied bias grows, inconsistent with a fixed lateral source-blur model, while the real-space coherence width stays near 1 nm. The same scans calibrate the device in situ, allow virtual orbital-angular-momentum sorting and, through a partial-coherence-aware transfer theory, indicate that purifying the output could improve dose efficiency roughly threefold. One acquisition thus becomes a quantum-state acceptance test for programmable electron optics, supplying the purity and coherence that emerging phase-plate and diffractive-imaging schemes assume but leave unquantified.

We solve cyclic finite-dimensional quantum histories for arbitrary time-dependent unitary steps, without assuming that one step has finite order. The propagation Hamiltonian is a unitary connection Laplacian on a cycle; its complete gauge invariant is the monodromy $M=U_{L-1}\cdots U_0$. Its spectrum is $λ_{a,k}=1-\cos((2πk-θ_a)/L)$, where $e^{iθ_a}\in\mathrm{spec}(M)$. Thus the exact history sector is isomorphic to $\mathrm{Fix}(M)$, while frustration, the gap above a nonempty zero-energy sector, the determinant, and the finite-temperature trace are obtained in closed form. Ordinary spectral data recover the multiset of monodromy phase cosines but not phase orientation; low energy certifies proximity to an exact relational history. We then define the predictive quotient of a sharp finite clock relative to an accessible operator system as the unique coarsest event alphabet preserving all conditional statistics on a history sector. A finite-error theorem shows that threshold clustering recovers this quotient when the minimum diamond separation of inequivalent event channels exceeds four times the estimation error, and proves an optimal record-count bound. With full matrix access and homogeneous step $U$, the minimal number of clock events is the projective order of $U$. We distinguish the normalizer of the clock algebra from transformations preserving the coherent history code and classify oriented exact sharp clock changes by $U(r)\times\mathbb{Z}_L$ on a rank-$r$ history sector; without orientation the cyclic factor becomes dihedral. Reversible changes of full-information clock fibers are necessarily unitary, so irreversible coarse-graining is not exact clock covariance. Minimal realizations of a complete history Gram kernel are uniquely unitarily equivalent, with a finite-data Procrustes bound. Independent finite-matrix code verifies the main results.

Quantum state tomography is fundamental to quantum information processing but becomes infeasible at scale due to the exponential growth of the state space. Shadow tomography alleviates this challenge by focusing on predicting measurement outcomes rather than reconstructing the full state. Its online variant models adaptive and potentially adversarial measurement scenarios, where a learner sequentially predicts outcomes while competing with the best fixed quantum state in hindsight. We show that exploiting additional structure in the measurements leads to significantly stronger regret guarantees. In particular, under the assumption that the adversarial measurements have bounded Frobenius norm, we analyze Projected Online Gradient Descent and derive regret bounds that depend on intrinsic structural properties, such as rank or sparsity, rather than the ambient Hilbert space dimension. As a complementary result, we show that one can achieve logarithmic regret, independent of both the number of qubits and measurement outcomes, for multi-outcome measurements under squared $L_2$ loss. These results demonstrate that incorporating realistic structural assumptions can substantially enhance the learnability of quantum states in online environments.

We investigate the entanglement entropy of a class of $N$-particle excited state of fermions confined in a two-dimensional harmonic trap rotating at an angular frequency $Ω$. The excited state is constructed by filling a particular set of $N$ single-particle energy levels. We analytically compute the Rényi entropies of order $q$ in a disc of radius $r$ around the centre of the trap, and the cumulants corresponding to number fluctuations of fermions within the disc. We found that the area law scaling of entanglement entropy holds even for a class of excited states. We also verified the well-known series expansion of entanglement entropy in terms of the particle number cumulants for non-interacting fermions. We further derive the centered cumulant generating function, demonstrating that the associated probability distribution function in the disc has identical scaling properties, up to a variable shift, to the known ground-state result. Finally, we extend our result to an annular region, showing that both the Rényi entropy and particle number cumulants of the annulus decompose into sums of the corresponding quantities of the two bounding discs. These additive relations hold as long as the width of the annulus is sufficiently large.

Distributing entanglement between distant qubits is a crucial element of scalable quantum computing. Here, we describe a scalable quantum interconnect that generates remote entanglement at rates approaching those compatible with two-qubit gates of current neutral-atom quantum processors. The proposed approach exploits the strong dipole-dipole interactions between atomic Rydberg states to generate entanglement between stationary qubits and propagating photons, without the need for an optical cavity. We provide a thorough description of the optimal conditions for the developed entanglement-generation protocol for realistic experimental parameters and demonstrate that entanglement-generation rates $\gtrsim 3\times 10^5$ s$^{-1}$ can be achieved using Rydberg states of ytterbium atoms. Given the inherent scalability and design flexibility of the proposed interconnect, our results suggest a promising approach towards distributed networks based on neutral-atom quantum architectures.

Non-Abelian anyons arise as exotic excitations in fractional quantum Hall (FQH) matter and have proved very elusive to realize in conventional platforms. In this work, we show that on a programmable quantum hardware platform, the more exotic FQH excitations are the less costly ones to prepare: clustered non-Abelian FQH states admit parallel quantum preparation circuits whose two-qubit depth is independent of system size, while constructing the more common Abelian Laughlin state requires a sequential circuit chain with linear depth. The centerpiece of this work is our new systematic framework for cataloging possible FQH states and preparing them on quantum circuits at unprecedented scale and variety. Our prepared parafermionic Read--Rezayi $\mathbb{Z}_3$ state holds depth 3 from 8 to 118 qubits, and full root sampling extends to a 154-qubit, 104-electron Read--Rezayi $\mathbb{Z}_4$ state. In all, our demonstrated 18-family catalog of prepared FQH states extends to all 156 qubits of an IBM Heron processor, limited only by existing hardware scale. Measurements on the prepared states recover the expected fractional quasihole charges, with the charge estimator exact in every symmetry-selected shot for the clustered states, and braiding data of the non-Abelian $e/4$ quasihole measured via interferometric extensions. Our work establishes a scalable route to studying FQH physics on quantum processors and opens new avenues for preparing and probing non-Abelian topological matter far beyond the reach of conventional platforms.

Near-term quantum hardware limits circuit depth and often imposes geometrically local connectivity for quantum generative models, restricting the output distributions accessible to shallow unitary Born models. Introducing stochasticity into a unitary quantum Born model can improve the empirical generative performance of the resulting channel model and, for a restricted small-scale architecture, has been proven to represent a strictly larger family of distributions than its unitary counterpart. However, whether such randomness provides a provable separation at fixed shallow depth for arbitrarily large systems has remained open. Here, we show that shared classical randomness, a comparatively weak resource from entanglement theory, is sufficient to establish such a strict scalable representational separation over the corresponding shallow unitary Born model. More specifically, we augment bounded-connectivity shallow unitary circuits, followed by computational-basis measurements, with spatially separated local Pauli operations, whose joint application is controlled by a single classically sampled random bit. The resulting shallow-depth channel model generates long-range correlations in the classical output distribution that no purely unitary shallow-depth model with bounded connectivity can reproduce. For one-dimensional nearest-neighbour architectures, reproducing such distributions with a purely unitary model can require depth $Ω(N)$ in the worst case. We further show that measurement-based quantum computation (MBQC) provides a natural implementation of the required shared classical randomness through suitable adaptation of the random measurement outcomes. Numerical experiments on MBQC-based generative models support the analytical results.

The quantum approximate optimization algorithm (QAOA) tackles combinatorial problems by tuning a quantum circuit in a classical loop, often guided by gradients. We show that the gradient used to tune the circuit's final parameter is bounded by imaginarity, which weights phase relationships between candidate solutions by how strongly the circuit connects them and how differently the problem scores them. Imaginarity is necessary but not sufficient for a nonzero gradient. We extend the bound to three common noise models and compare it numerically with the gradient in Max-Cut simulations.

Perfect prepare-and-measure games exhibit an all-or-nothing quantum advantage: a quantum system of dimension $d$ satisfies every prescribed winning constraint, whereas a classical $d$-level message cannot. We establish two structural results for such forbidden-output support constraints. First, every binary-output support game reduces exactly to a conflict graph: perfect classical realization with a $d$-level message is equivalent to $d$-colorability, perfect $d$-dimensional quantum realization is equivalent to a $d$-dimensional orthogonal representation, and the minimum number of Bob inputs realizing a fixed conflict graph is its edge biclique-cover number. Second, for an arbitrary finite output alphabet, every perfect qubit strategy admits a perfect classical-bit realization. As a flagship application, the $13$-ray qutrit graph yields a compressed game $(X,Y,B)=(13,8,2)$ with $C_3=39<Q_3=S=40$, and eight Bob inputs are minimal among all binary-output realizations of that graph. Graph extensions demonstrate the mechanism in every dimension, while Torpedo and antidistinguishability games illustrate the genuinely nonbinary regime. These results connect exact communication, graph coloring, contextuality, state exclusion, and zero-error information theory.

Exceptional points (EP's) are a hallmark of non-Hermitian quantum systems. We show that momentum-space deformation provides a general design principle for creating and controlling EP's in quadratic many-body Hamiltonians. We identify universal criteria for the momentum sectors to host EP's and the corresponding critical deformation strengths, while revealing that a single momentum-sector EP induces quite remarkably an exponential proliferation of many-body eigenvector coalescences. We further establish EP's as a universal mechanism for purifying arbitrary mixed quantum states, uncovering distinct purification regimes and a fundamental odd-even system-size dichotomy in the thermodynamic limit. Our framework also provides a systematic reverse-engineering protocol for generating short- and long-range, reciprocal and nonreciprocal non-Hermitian quantum matter, together with an explicit Lindblad embedding. These results thus establish momentum-space deformation as a unified route to exceptional-point engineering and controlled design of many-body non-Hermitian quantum systems.

Liouvillian eigenvalues determine decay rates and oscillation frequencies, but not how the corresponding modes are excited, propagated, and detected in a chosen protocol. We develop an operational spectral theory based on matched left and right eigenoperators. Left eigenoperators determine excitation by an input or source; right eigenoperators determine the propagated density deformation and readout overlap; their product is a gauge-invariant modal weight. For bosonic systems, coherent preparations turn left eigenoperators into phase-space excitation maps whose zeros identify mode-selective suppression, while right eigenoperators yield the corresponding Wigner deformations. Resolved slow subspaces define operational coordinates and, when positivity and Markov-admissibility hold, a projected routing generator. In driven Kerr resonators, the framework identifies preparations that suppress a switching mode, separates symmetry-resolved relaxation channels, and reveals bias-induced crossovers in projected multichannel routing while the coherent-preparation partition continues to deform. Preparation geometry and slow-sector propagation thus provide complementary operational information beyond Liouvillian eigenvalues alone.

Understanding the effectiveness of quantum compilation techniques requires visibility into the entire transpilation process, not just the final circuit metrics. This demonstration presents an MLflow-inspired autologging framework for Qiskit that automatically captures compiler provenance, including transpilation stages, pass-level execution data, backend characteristics, compiler configuration, and execution results. The framework extends the QProv provenance model with compiler-specific information and stores the collected data in an MLflow Tracking Server for analysis and visualization. By eliminating manual instrumentation, the proposed approach improves compiler observability and supports reproducible evaluation of quantum compilation workflows.

We introduce and analyze a quantum-assisted classical communication protocol that encodes symbols from a finite alphabet onto temporal modes using the LM05 operation as a building block. The protocol applies a bit-flip gate independently to temporal slots corresponding to message symbols, yielding a tensor product of LM05 operations on parallel channels. This tensor product structure enables collective attacks not covered by standard LM05 security proofs. We derive a theoretical upper bound on the success probability for complete recovery under random guessing, accounting for the receiver's 50\% guessing ability on lost photons, and emphasize that this bound assumes perfect loss identification. We characterize the intended transmission, derive an asymptotic collective-attack bound for the symbol-set mode, and identify open challenges for composable security. The protocol is not a standalone Quantum Secure Direct Communication scheme, as the classical ordering information requires encryption. For a 53-symbol alphabet, the optimistic 1\% success bound occurs at about 0.8 kilometers under zero QBER and reduces to about 0.6 kilometers for QBER equals 0.01; practical constraints severely limit performance.

Neutral atom quantum computing utilizes laser-trapped neutral atoms as qubits and realizes quantum logic gate operations through Rydberg-state interactions. In recent years, it has become one of the most vibrant directions in quantum computing hardware. This paper systematically reviews the working principles of neutral-atom quantum computers, including qubit encoding, atom trapping and manipulation, Rydberg states and interactions, the Rydberg blockade quantum gate mechanism, and atom rearrangement with reconfigurable architectures. The mainstream technical routes are surveyed, represented by optical tweezer arrays combined with Rydberg interactions, optical lattice schemes, and dipole trap arrays. A panoramic review is provided of domestic and international research progress from theoretical foundations in 2000 to the latest achievements in 2026, including thousand-qubit-scale systems, logical qubits, and quantum error correction experiments. Key breakthroughs are highlighted, such as the 6100-atom qubit array, continuous operation of a 3000-qubit system, quantum simulation of the Kitaev honeycomb model, toric code error correction demonstrations, encoding rates exceeding 1/2, and fault-tolerant architectures. The core bottlenecks are analyzed in depth, including the scalability--fidelity trade-off, engineering implementation of quantum error correction, atom loss and mid-circuit replenishment, laser system industrialization, control electronics scalability, and long-distance quantum interconnection. This paper aims to provide a systematic reference for academic research and technological development in this field.

Multiport interferometers with $N$ ports are basic devices in both classical and quantum photonics. Ideally, they implement a linear unitary transformation between the input and output electric field vectors with $N$ components, each associated with a spatial mode of classical coherent light or a single photon. Standard designs for a fully reconfigurable universal multiport interferometer are given by the Reck or the Clements schemes. In this work, we introduce routing schemes to implement a generic unitary transformation on classical coherent light or single photons using linear or tree geometries via multiple projective measurements on a single detector with the minimum number of components. Then, we generalize this result to the case of any multi-photon state for scattershot boson sampling experiments with multi-routing schemes. Finally, we test the robustness of routing schemes compared to universal schemes with respect to losses and phase noise.

Bergemann and Morris (2016) show that one information structure is more informative than another exactly when it induces a smaller set of Bayes correlated equilibrium outcomes in every game. We build the quantum analogue. An information structure becomes a family of density operators indexed by the payoff state, which the mediator observes. We show that obedience is equivalent to a Loewner domination between operators on one player's subsystem. The equilibrium set is then a nonempty compact spectrahedron computable by semidefinite programming, classical structures embed exactly, and under quantum individual sufficiency more information shrinks the equilibrium set in every game.

Fast preparation of quantum error-correcting codes is essential for scalable quantum memories, but geometric locality and $U(1)$ charge conservation impose an unavoidable transport constraint. We combine exact complementary-channel geometry, charge-sector Haar analysis, and a gate-resolved connected-moment expansion to study one-dimensional covariant encoders under flagged erasure. Charge-Haar codes attain the universal adjacent-charge lower bound up to exponentially small corrections, yielding an exact $n^{-1/2}$ extensive-erasure law and a sharp half-erasure transition. For local number-conserving brickwork circuits, diffusion of the logical charge enforces an $Ω(n^2)$ encoding-time lower bound; we also prove an $O(n^3)$ mixing bound for the classical component and reduce the remaining full-channel upper bound to a source-restricted low-support operator-spreading problem. These results identify diffusion as an operational limit on symmetry-constrained quantum coding and establish a route to its exact formation time.

We determine the sharp modulus of continuity, in trace distance, of the optimized Petz and sandwiched Rényi conditional entropies for every order $α\in[\frac12,1)$. If two bipartite states are within trace distance $δ$, then both conditional entropies differ by at most $\frac{1}{1-α} \log[(1-\varepsilon)^α +(D-1)^{1-α}\varepsilon^α]$, where $\varepsilon := \min\{δ,1-1/D\}$ and $D$ is the effective dimension, given by the dimension of the first subsystem times the largest possible Schmidt rank. For every distance constraint $δ\in[0,1]$, the bound is attained by an isotropic pair with a maximally entangled anchor. Taking $α\uparrow1$ recovers the recent sharp continuity bound of quantum conditional entropy by Berta et al. [arXiv:2607.24687]. The proof linearizes the relevant concave Rényi functional at a comparison point dictated by the isotropic equality family. Schmidt-rank domination extends the equality geometry to an arbitrary anchor state, after which trace-distance duality and a noncommutative calibration estimate control the perturbation and anchor term without weakening the sharp constant. The latter estimate requires matrix analysis and is assisted by ChatGPT 5.6 Sol.

Quantum computing is a deep technology whose progress cannot be driven effectively from one direction alone. While the field has developed a growing catalogue of mathematically grounded algorithmic speedups, industrial impact will depend just as much on starting from real industrial decision contexts and working downward to what must be computed, validated and integrated. In this Perspective, I argue that sustained progress requires treating these two directions: bottom-up development from physics, hardware and algorithms, and top-down development from industrial needs and constraints. Equally primary and continuously coupled. This dual-viewpoint is not a matter of balance for its own sake. Quantum computers cannot solve arbitrary problems, so engagement with industry must remain anchored in algorithmic tractability. Yet tractable computations are rarely valuable unless they connect to decision points in established workflows such as candidate selection in drug discovery or the design of a new aircraft shape with improved aerodynamics. I analyse how historical narratives and structural separations of expertise slowed the formation of this coupling and outline what it takes to build it: explicit interfaces between technical teams and domain context and intermediate layers that translate quantum outputs into decision-relevant observables without suffocating foundational innovation. Framed this way, quantum computing's opportunity is clearest where deep physical modelling meets high-value decisions. Provided the field co-designs both sides from the outset.

Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the same classical correlation twice. We establish that qubits are protected from such overcounting. For every two-qubit state, the correlations observed in two complementary local bases are bounded by the premeasurement quantum mutual information. The proof traces this protection to binary-entropy curvature on the Bloch ball and combines a qubit information-exclusion tradeoff with data processing under local dephasing. Consequently, two correlation tables give a tomography-free lower bound on total correlation. A score above one bit also certifies a quantitative one-way entanglement-distillation rate; when applied to the Choi state of a qubit channel, the same data lower bound its quantum capacity. The theorem therefore identifies both an operational use of complementarity and the trusted two-dimensional setting in which its correlation accounting is valid.

Quantum superresolution reveals that the vanishing of separation sensitivity in conventional imaging below the Rayleigh limit does not necessarily indicate a fundamental loss of information in the optical field. However, the quantum limit for estimating the physical distance between two incoherent point sources in three-dimensional imaging systems and its dependence on the spatial structure of the point-spread function remains largely unknown. In this work, we derive the quantum-limited precision for estimating the full distance between two incoherent point sources with arbitrary intensity imbalance in a three-dimensional spatially invariant imaging system. We show that the distance information remains finite in the sub-Rayleigh regime and is governed by the second-order displacement-response tensor of the point-spread function. The eigensystem of this tensor determines the optimal relative orientation between the two sources, and reflection symmetries of the point-spread function can further provide a simplified means of identifying the optimal orientation. This geometric structure is coordinate invariant and provides a direct strategy for improving resolution by physically rotating an anisotropic imaging system to align its optimal principal response direction with the source displacement. For a general three-dimensional Gaussian point-spread function, the response tensor is proportional to the inverse spatial covariance, establishing a direct connection between quantum-limited distance precision and the geometry of Gaussian distribution.

Qualification of quantum states judges which of two sets of quantum states an unknown state lies in, where the two sets are labeled by two distinct parameter regions. We formulate this problem as a composite quantum hypothesis test and uncover universal scaling laws for the minimum error probability for $N$ copies. Taking polarization-direction qualification and purity qualification as examples, we show that the $N$-copy permutation symmetry and the geometric symmetries of the parameter regions identify the optimal measurements and the "worst pairwise states". The minimum error probability scales as $N^{-3/2}\exp(-Nξ)$ for disjoint regions and as $(NF)^{-1/2}$ for adjacent regions, where $ξ$ and $F$ are the quantum Chernoff divergence and quantum Fisher information associated with the "worst pairwise states", respectively. With the minimum error probability serving as an order parameter, the transition between the scaling behaviors becomes a second-order phase transition as $N\to\infty$. Our approach determines whether a quantum state belongs to a given set without full state tomography, thereby enabling qualification of large ensembles using finite samples.

The recently proposed spontaneous disentanglement hypothesis is formulated using a modified Schrödinger equation having an added nonlinear term. The hypothesis is motivated by some outstanding issues in the foundations of quantum mechanics, including the problem of quantum measurement. Spontaneous disentanglement is explored in the current study for the macroscopic limit. This is done using some many--body models having known exact solutions. For the under--study models, it is found that non--local entanglement becomes unstable in the macroscopic limit. On the other hand, stability in the macroscopic limit of local entanglement is not excluded. These findings demonstrate that the spontaneous disentanglement hypothesis can bridge between the quantumness of the microscopic realm, and the classicalness of the macroscopic one.

Although Arnoldi reduction of a generally non-Hermitian Hamiltonian yields an upper Hessenberg matrix rather than the tridiagonal form of Hermitian Lanczos theory, we show that a closed Toda sector survives in its diagonal and subdiagonal coefficients. For a fixed finite-dimensional Hamiltonian and a cyclic state vector deformed holomorphically, the Krylov Gram determinants are $τ$ functions of the finite two-dimensional Toda lattice, whose Flaschka variables coincide exactly with these Arnoldi coefficients. The Toda dynamics therefore closes on this sector without determining the remaining upper Hessenberg entries. The subdiagonal part of the same sector also has a direct geometric meaning: the squared subdiagonal coefficients determine both the Fubini--Study metric and the Berry curvature of holomorphic Krylov subspaces, whereas the geometric quantities associated with subspaces lost at Arnoldi breakdown cease to be defined. Along a smooth real path in the cyclic region, the Arnoldi-frame connection further provides a Hermitian tridiagonal generator of exact isospectral transport. When added to the Arnoldi matrix, this generator cancels transitions between instantaneous eigenspaces and realizes counterdiabatic driving whenever the matrix is diagonalizable with a nondegenerate spectrum.

We study the dynamics of a single quantum particle on a finite-size square lattice with a fractal structure resembling the Sierpiński carpet, and compare it to the dynamics on a uniform lattice of the same size. For a particle initially localized at a corner of the lattice, we monitor the probability of finding it near the initial and opposite corners using zone-integrated probabilities, allowing a consistent comparison across fractal orders. While on the uniform lattice the particle reaches the opposite corner ballistically, in a time proportional to the lattice size, on the Sierpiński lattice it becomes increasingly confined to the vicinity of its initial position. We show that this trapping builds up self-similarly across the whole hierarchy of corner zones of the lattice.

All realistic quantum systems are inevitably in contact with the environment. Suppressing theimpact of environmental noise is a critical challenge in cutting-edge quantum technologies. In thiswork, we introduce and systematically analyze a scheme for the protection of quantum states againstamplitude-damping (AD) noise based on the circuit structure called the quantum filter. Filtrationcircuits employing single- and multi-control qubits are examined, and their capability to enhance stateprotection fidelity while preserving a high success probability is discussed. Moreover, for many-bodyqubit states, those with a fixed quantum Hamming weight can be perfectly protected against ADnoise, whereas states with the largest Hamming weight difference set a lower bound on the achievableprotection fidelity. Our work provides a resource-efficient route for quantum state protection withoutrequiring full quantum error correction.

Rydberg entangling gates in optical-tweezer arrays are commonly executed with the trapping light switched off, so every gate contains a release--and--recapture cycle that heats the atomic motion and can ultimately limit circuit depth. We develop a motional refocusing protocol that exactly removes this heating in the harmonic approximation using only programmable intensity switching of the trapping light. The protocol closes the release--and--recapture cycle for every matched harmonic mode, returning arbitrary motional populations and coherences exactly up to ordinary evolution under the static trap. We derive the recovery sequence in closed form for arbitrary catch depth and prove that, within the experimentally relevant regime, it is the unique globally time-optimal solution under bounded trap intensity. The harmonic theory is then extended in two directions. First, we construct exact common-intensity recovery sequences that simultaneously refocus several nondegenerate harmonic modes, including radial--axial and fully anisotropic three-dimensional traps. Second, we derive a composite sequence that suppresses the leading anharmonic correction of weakly anharmonic traps by canceling all first-order motional transitions induced by the quartic anharmonicity, changing the residual heating law from $U_0^{-2}$ to $U_0^{-4}$. Wave-packet simulations in realistic Gaussian tweezers validate the analytic theory and quantify the residual effects of anharmonicity, finite switching ramps, trap ellipticity, and control errors. Applied to representative cesium Rydberg gates, the protocol suppresses the dominant recapture heating to the anharmonic floor and prevents the associated motional Doppler contribution from increasing with circuit depth. The resulting framework provides a practical route toward heating-free trap-off neutral-atom gates using only trap-intensity modulation.

The tin-vacancy (SnV) center in diamond is a promising spin-photon interface for quantum networks, combining favorable optical properties with spin coherence above 1K. Unfolding the full potential requires cavity enhancement to increase photon-emitter coupling efficiency. Here, we demonstrate cavity-enhanced light-matter coupling of SnV centers in a fully tunable Fabry-Pérot microcavity operating at temperatures down to 1K with in-situ magnetic field control. We access the diamond-like regime of hybrid cavity modes through integration of low-roughness diamond membranes, where the field is concentrated inside the diamond and Purcell enhancement is maximized. Diamond-like modes deliver a more than two-fold increase in the effective Purcell factor over air-like modes, reaching $C_0 = 4.1(1)$ compared to $C_0 = 1.85(5)$ in the air-like case, while simultaneously relaxing mechanical stability requirements. Resonant probing reveals coherent cavity-emitter coupling with 96% extinction contrast and a coherent cooperativity of $C = 4.0(14)$. By applying a magnetic field, we further achieve spin-resolved cavity extinction, observing spin-selective optical transitions with a contrast of ${\cal C}_{\rm spin} = 0.91$. These results establish SnV centers in diamond coupled to open Fabry-Pérot microcavities as a promising platform for efficient spin-photon interfaces.

Dynamic quantum circuits (DQCs) provide a hardware-efficient route to quantum computing by reducing physical-qubit overhead and compressing circuit topology through mid-circuit measurements, qubit reset and reuse, and classical feed-forward control. Here, we demonstrate the advantages of DQCs on a single hybrid superconducting qubit-cavity processor by implementing a hierarchy of algorithms with increasing complexity. This hybrid architecture consists of a high-dimensional cavity qudit serving as the computational register and a dispersively coupled superconducting transmon ancilla that is repeatedly measured, reset, and reused to enable dynamic control. Using this device, we implement a 10-bit Bernstein-Vazirani algorithm with an average success probability of 82%, surpassing state-of-the-art dynamic and static implementations in both scale and performance; an 8-bit quantum phase-estimation protocol with estimation errors below 10-3; and the first dynamic-circuit implementation of Shor's algorithm on a superconducting platform, factoring 15 over all coprime bases with squared statistical overlap values above 99.8%. These results provide concrete benchmarks for future DQC implementations and highlight the versatile advantages of DQCs with the hybrid qubit-qudit architecture, establishing it as a promising route toward scalable, programmable quantum computation.

Programmable quantum control systems increasingly rely on predictive modules for certification, real-time feedback, and autonomous decision-making. This development raises a fundamental question: can self-analyzing quantum platforms universally predict their own experimental outcomes? Wolpert formalized a general impossibility of universal self-prediction. Here we translate that limitation into an explicit laboratory obstruction that can be realized with finite resources. We consider settings with programmable quantum control in which predictors can be embedded as subroutines within the experiments they analyze. Our diagonal construction uses Kleene's recursion theorem to transform any deterministic bounded-time predictor into a reversible protocol encoding its own specification. The resulting protocol invokes the predictor on that specification and deterministically produces a classical pointer record that contradicts the forecast. For efficient predictors, the compilation has polynomial overhead and admits concrete physical realizations as a fault-tolerant quantum circuit and as a minimal Mach-Zehnder interferometer. These realizations connect computability-theoretic self-reference to programmable quantum hardware. We also introduce and formally define Gödel-safe architectures. These architectures block the forbidden causal path from the protocol description to an actuator that can affect the pointer during the same run. We analyze their implications for real-time quantum error correction, including the resulting expressiveness trade-offs. As quantum control loops grow in computational expressiveness, the limits of self-reference cease to be mere mathematical abstractions and become explicit engineering constraints for the reliable operation of autonomous quantum technologies.

Efficient simulation of Markovian open quantum systems remains a central challenge because the density-matrix description grows exponentially with system size. Quantum trajectory methods provide an alternative by replacing mixed-state evolution with stochastic pure-state realizations. Here we investigate this framework for normal Lindblad generators, whose orthogonal eigenoperator decomposition precludes transient amplification. By decomposing the Lindbladian into deterministic smooth and stochastic jump contributions, we derive an exact steady-state balance relation that identifies the interplay between these processes as the mechanism underlying Liouvillian normality. We further show that normal Lindbladians exclude exceptional points and that, although individual quantum trajectories generally exhibit stochastic coupling between Liouvillian eigenmodes, these couplings cancel upon ensemble averaging, recovering independent orthogonal relaxation modes. These results provide a trajectory-level interpretation of Liouvillian normality and clarify how a global property of the Lindblad generator is realized through stochastic quantum dynamics.

We propose and numerically validate an efficient single-eigenstate diagnostic for the eigenstate thermalization hypothesis (ETH) based on a perturbed eigenstate quench protocol. By introducing a weak random perturbation to an energy eigenstate to break its stationarity, we characterize the time-averaged subsystem evolution speed as a function of the subsystem-to-total system size ratio. The diagnostic relies on a robust qualitative distinction: eigenstates satisfying ETH exhibit an S-shaped curve with a clear inflection point near half the system size, while ETH-violating eigenstates display a convex J-shaped profile. We benchmark the criterion across paradigmatic one-dimensional spin chains covering chaotic, integrable, many-body localized, and quantum many-body scar regimes, obtaining full agreement with established thermalization phenomenology. Our method circumvents the need for explicit thermal ensemble construction, providing a robust, experimentally feasible probe of eigenstate thermalization at the single-eigenstate level.

Indefinite causal order extends quantum information processing beyond fixed causal structures, with the quantum SWITCH serving as its canonical realization. By coherently superposing different orders of quantum channels, the quantum SWITCH has been shown to provide operational advantages in communication, computation, metrology, and related tasks. Despite these advances, the physical resources responsible for these advantages remains unclear. Recent studies have further revealed that the quantum SWITCH can generate memory effects, manifested as non-Markovian information backflow. In this work, we examine the origin of such memory and determine whether they reflect genuine (quantum) non-Markovianity or instead arises from classical origin. To this end, we analyze two representative scenarios: one based on discrete-time evolution and another formulated through dynamical maps in open quantum systems. We show that the memory effects generated by the quantum SWITCH are not genuinely quantum non-Markovian, thereby prompting a re-examination of the source of quantum advantage in indefinite causal order frameworks.

High-Q silicon nitride microresonators are versatile sources for generating photon pairs via four-wave mixing. We investigate the spectral coherence of this process, tracking the transition from the spontaneous quantum regime to the onset of optical parametric oscillation. By combining time-correlation measurements with phase-sensitive measurements, we continuously monitor the emission linewidth as it evolves from a cavity-lifetime-limited linewidth toward the pump-linewidth scale. This characterization is essential for optimizing integrated sources for scalable quantum networks.

We investigate the reduced dynamics of a qubit subject to correlated longitudinal and transverse noise arising from its coupling to a shared bosonic bath. The environmental fluctuations are characterized by a positive-semidefinite matrix-valued spectral density, whose complex off-diagonal elements encode correlations between dephasing and relaxation channels in the frequency domain. Within the second-order time-convolutionless framework, we derive closed time-local equations for the Bloch-vector components of the reduced density matrix. The numerical implementation is validated against the exact pure-dephasing solution and the established behavior of the transverse-coupling spin-boson model. When both noise channels are present, the cross-spectral terms couple the otherwise distinct dephasing and relaxation sectors, producing dynamics that cannot be reproduced by adding independent noise contributions. In particular, the correlations generate non-monotonic population relaxation and a transient revival of coherence following its initial decay. The strength, bandwidth, delay, and phase of the cross spectrum provide control parameters for the magnitude and temporal structure of these effects. Our results demonstrate that correlated multi-axis noise can redistribute coherence loss and energy relaxation in time, thereby providing finite temporal windows of enhanced coherence or suppressed relaxation within the weak-coupling regime.

Individual, scannable nitrogen vacancy (NV) centers in single crystal diamond nanostructures enable nanoscale, quantitative imaging of magnetic stray fields. Nevertheless, important parameters like distance between the NV center and the sample and the orientation of the NV high symmetry axis are often not known precisely and enter data evaluation as free fitting parameters. We here use scanning NV imaging on micro-patterned, perpendicularly magnetized stripes and discs. From these measurements, we directly infer NV - sample distance d_NV and the NV's azimuthal orientation without the need for an external vector magnet control. We determine d_NV = 31.5 nm, while we infer the azimuthal orientation with a precision of 3°. We additionally employ commercially available silicon needles to image the apex topography of our diamond nanostructures to detect surface contamination. Simultaneously, monitoring NV fluorescence as a function of the needle's position allows us to estimate the lateral placement of the NV inside the diamond nanostructure.

Hamming weight computation maps an $n$-bit input to the number of ones it contains. It is a basic subroutine in quantum computing, and the core building block for symmetric Boolean functions, whose value depends only on the Hamming weight of the input. Moreover, symmetric Boolean functions are among the most common primitives in quantum computing. Efficient circuits for both problems are therefore important for the efficiency of many quantum algorithms. We study the depth-ancilla tradeoffs of Hamming weight computation under two qubit connectivity models, all-to-all and two-dimensional nearest-neighbor square grid (2D), in both the standard and dynamic circuit models. In the standard all-to-all model, we obtain depth $O(\log n)$ with a sublinear number of ancillas. In the standard 2D model, we give a circuit of depth $O(\sqrt n)$ with $O(\log^2 n)$ ancillas, and a matching lower bound showing that $Θ(\sqrt n)$ is optimal. In both dynamic models, we obtain constant-depth circuits with $O(n^{1+\varepsilon}\operatorname{polylog}\,n)$ ancillary qubits for every fixed $\varepsilon>0$. All constructions give a smooth depth-ancilla tradeoff, and they also extend to arbitrary symmetric Boolean functions.

Most existing quantum annealing approaches are formulated for qubit-based architectures. Consequently, applying them to continuous-variable optimization problems requires discretizing the variables, which can incur substantial qubit overhead. Continuous-variable quantum annealing based on bosonic systems has recently been proposed as an alternative framework, in which each optimization variable is directly encoded in a bosonic mode, such as a cavity mode. In this work, we develop a continuous-variable quantum annealing formulation for solving linear differential equations. By recasting the determination of the solution as a continuous-variable optimization problem, the differential equation can be mapped onto an objective function compatible with bosonic quantum annealing. Numerical simulations of second-order linear differential equations demonstrate that, under the conditions considered, the proposed formulation reproduces the corresponding analytical solutions. These results establish a potential route toward solving differential equations without the discretization overhead inherent in qubit-based implementations.

Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom--cavity interactions, and atomic postselection. The atom--cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.

Fault-tolerant quantum computation enables the deployment of practical quantum algorithms but incurs substantial overhead from error correction, making resource estimation a central concern. Beyond case-by-case analyses, existing quantum programming languages either require programmers to manipulate low-level hardware details, rendering fault-tolerant implementations cumbersome, or abstract away the underlying error-correction schemes, reducing the effectiveness of resource utilization and estimation. To address these limitations while preserving programmability, we present a quantum programming language that enables efficient resource utilization, together with a resource-estimation framework for comprehensive resource analysis. Our framework features programmer-visible abstractions of error-correction schemes and cross-layer program-hardware analysis, allowing systematic exploration of resource trade-offs. We evaluate our approach on detailed fault-tolerant implementations of practical large-scale quantum algorithms, including components typically treated as black boxes in existing frameworks. The results demonstrate that our framework enables substantial resource savings while delivering detailed, fine-grained, and accurate resource estimates for fault-tolerant quantum programs.

Programmable quantum annealers are used for optimization, probabilistic sampling, and simulation, but their performance is commonly reported without the energy exchanged during computation. Here we characterize the D-Wave quantum annealer as a closed thermodynamic cycle. From initial and final Ising energies and an effective temperature fitted to the output distribution, we obtain lower bounds on entropy production, environment energy exchange, work, and power. By varying the prepared distribution and the reverse annealing turning point, we map heater-, accelerator-, refrigerator-, and engine-compatible regimes in one dimensional chains and higher connectivity instances, and apply the same analysis to Advantage and Advantage2 hardware. For an encoded optimization problem, the measured processor energy change states whether final candidates improve or worsen the programmed objective on average. For sampling, the fitted temperature provides an operational measure of how strongly probability is concentrated among low energy configurations. The thermodynamic mode therefore adds information absent from solution quality or runtime alone: it distinguishes driven refinement, net heating, and heat pumping while quantifying their energetic consequences. This framework connects quantum optimization, probabilistic computing, statistical physics simulation, hardware diagnostics, and energy-aware assessment without assuming that a thermodynamic label alone determines computational performance.

Representing continuous environments by finitely many Markovian auxiliary modes is fundamental in non-Markovian open quantum systems, yet a critical question remains: at a fixed mode budget, can coherent intermode coupling reduce the spectral approximation error? We prove that intermode coupling offers no advantage when passive, number-conserving Gaussian Lindblad auxiliary networks approximate a $1/|ω|$ spectrum over a finite two-sided frequency band. For any mode budget $N$, the general coupled class and its uncoupled diagonal subclass share the same optimal error, which is exactly the degree-$2N$ Zolotarev error for sign approximation. This optimum is attainable by $N$ independent damped auxiliary modes at zero detuning. The result holds when the auxiliary network is in a stationary vacuum state, the system couples to it via a single Hermitian bath operator, and no white-noise feedthrough term is present. Consequently, although a general coupled network has $O(N^{2})$ real parameters, coherent intermode coupling, collective dissipation, and nonnormal structure cannot reduce the number of auxiliary modes required to reach a prescribed tolerance. This exact relation yields both the minimum mode count for a prescribed positive-frequency dynamic range and tolerance, and the maximum dynamic range attainable for a prescribed mode budget and tolerance.

We consider a quantum system on the real line obeying a deformed Heisenberg algebra originally proposed by Wigner in 1950. Its explicit coordinate representation was provided by Yang in 1951 and in essence is identical in form with Dunkl's difference-differential operator introduced in 1989 in connection with roots systems of refection groups. Under certain conditions such quantum systems exhibit a supersymmetric (SUSY) structure where the reflection operator acts as the grading operator. We present a generalisation of Yang's representation by first considering only of one the two equations of motion in phase space. The corresponding non-interacting system is found to represent Witten's model of SUSY quantum mechanics. Imposing also the second equation of motion the original result of Wigner and Yang is reconsidered by extending their discussion to general symmetric potentials on the real line. As explicit example we discuss the harmonic oscillator and an attractive Coulomb-like potential $V(x)=-γ/|x|$. We also establish a Hooke-Newton duality between this Coulomb-like system and the original Wigner-Yang harmonic oscillator system.

High-coherence superconducting cavities offer a promising platform for quantum information, with long coherence times and negligible intrinsic dephasing. However, cavity control generally relies on nonlinear Josephson elements whose frequency fluctuations are inherited by the cavity as dephasing, potentially limiting control fidelities and eroding the noise bias used in error-correction protocols. Here, we introduce Stark-Assisted Flux-noise Evasion (SAFE), a hardware-efficient protocol that protects the cavity from inherited dephasing using only a weak off-resonant microwave drive applied to the nonlinear element. As a concrete setup, we analyze a 3D superconducting cavity dispersively coupled to a flux-tunable transmon (FTT) subject to $1/f$ flux noise. Analytical predictions are confirmed by Monte Carlo simulations with realistic parameters, which show that SAFE can extend the cavity dephasing time by more than an order of magnitude while keeping residual drive-induced decoherence subdominant.

Optically addressable solid-state spin defects have emerged as powerful multimodal quantum sensors, with nitrogen-vacancy (NV) centers in bulk diamond providing benchmark quantum control and sensitivity under ambient conditions. Embedding such defects in nanodiamonds (NDs) extends these capabilities to mobile probes capable of accessing complex biological and nanoscale environments. Reduced dimensions, however, introduce constraints beyond volumetric spin impurities, notably enhanced lattice strain and surface-induced noise sources, which shorten NV spin relaxation times (T1 and T2) and destabilize the NV charge state, as well as resulting in pronounced particle-to-particle variability in NDs typically produced by top-down approaches. These effects complicate both sensing performance and the quantitative interpretation of multimodal signals in realistic environments. This article provides a structured perspective on the physical mechanisms by which material properties constrain NV behavior in NDs, together with mitigation strategies that shape the robust use of these mobile quantum sensors for biosensing and nanoscale science.

Partial dynamical symmetry (PDS) is an algebraic structure in which a prescribed symmetry is neither exact nor completely broken: a subset of eigenstates keeps good quantum numbers and remains solvable while the rest of the spectrum mixes. PDS is currently identified from spectroscopic data, band-head energies, level systematics, and $B(E2)$ ratios. We ask whether it also has a purely structural signature in the eigenstates, and find that it does, though not in the magnitude of entanglement. The natural diagnostic is the variance of a symmetry Casimir, the label variance $\Var\,\C[G]$, which we show coincides with a block-coherence entropy and a block impurity: all three vanish exactly when a state carries a single irreducible-representation label. Resolved state by state, this quantity is zero on the solvable subset and of order $N^2$ on the mixed states, at stable symmetry points and at Leviatan's first- and second-order critical points, where it takes two distinct forms set by the order of the transition. The magnitude of bipartite entanglement, by contrast, does not separate solvable from mixed states and drifts even where the labels are exact. We anchor the analysis in $^{168}$Er, connect the block purity to the ``purity/coherence'' language of the quasi-dynamical-symmetry literature, and show the label variance is uncorrelated with multipartite entanglement and with magic. Finally we encode the model on a qubit register and prepare its solvable and mixed eigenstates variationally, as a step toward evaluating the diagnostic on a quantum device.

We investigate how molecular orbitals used as the basis of wave function expansion and how operator coefficient-based and locality-based Hamiltonian truncation affects the computational cost of Trotter decomposition-based Hamiltonian simulation in one-dimensional hydrogen chain systems. The analysis is performed using both Hartree--Fock canonical molecular orbitals (CMOs) and Pipek--Mezey-based localized molecular orbitals (LMOs). For short hydrogen chains, we evaluate the ground-state energy and fidelity and find that, in the CMO-based wave function expansion, introducing a threshold on Hamiltonian coefficients is effective in reducing the gate cost while maintaining computational accuracy. In contrast, in the LMO-based wave function expansion, operator locality-based Hamiltonian truncation is found to be more effective. By fitting the relationship between the truncation threshold and the ground-state energies and fidelities with empirical formulas, we estimate the threshold values required to achieve high fidelity ($F \ge 0.99$) in the ground-state wave function. Using the estimated thresholds, we then perform quantum gate resource estimation for longer hydrogen chains up to H$_{100}$. The results suggest an exponential advantage of the LMO-based wave function expansion with Hamiltonian truncation: the number of quantum gates required for Hamiltonian simulation grows polynomially when the CMO-based wave function expansion with operator coefficient-based Hamiltonian truncation is adopted, whereas it grows polylogarithmically when the LMO-based wave function expansion is combined with operator locality-based Hamiltonian truncation. These results provide useful guidelines for choosing orbital representations and Hamiltonian truncation strategies in large-scale quantum chemical simulations.

Non-Gaussian operations can reshape the photon statistics of continuous-variable probes, but their metrological advantage is meaningful only when heralding probability and photon-number resources are counted consistently. We compare photon subtraction, photon addition, and photon catalysis as input-side heralding operations in a balanced SU(1,1) interferometer with parity detection. A unified finite-transmissivity map supplies closed conditional moments and the corresponding quantum Fisher information at arbitrary operation order; internal loss is absorbed into a single effective parity observable whose lossless limit recovers the ideal pulled-back measurement. At fixed preparation parameters, single-photon subtraction and addition improve the conditional phase information over the Gaussian reference across most of the high-transmissivity regime, while multi-photon catalysis opens useful low-transmissivity windows. However, when the coherent--squeezed allocation is independently optimized at fixed conditional-probe energy and fixed interferometer gain, the success-weighted Fisher information of all three non-Gaussian operations remains below the optimized Gaussian benchmark. This conclusion is subject to the tested constraints: single-photon operations, a coherent-plus-squeezed-vacuum Gaussian family, fixed gain, and parity readout. Photon catalysis separately generates a conditional branch with high local quantum Fisher information that dark-point parity extracts poorly, identifying a measurement mismatch rather than a state-preparation failure. The result draws a sharp boundary between conditional non-Gaussian enhancement and practically available precision under explicitly stated resource constraints.

We derive an analytic correspondence between multipartite concentratable entanglement (CE) and quantum phase transitions in one-dimensional quantum spin systems. We prove that CE shares the same analyticity structure as generalized order parameters, identifies the same quantum phases, and, for Gaussian ground states, is completely determined by the same single-particle correlation matrix. Numerical validation on the transverse-field Ising and generalized cluster-Ising models confirms these analytical predictions for both symmetry-breaking and symmetry-protected topological quantum phase transitions. Since CE can be measured directly using a constant-depth parallelized SWAP-test circuit, our results establish CE as an experimentally accessible, model-independent probe of quantum phase transitions without requiring model-specific order parameters.

A classical linear code $C$ of length $n$ is said to have symbol locality $(r, δ)$ if for any index $j$ there exists a repair group $J_j \subseteq \{1, \ldots, n\}$ with $j\in J_j$ and $|J_j| \leq r+δ-1$ such that any $δ-1$ or fewer erasures in $J_j$ can be corrected by using codeword symbols only in $J_j$. Later it turned out that this way of defining $r$ overestimates the number of necessary codeword symbols for multiple-erasure correction, and information locality was proposed to define $r$ as the dimension of the punctured code of $C$ onto $J_j$. Recently locality $(r,δ)$ was proposed for quantum error-correcting codes by following the original definition of symbol locality $(r, δ)$. We propose a quantum counterpart of the information locality for quantum stabilizer codes constructed by Hermitian orthogonality, and a linear algebraic procedure computing a smaller repair group predicted by the proposed information locality and simultaneously reducing the number of measured observables in decoding to its minimum possible value. Then we demonstrate that the previously proposed definition of quantum locality $(r,δ)$ has the same drawback of overestimating the number of necessary codeword symbols for erasure correction by providing an explicit example of a quantum stabilizer code. Finally, we will give another example of a quantum stabilizer code constructed by Euclidean orthogonality and two different linear codes, with which a natural translation of the classical information locality into the quantum setting underestimates the number of necessary codeword symbols for erasure correction.

We establish scaling relations governing the equilibrium thermodynamics of real-spectrum non-Hermitian Dirac fermions in a magnetic field. Assuming thermalization with respect to the quasi-Hermitian Hamiltonian, a similarity transformation maps the system at the same applied field onto a Hermitian Dirac model with reduced velocity, while the Landau-level spectrum also admits a representation in terms of a reduced effective magnetic field. This structure yields scaling relations for the chemical potential, entropy, heat capacities, and orbital magnetic response in different thermodynamic ensembles. At fixed projected filling factor (PFF), the self-consistent chemical potential follows the compressed ladder of Landau levels, and the canonical thermodynamic functions are rescaled Hermitian responses. At fixed chemical potential, Landau-level crossings generate oscillatory caloric and magnetic responses governed by the same spectral compression. Quasistatic non-Hermitian deformation at fixed PFF further yields adiabatic temperature scaling. More broadly, these results establish a thermodynamic framework for real-spectrum non-Hermitian quantum matter and provide a starting point for incorporating the effects of interactions and disorder within the same formalism.

This paper presents self-contained, constructive proofs of two new theorems about stochastic matrices, with direct relevance to quantum theory. The first theorem, herein called the Born Representation Theorem, shows that each entry of any stochastic matrix can be expressed as the trace of a pairwise product of matrices, where the first factor in the pairwise product belongs to a positive-operator-valued measure (POVM) and the second factor belongs to a projection-valued measure (PVM). As its name suggests, this theorem entails that the entries of any stochastic matrix can be expressed in terms of a generalized version of the quantum-theoretic Born rule. It follows as a corollary that if the POVM in this first theorem is a PVM, then the stochastic matrix is unistochastic, meaning that its entries are each the modulus square of the corresponding entry of a unitary matrix of the same size. The second theorem proved in this paper, called the Unistochastic Theorem, then shows that by dilating the underlying vector space by a bounded number of additional dimensions if necessary, each entry of any stochastic matrix can be expressed in terms of the trace of a pairwise product for which both factors belong to PVMs, and can thus be derived via marginalization from a larger unistochastic matrix. This second theorem therefore establishes a kind of primacy of unistochastic matrices over stochastic matrices, and hints at a close connection with unitary time evolution in quantum theory. The paper concludes with a brief discussion of potential applications to discrete-time deterministic processes and Markov chains.

Measurement-based quantum simulation (MBQS)---a recently proposed architecture for simulating lattice gauge theories---implements Hamiltonian dynamics by consuming a model-specific entangled resource state with adaptive mid-circuit measurements, rather than by a gate-based circuit. The local constraints in lattice gauge theories are mirrored by the higher-form symmetries of the resource state. Here we report, to our knowledge, the first experimental realization of MBQS of real-time dynamics in the $(2+1)$-dimensional $\mathbb{Z}_2$ gauge theory using the Quantinuum System Model H2 trapped-ion processor. We observe coherent evolution of gauge-invariant observables on $2\times2$ and $3\times3$ spatial lattices, consuming virtual three-dimensional cluster states of 200 and 288 resource-state qubits that are generated from instantaneous blocks of 48 and 54 qubits within the 56-qubit register by measurement, reset, and re-entanglement. The measurement record that drives the evolution simultaneously provides one-form-symmetry syndromes at no additional cost, enabling postselection that strongly suppresses observed Gauss-law violations and improves aggregate agreement with ideal Trotterized dynamics. Our results demonstrate that MBQS is a viable, symmetry-aware architecture for simulating lattice field theories on present-day hardware.

We study quantum implementations of the contraction $\exp(-T H^α)$ for $H=H^\dagger\succeq0$ and $α>0$. Poisson summation provides an exact target--alias--tail decomposition whose Fourier samples are compiled classically into a single Chebyshev polynomial, so the quantum circuit uses polynomial eigenvalue transformation rather than a frequency linear combination of unitaries. We compare block encodings of $H/\norm{H}$ and of the shifted signal $2H/\norm{H}-I$. Under ordinary single-sequence QSVT, parity forces the former to use an even extension, which is entire only for even positive integers. An exact quadratic lift for the shifted signal makes every positive integer entire and improves the fixed-scale approximation error for noninteger powers from $Θ(d^{-α})$ to $Θ(d^{-2α})$ within the stated access and parity classes. We derive matching degree bounds in the large-scale fixed-error and fixed-scale high-precision limits, including the output-normalization overhead $u_r$. Nearest-neighbor Laplacians give a unit-normalized shifted signal. We further establish a noncommutative Weyl--Poisson identity compatible with LCHS quadrature, and use the same polynomial construction to implement controlled dissipative families in amplitude--phase separation.

In this paper, we derive a quantum optics model in a non-inertial rotating ring cavity from first principles. We begin with the Dirac equation in curved spacetime, add minimal coupling to the electromagnetic field, and then find the Dirac Hamiltonian for the generalized Born metric. We then formally take the non-relativistic limit by way of Foldy-Wouthuysen transformations and project onto a fermionic Fock space for the atoms' electrons, protons, and neutrons. Focusing on a protium atom, we next move from a minimal coupling gauge to a multipole expansion gauge by taking a Power-Zienau-Woolley transformation under the dipole and long-wavelength approximations. Here, we find additional terms from the rotation of the system including a rotation-induced hyperfine shift of the atomic transition which could possibly be observed experimentally even for small rotation rates. Making the electric dipole, two-level, and rotating-wave approximations, we arrive at a Jaynes-Cummings-like Hamiltonian which also accounts for rotational effects, such as the rotation-induced hyperfine shift and the Sagnac shift for the cavity's counterpropagating modes.

Tensor-network contraction simulates quantum circuits, but modern matrix accelerators (NPUs, TPUs) expose only real GEMM pipelines, so the complex networks of quantum simulation must be reconstructed in software. We resolve the mismatch by a realification rewrite that maps any complex tensor network to a real one. At each merge of two complex tensors, a rank-3 structure tensor realizes Gauss's three-multiplication (3M) formula; contractions with one or no complex operand need only two or one real products. We prove a tight cost law: overhead $1 + 2m + r$ in real multiplications, where $m$ and $r$ are the volume fractions of two- and one-complex-operand contractions, never exceeding $3\times$ relative to real contraction, with every intermediate at most doubled in size. On 67 circuits (random, Clifford+$T$, QAOA, VQE), the law holds across the real-to-complex range and complex-gate placement, not count, governs cost. Contraction orders transfer from the complex network with a relative arithmetic-cost gap below $5\times 10^{-4}$ on 66 of 67 circuits; the exception closes under a few steps of low-temperature simulated annealing. On an Ascend 910 NPU the rewrite beat both the four-real-GEMM baseline and a per-GEMM Gauss lowering on all twelve random circuits and on 52 of 55 structured cells (three cells slower by at most 12\%); the four-GEMM baseline was slower by a median $1.7\times$ (random) and $1.4\times$ (structured). Realification makes complex tensor-network contraction native to real-only matrix engines.

It is well established that quantum strategies outperform classical ones in several communication tasks. We study the quantum communication complexity of correlations arising from joint measurements on quantum systems distributed across a star network, where several parties each send a quantum system to a central node. We introduce an exclusion task that can be solved perfectly when each party sends a quantum $d$-level system, but would require a large classical message otherwise. In fact, the task cannot be solved with certainty if each of the $n$ parties sends a classical message with less than $n^{(d-1)}$ symbols. This implies an advantage of using quantum over classical messages in that scenario that scales with both, the dimension of the quantum system and the number of systems measured simultaneously. As an application, this shows that no finite-size classical description of a qubit suffices to reproduce the statistics of a joint measurement on sufficiently many qubits.

Characterizing multinode quantum networks without ubiquitous local entanglement sources presents significant experimental challenges. We introduce ``quantum telephone,'' an iterative ancilla-assisted process tomography protocol that leverages intermediate detection events, effectively treating previously probed links as ancillae for subsequent links. Implemented on a deployed multinode fiber network, we observe noisy intermediate channels create fundamental parameter degeneracies that compound inference errors under sequential estimation. Counterintuitively, the inclusion of downstream near-unitary channels provides boundary constraints that, when used in tandem with global inference, can resolve ambiguity in channels earlier in the sequence. By compensating for localized information loss, this approach obviates the strict full-rank requirements of standard ancilla-assisted process tomography, even when intermediate states become completely depolarized. Overall, quantum telephone offers a hardware-efficient and information-maximizing path toward characterizing complex quantum networks with limited resources.

Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional separations between low-depth quantum computation and the corresponding bounded-resource classical language-model architectures in both regimes. Concretely, we exhibit the following: 1. Distributional separation. We give a distribution that is sampleable by $\textsf{QNC}^0$ circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model ($\textsf{DLM}$) with shallow scheduling and denoising can sample within constant distance, even when allowed sublinear chain-of-thought and output-token revision/remasking events, the very features modern $\textsf{DLM}$s rely on. 2. Functional separation. We exhibit a function computable in $\land \circ \textsf{QNC}^0[\log\log n]$ (i.e., a family of O$(\log\log n)$-depth $\textsf{QNC}^0$ circuits, where $n$ is the input length, followed by a single classical $\mathsf{AND}$ gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width $n^{Ω(1)}$. Together, our work initiates the study of quantum advantage in the era of large language models.

Integrated photon-pair sources are a core component of chip-based quantum computing, communication, and metrology. Although such sources have been demonstrated at conventional telecom wavelengths, the 2 $μ$m band remains comparatively less explored, despite offering advantages for free-space quantum communication, low-loss transmission in emerging fiber networks, and integration with silicon photonic platforms. In this paper, we demonstrate spontaneous parametric down-conversion (SPDC) in straight GaAs- and AlGaAs-on-insulator waveguides. This platform offers strong second-order nonlinearity and geometry-tunable dispersion, which are advantageous for efficient on-chip pair generation. Measurements of the joint spectral intensity and heralded second-order correlation function show broadband emission around 2 $μ$m with strong spectral anti-correlations. To our knowledge, this is the first direct joint-spectral characterization of an integrated SPDC source in this wavelength regime.

Quantum error correction (QEC) is indispensable for building scalable fault-tolerant quantum computers. Effective QEC demands stringent real-time decoding: the decoder must process syndrome measurements and determine corrections within a time scale--typically on the order of microseconds, to avoid data backlog. Scaling to large number of logical qubits further necessitates significant computational resources. In this work, we propose an architecture, called \emph{THQLink}, for real-time decoding of quantum error correction codes using high-performance computing (HPC) resources. The network connecting the HPC and the control system of quantum processing unit (QPU) is built on TH-Express and can be adapted to different quantum technologies and their associated control stacks. We report a round-trip latency of 2.944 $μ$s on average, with an incremental overhead of 130 ns per additional hop. Using a parallel window strategy, we demonstrate real-time decoding (1 $μ$s per QEC round) of the surface code up to distance 19 using a matching-based decoder on CPUs. Our work presents a scalable framework for real-time decoding in fault-tolerant quantum computing. It can be readily applied to quantum-centric supercomputers that feature tight integration between QPU and HPC resources, thereby enabling efficient support for hybrid quantum-classical algorithms and computation-intensive workloads offloaded from the QPU.

Quantum error correction (QEC) and Quantum Darwinism describe opposing consequences of system-environment interactions: QEC seeks to preserve logical quantum information, whereas Quantum Darwinism explains the emergence of objective classical information through its proliferation into the environment. Despite their common physical origin, no direct quantitative connection between these paradigms has previously been established. We introduce an exactly solvable block-environment model based on the logical GHZ block of the Shor [[9,1,3]] quantum error-correcting code, collectively coupled to N environment qubits. The logical fidelity, Holevo information, and Darwinistic redundancy are obtained systematically for arbitrary environment size and imperfect recovery efficiency. Eliminating the common decoherence parameter yields an exact tradeoff relating Darwinistic redundancy directly to the post-recovery logical fidelity, demonstrating that the emergence of redundant classical records occurs at the expense of logical quantum information. We further prove a model-independent no-go theorem showing that the logical fidelity exceeds a critical threshold precludes the emergence of Darwinistic redundancy, irrespective of the microscopic Hamiltonian or environment structure. The solvable model saturates this general bound, establishing the first quantitative information-theoretic connection between logical quantum information protection and the emergence of redundant classical records.

Current quantum programs are mainly designed at the level of quantum gates acting on individual qubits; on a large scale and for complex problems this may involve a high cognitive load on the programmer, making the program specification nontrivial and error-prone. In this context, providing quantum programming with higher abstraction mechanisms will assist in making this task more manageable and robust against design errors. In this work, a conceptual framework is addressed following the notion of the whole quantum computation as a structure composed of quantum registers representing each an undivided entity. Thus, computation progresses through semantically well-defined transformations that act on, or entangle, quantum registers, thereby modifying the global state. Ultimately, the program reaches the desired state by following a specific composition strategy. With this in mind, high-level syntax is presented through an algebraic formalism that bridges them with their low-level semantics. Proposed syntax is based on certain well-know operations used on quantum algorithms that apply phase shifts upon logical condition satisfaction or leverage on parallel evaluation. Based solely on the formalized operations, a quantum satisfiability modulo theories (SMT) solver can be designed. At its core, this work contributes to establishing some methodological principles towards realizing a high-level quantum structured programming.

Multi-tone external driving offers a route to parametric physics without directly modulating the device. However, the validity of the parametric response in the few-photon regime remains underexplored. Here, we apply two coherent microwave tones to a Josephson-junction Kerr oscillator and stimulate degenerate parametric downconversion via four-wave mixing. Using transmission spectroscopy, we observe that the response retains the qualitative semiclassical Kerr parametric oscillator structure, including its instability lobe and bistable phase-space topology. Interestingly, we demonstrate that a conventional single-mode reduction fails to capture the system quantitatively: the predicted AC Stark shift is severely underestimated, and the reported distributions might not be fully physical when the single-photon Kerr shift $K$ exceeds the cavity linewidth $κ$. Instead, we show that a full three-tone quantum description accurately reproduces the experimental observables. There, quantum fluctuations of the drive tones become dynamically dominant over dissipation, and all three interacting tones operate in a deep few-photon limit where the expected semiclassical macroscopic lobes undergo fundamental renormalization due to profound mixing with quantum variance. Our results establish two-tone-driven Kerr oscillators as potential parametric amplifiers and open new horizons to explore the quantum-to-classical crossover in driven-dissipative circuits.

The influence of environmental decoherence on quantum teleportation is investigated by considering the three-qubit Maximally Sliced (MS) state as the shared entangled resource. Using the Kraus operator formalism, analytical expressions are derived for the teleportation fidelity under amplitude damping and phase damping channels. The corresponding basis-independent coherence is obtained, establishing explicit analytical relations between coherence and teleportation fidelity under both decoherence mechanisms. The results are further expressed in terms of the Coffman-Kundu-Wootters (CKW) three-tangle, thereby connecting genuine tripartite entanglement with teleportation performance. The analysis reveals distinct effects of the two noise channels: amplitude damping introduces a state-dependent threshold for achieving quantum teleportation, whereas phase damping preserves the quantum advantage until complete dephasing. These results provide a unified analytical framework for understanding the interplay among multipartite entanglement, quantum coherence and teleportation in noisy three-qubit MS states.

Symmetry-protected topological (SPT) phases provide a platform for encoding quantum information in protected boundary degrees of freedom. Here we study the three-leg Affleck-Kennedy-Lieb-Tasaki (AKLT) ladder as an exactly solvable SPT system with on-site symmetry $SO(3)\times \mathbb{Z}_2$. Using an exact matrix product state construction, we characterize the symmetry action on the edge encoding space and the accessibility of this space by local operators. We find that the continuous $SO(3)$ symmetry induces boundary rotations, while the leg-exchange symmetry generates a geometry-dependent logical permutation of edge qubits. Furthermore, by introducing a distinguishability measure motivated by the Knill--Laflamme condition, we derive a symmetry-resolved decay law for local accessibility. The decay is controlled by a selection rule raised from the Wigner--Eckart theorem, whereby a rank-$\ell$ local operator couples only to the $\mathcal L=\ell$ transfer-matrix sector, with a decay length determined by the corresponding correlation length. We further identify a finite-size channel that is independent of the probe operator position. These results establish a quantitative connection between SPT symmetry, lattice geometry, and the protection of boundary-encoded quantum information.

Correlations measured in complementary local bases provide an experimentally accessible probe of the total correlations in a bipartite quantum state. The complementary-quantum correlation conjecture asserts that the sum of two such classical mutual informations never exceeds the premeasurement quantum mutual information. We disprove this conjecture in every local dimension $d\geq3$ with an explicit rank-two separable state. One of the two complementary measurements recovers the complete one-bit branch label, while the other retains additional classical correlation. For qutrits the excess is exactly $\frac13\log_2(3456/3125)=0.0484156759\ldots$ bits. Continuity yields full-rank separable violations. The effect therefore requires neither entanglement nor quantum discord; it arises from two complementary readouts of the same classical latent variable.

Given $A\in\operatorname{GL}(N,2)$ and an integer $K$, we ask whether $A$ can be implemented by at most $K$ CNOT gates on fixed labelled wires with all-to-all connectivity. We prove that this problem is NP-complete. From a finite simple graph $G=(V,E)$, we construct an upper-unitriangular matrix $A_G\in\operatorname{GL}(2|V|+|E|+1,2)$ satisfying $\ell_{\mathrm{CNOT}}(A_G)=2|V|+2|E|+τ(G)$, where $τ(G)$ is the minimum vertex-cover size. Each target matrix has $O(N)$ nonzero entries and row Hamming weight at most four. The lower bound unfolds an arbitrary CNOT circuit into an XOR directed acyclic graph and applies projection--contraction operations, allowing cancellation and unrestricted reuse of intermediate parities. For this family, the optimum is unchanged by any finite number of clean or borrowed ancillary wires that must be restored. A polynomial-time decoder further yields NP-hardness of approximation within every fixed additive constant and, through an L-reduction from Minimum Vertex Cover on cubic graphs, APX-hardness of the associated CNOT-circuit optimisation problem.

This paper proves that it is impossible to construct perfectly complete quantum key agreement protocols (QKA) from quantumly secure one-way functions (OWFs) in a black-box manner. Specifically, consider any protocol in which Alice and Bob exchange only classical messages, make at most $q_{\mathsf{A}}$ and $q_{\mathsf{B}}$ quantum queries, respectively, to a Boolean-valued random oracle, and agree on a shared key with certainty. This paper shows that there exists an eavesdropper, given the classical messages, that can recover the shared key with certainty using $O((q_{\mathsf{A}}+q_{\mathsf{B}})^5)$ classical oracle queries. The bound is independent of the number of rounds, transcript length, key length, and oracle-domain size. Previous results only applies to two-round key agreement (Li et al. CRYPTO 26) or relies on unproven conjectures (Austrin et al. CRYPTO 22). GPT-5.6 Sol Ultra found this proof in a one-shot conversation and drafted a preliminary version of this paper. The authors are fully responsible for the correctness, writing and discussions of this paper.

Vacuum Rabi oscillations between a single photon and a single spin demonstrate the capability of harnessing light-matter interaction at the level of a single quantum of energy. Since the observation of strong spin-photon coupling in gate-defined quantum dots, probing this interaction in the time-domain has been a major objective. Here, we carefully engineer a device composed of two spatially separated double quantum dots hosting single electron spin qubits and a superconducting cavity to accommodate microwave photons. We observe multiple vacuum Rabi oscillations between each spin qubit and the cavity. By concatenating vacuum Rabi oscillations involving the two spins, an energy excitation in one qubit can be emitted as a photon and then transferred to the other qubit. When a single photon is emitted, the cavity is prepared in a Fock state, leading to an accelerated vacuum Rabi frequency. These results serve as building blocks not only in exploring light-matter interactions, but also in interfacing semiconductor spin qubits to photonic links.

The simplex of complete graphs, also known as the first-order truncated simplex lattice, is a network of $M+1$ identical complete graphs, each with $M$ vertices, such that each clique contains an edge or bridge to every other clique. It contains $N = M(M+1)$ vertices, and previous asymptotic results using a continuous-time quantum walk to search this graph for a single marked vertex have either numerically demonstrated an optimal runtime of $O(\sqrt{N})$, or analytically proved a deterministic success probability of 1, but not both, even when the bridges are weighted. In this paper, we give the first analytical proof of optimal quantum search on this graph, proving that it occurs when the weight of the bridges equals $M$. In addition, we numerically show that the optimal runtime is achieved more broadly whenever the weight is at least $\sqrt{M}$. Furthermore, the algorithm is also deterministic when the weight scales between $\sqrt{M}$ and $M$, and this is the first example of quantum search on the simplex of complete graphs that is both asymptotically optimal and deterministic. In addition, for weights where the algorithm is nondeterministic, we give a way to find the marked vertex by inspecting neighboring vertices. Finally, while it is known that connectivity is not a reliable indicator of fast quantum search when comparing different graph families, we show that it is also unreliable within the graph family of weighted simplex of complete graphs.

Gaussian states are fundamental in continuous-variable quantum information, yet characterizing non-Gaussianity remains challenging due to the non-convexity of the Gaussian set. Existing witnesses typically rely on Wigner negativity or other information-theoretic quantities. In this work, we develop a group-theoretic, multi-copy approach to detect non-Gaussianity in bosonic systems. We study passive linear optical transformations that mix copies of a quantum state and analyze their commutation with identical Gaussian unitaries applied to each copy. Orthogonal copy-mixing transformations commute with the symplectic part of the Gaussian action, while the displacement part restricts the symmetry to the stabilizer of the collective mode. This structure yields a family of witnesses satisfied by all single-mode Gaussian states. Fixing the thermal reference parameter via the purity, violation of these identities certifies non-Gaussianity. We illustrate the method with several single-mode examples and present an experimental protocol based on passive interferometry and photon-number-resolved detection, showing that the relevant multi-copy expectation values can be estimated from bounded phase observables. Finally, we extend the construction to multi-mode systems and discuss how the same symmetry framework may lead to quantitative measures of non-Gaussianity.

Solids appear to have localised centres of mass, yet many-body quantum theory describes them using translationally symmetric models that preclude localisation. Conventionally, this is resolved through spontaneous symmetry breaking by introducing an interaction with a semiclassical environment that breaks the symmetry. In the thermodynamic limit, the interaction can be removed while leaving the state localised. This, however, raises the question of how localisation arises outside the thermodynamic limit, i.e., in finite quantum systems (Wallace, 2018). Here, we show that, by quantising the environment, the localisation of finite systems occurs within decoherent branches, while the state vector of the composite system remains translationally symmetric. Our approach is analogous to the Page-Wootters construction (Page & Wootters, 1983) and quantum reference frames; moreover, we recover the semiclassical description as a limiting case while predicting experimentally distinguishable corrections away from this limit.

Cavity quantum electrodynamics offers a route to control quantum phases by using vacuum fluctuations of confined electromagnetic fields. In particular, planar cavities based on polar van der Waals materials can generate strongly confined modes and are promising for controlling two-dimensional correlated materials. Recently, moiré materials have become central platforms for studying two-dimensional heavy-fermion systems and their quantum phase transitions. Kondo lattices provide a prototypical model for studying quantum phase boundaries, driven by competition between Kondo screening and the ordering of local magnetic moments. We show that a cavity-induced interaction can shift the quantum phase transitions between a heavy-fermion phase and an antiferromagnetic phase in a two-dimensional Kondo lattice through a momentum-dependent self-energy of the conduction bands. For the longitudinal projected field motivated by h-BN hyperbolic phonon polaritons, the self-energy favors Kondo hybridization and expands the heavy-fermion region. Transverse and circular in-plane model structures give distinct effects, with the transverse case relatively favoring the magnetically ordered phase and the circular case lying between the longitudinal and transverse cases. These results indicate that electromagnetic vacuum fluctuations can effectively modify the control parameters of strongly correlated two-dimensional Kondo materials.

Entanglement distillation is a fundamental task in quantum information processing. In this work, we investigate the distillability properties of a class of two-qutrit symmetric NPT states of rank five. We resolve the 1-distillability problem for this class by proving that the previously open interval of the eigenvalue parameter is 1-undistillable. For the 2-distillability, we uncover a structural obstruction showing that no Schmidt-rank-two vector has a negative expectation in the relevant subspace. We also perform numerical investigations to explore the 2-distillability beyond this obstruction.

Quantum optimal control is a key tool for steering quantum dynamics, but its computational cost grows rapidly with the Hilbert space dimension. Here, we introduce a Fourier Neural Operator (FNO)-based framework for learning high dimensional molecular quantum dynamics and accelerating the inverse design of control protocols. Given an initial molecular population distribution, laser frequency, and polarization, the FNO predicts molecular-motional population dynamics up to $10^7$ times faster than GPU-accelerated numerical propagation with CUDA-Q Dynamics. Using this fast and differentiable surrogate, we develop the FNO stochastic pulse-measurement planner (FNO-SPMP), which constructs pulse sequences to purify an initially mixed Boltzmann distribution. We demonstrate the protocol in an 888-dimensional subspace of the hydronium molecule at 20 K, achieving a target-state population of 0.98 with a sequence success rate of up to 86.2%. In a shared discrete control space, FNO-SPMP achieves nearly twice the success rate of a reinforcement-learning baseline while using roughly half as many quantum control pulses and reducing pulse-sequence generation time from approximately 10 hours to 10-20 minutes. These results show that operator-learning surrogates can enable inverse design in quantum systems whose Hilbert spaces are too large for conventional direct optimization.

We develop a structure-specific fidelity-threshold robustness margin for finite-dimensional closed quantum systems under piecewise-constant coherent control. A scalar physical parameter may perturb the drift, a control Hamiltonian, or another declared Hamiltonian component across the control horizon. A differential sensitivity bound for trace-amplitude gate fidelity yields a threshold-dependent Lipschitz constant on the connected safe parameter component and hence a certified finite perturbation radius. Recentering this certificate produces an iterative one-dimensional method that takes certified safe steps toward the first fidelity-threshold boundary in either parameter direction. A three-qubit gate-control example shows that these finite margins vary by up to a factor of three across controllers of comparable nominal fidelity and contain structure-dependent information not captured by nominal differential sensitivity alone.

DAMPyF is an open-source Python implementation of the dissipation-assisted matrix product factorization (DAMPF) method, a tensor-network-based approach for the numerically exact simulation of finite-dimensional quantum systems coupled to bosonic environments. The method relies on a pseudomode representation of structured reservoirs and a matrix-product-state representation of the density matrix of the extended system, comprising the system and the pseudomodes. DAMPyF currently provides two workflows. First, it supports excitation energy-transfer dynamics within the single-system-excitation manifold, in which a system excitation is propagated in time. Second, it provides a high-level workflow tailored to molecular spectroscopy, in which the system levels represent electronic states and optical coherences are propagated for the subsequent computation of linear spectra, including absorption and circular dichroism. This paper describes the physical model, the DAMPF algorithm, the user-facing code structure, installation and execution, input and output formats, and minimal examples.

Two-dimensional quantum gases provide a distinctive setting in which enhanced thermal fluctuations, finite-size effects, and two-body bound-state formation are intrinsically intertwined. In this work, we study a single attractive impurity immersed in a finite, weakly interacting two-dimensional Bose gas, where finite size stabilizes a nonzero condensate fraction by introducing an infrared momentum scale, thereby enabling a Bogoliubov description of the bath. Using a hybrid approach that combines finite-temperature many-body scattering theory with input from path-integral Monte Carlo, we analyze the impurity quasiparticle energy across the condensate and normal regimes. The infrared scale generates a phonon-activation temperature below which the impurity energy remains nearly temperature independent. Once the resolved phonon modes become thermally populated, their contribution competes with condensate depletion, producing a nonmonotonic temperature dependence of the polaron energy. These results suggest that attractive Bose polarons may serve as sensitive probes of finite-size thermal fluctuations, phonon dressing, and bound-state physics in low-dimensional Bose gases.

We investigate the generation of deterministic and heralded non-Gaussian states of light, using a single two-level system coupled to a chiral waveguide. We study the case of a single two level system driven by pulsed coherent and squeezed drive in a chiral waveguide. For coherent input pulses, we show that the emitter can deterministically generate Wigner-negative states, albeit of limited rank. Going beyond, using squeezed-vacuum inputs, we show that the interaction produces bimodal non-Gaussian states from which higher-stellar-rank states, including large squeezed cat states, can be experimentally extracted with a substantial success rate. Motivated by experimental implementations, we further analyze the effect of imperfect coupling and of the intrinsic $50\%$ collection limit of symmetric, non-chiral waveguides. Finally, we propose a simple interferometric scheme that recovers an effectively chiral interaction in an otherwise bidirectional waveguide.

In quantum optimal control theory, gradient-based trajectory optimization techniques have proven versatile in designing multi-qubit quantum gates. Furthermore, incorporating the underlying Lie-group structure can accelerate the optimization process. In this work, we adapt the Lie-group formulation of the iterative linear quadratic regulator (iLQR) to the special unitary group SU(N) and apply it to quantum gate synthesis, systematically comparing it against the standard Euclidean iLQR formulation across multiple two- to five-qubit gates. We find that in the idealized, unconstrained setting, where all Lie-algebra basis elements are available as drive Hamiltonian terms, the Lie-group formulation converges faster than the Euclidean iLQR formulation. If drive terms are constrained to 2-local Hamiltonian terms, the Lie-group variant converges faster in early optimization iterations, but exhibits greater sensitivity to initialization and a stronger tendency towards local minima. These results demonstrate that incorporating Lie-group geometry into iLQR substantially improves convergence and highlight important next steps for improvements in constrained control settings.

The quality of multi-scale modelling techniques in molecular electronic structure calculations, such as embedding and subspace methods, relies upon the chosen active space. The automation of active space selection is vital for ensuring the accuracy, reproducibility, and scalability in such calculations. In this work, we introduce Tensor Network Active Space Selection using the Entanglement Feature. Through the isolation of strongly correlated electrons, this method provides a scalable foundation for embedding methods in multi-scale modelling. By representing the purities of all possible orbital partitions as a Matrix Product State, our method isolates regions of strong electron correlation without requiring manual preselection of target atoms or the calculation of expensive high-order density matrices. The results demonstrate that this approach leads to lower ground state energies and more accurate dipole moments than other fully automated selection schemes such as those based solely on single-orbital entropy or the selection of spatial orbitals around the HOMO/LUMO gap.

An isolated occupied multiplet may admit local tensor-product descriptions without a globally consistent subsystem structure. We characterize the obstruction by comparing the transition functions of the occupied multiplet with those generated by independent basis changes in the two candidate subsystems. When a decomposition into rank-one sectors over a closed surface is specified, the resulting quotient removes row- and column-additive Chern data and yields mixed Chern classes. Momentum-dependent mixing of the sector labels adds the Gauss--Codazzi curvature of the moving lines, while in the label-conserving limit the mixed class is measured by a crossed Thouless pump. When only the factor dimensions $p$ and $q$ are specified, the comparison is made at the level of the clutching map of a rank-$pq$ bundle over $S^4$. Product frames generate winding numbers in $q\mathbb Z+p\mathbb Z$, so global factorization is possible exactly when $C_2$ is divisible by $\gcd(p,q)$; in particular, odd $C_2$ obstructs a $2\times2$ factorization. We illustrate the two settings with finite eight-level Hamiltonians and give pumping and occupied-projector tomography protocols for their readout.

Quantum technologies have been widely recognized as unprecedented opportunities for ultra-high precision metrology. As a celebrated example in modern quantum optics, the Hong-Ou-Mandel (HOM) interferometer is well-known for enabling temporal resolutions on the attosecond scale. However, the relatively low Fisher information per trial in ordinary HOM measurements typically necessitates tens of thousands of repetitions to achieve such precision. Here, we propose and demonstrate a sample-half-inserted HOM (SHOM) interferometer, which enhances the Fisher information by five orders of magnitude in a single interference event. By introducing an asymmetric photon-sample interaction, the SHOM configuration produces a distinctive dip-bump-dip interference structure, converting what was previously viewed as an artifact into a helpful metrological resource. Experimentally, we measured the optical path difference with an average precision of 4.09 nm (13.63 as) and an average accuracy of 1.22 nm (4.07 as) using $O(10^7)$ photons. Our results establish SHOM interferometry as an efficient phase-insensitive approach, not only paving the way toward practical quantum-enhanced thickness measurement for transparent materials, but also serving as an elegant strategy to improve the performance of various quantum devices.

This study investigates the generation and enhancement of quantum entanglement in an electro-optomechanical ring cavity system. The setup integrates two Coulomb-coupled mechanical resonators, which serve as the fundamental mechanism for the generation of bipartite and tripartite entanglement via charge mediated coupling. We then demonstrate the significant enhancement of this entanglement via a nonlinear parametric drive (an optical parametric amplifier, OPA), which injects a controllable nonlinearity into the cavity. We derive the system's Hamiltonian and the corresponding quantum Langevin equations, which are linearized around steady-state solutions to analyze Gaussian quantum fluctuations. Employing the covariance matrix formalism, we quantify bipartite entanglement via logarithmic negativity and tripartite entanglement via the minimum residual contangle. Our results unequivocally show that while the Coulomb interaction is indispensable for creating entanglement, the OPA acts as a powerful control tool, dramatically amplifying the degree of quantum correlations for all subsystems. We find that the strength of entanglement is highly sensitive to several parameters and can be optimized through the strategic selection of the OPA's gain and phase, the laser detuning, and the input power. A key finding is the existence of a trade-off, where parameters that maximize entanglement also constrain the stable operating regime of the system. Furthermore, thermal noise is shown to progressively degrade all quantum correlations, underscoring the necessity for low-temperature operation. These findings provide comprehensive guidance for parameter optimization, outlining a clear path from generation to enhancement, and highlight the potential of such hybrid systems as versatile platforms for controlling multipartite entanglement in quantum technologies.

Quantum causal networks enable tests of nonclassicality beyond Bell nonlocality while relaxing some physically unwarranted assumptions. By relaxing the freedom-of-choice and spacelike-separation assumptions, the unrelated-confounders causal networks provide a simple and robust route to certify quantum nonclassicality. Here, we implement the minimal three-node unrelated-confounders network in an optical experiment using two independent polarization-entangled photon sources and an intervention at the central node, experimentally achieved with a high-fidelity entangling measurement. We employ a causal data-fusion protocol that combines observational and interventional data to significantly improve the protocol's noise tolerance, and observe a violation of the corresponding hybrid causal inequality by more than three standard deviations. Our results provide deeper insights into quantum nonlocality in networks and highlight the UC network as a compact, experimentally accessible platform for device-independent quantum protocols that do not require actively chosen measurement settings.

The gravitational frequency shift of light is well understood in the theory of classical electromagnetism. Nevertheless, its description in quantum theory is not yet fully developed. Recent work pointed out inconsistencies in previously developed models aimed at describing gravitational redshift as an effective multi-mode mixer (MMM) acting on modes of light, however, a complete solution of the issues was not obtained. Here, we identify the root cause of the MMM model's inconsistency and provide two complementary approaches to correct it: a "natural" one from a field-theoretic perspective, and another adapted to the language of quantum mechanics of finite-dimensional systems. We show that the second approach allows for modeling of the redshift in a multi-mode transmission setup as a quantum channel that can be characterized using standard quantum information-theoretic techniques when restricting the input states to Gaussian states of light.

Classical simulation of quantum circuits is an essential tool in quantum information science, but its applicability is constrained by the exponential growth of the Hilbert space and the entanglement structure of quantum states. In this work, we introduce Matrix Product Evolution (MPE), a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index. Within this formulation, the simulation of a quantum circuit is modeled as the contraction of multiple MPE tensors. We develop an efficient contraction strategy based on a zip-up procedure to carry out this contraction in practice. We investigate the numerical behavior of this MPE-based contraction framework through simulations of random quantum circuits and the time evolution of a quantum many-body state. Our results characterize the growth of temporal bond dimensions, clarify how post-selection modifies the contraction cost and approximation accuracy, and identify regimes in which depth-oriented tensor-network contractions provide a useful complement to standard MPS-based simulation approaches.

Resonance-frequency fluctuations can limit the sensitivity and stability of superconducting microwave cavities used for qubit readout, optomechanical displacement sensing, and magnetic flux detection. Here, we demonstrate the suppression of resonance-frequency fluctuations by locking a noisy nonlinear superconducting microwave cavity to a strong pump tone. The Kerr nonlinearity of this system, whereby the resonance frequency depends on the intracavity field amplitude, gives rise to an intrinsic feedback mechanism that enables passive stabilization without active external feedback. Using two-tone spectroscopy, we experimentally characterize the intrinsic nonlinear feedback mechanism and investigate its temporal stability through Allan deviation analysis. The frequency fluctuations of the locked cavity mode are reduced by nearly two orders of magnitude, reaching the $1/f$ noise floor, without continuous frequency tracking or active control. Kerr locking provides a general approach for self-stabilizing nonlinear microwave resonators by suppressing low-frequency cavity noise while preserving sensitivity to signals outside the locking bandwidth. This approach may benefit a broad range of systems, including SQUID-based resonators, optomechanical devices, and parametric amplifiers.

Mesoscopic optical states are a promising resource for quantum communication, combining robustness against losses with the preservation of genuine quantum features. Here, we propose a quantum communication protocol in which information is encoded in the first and second moments of the photon-number distributions of classical optical states, and then decoded by photon-number-resolving detectors. Security relies on the nonclassical photon-number correlations of a twin-beam state transmitted alongside the signal in the quantum channel, providing an experimentally accessible security witness against both intercept-resend and beam-splitter attacks investigated in this work. Numerical simulations performed in experimentally accessible parameter regimes support the feasibility and security of the proposed communication protocol, yielding nonzero key generation rates under the considered eavesdropping attacks, and motivating its future experimental implementation.

Integration of quantum optical technique on-chip is crucial for large scale applications of quantum technology, which were proven in a free space environment to be superior to the corresponding classical technology. Squeezed states of light can be used for enhancing the sensitivity of quantum sensors and for fault-tolerant quantum computing. Although chip-based squeezed light generation has advanced significantly, practical impact remains limited because coupling losses between the chip and off-chip detectors destroy delicate quantum correlations, restricting the amount of observed squeezing. Here, we overcome this limitation by implementing the idea of on-chip quantum measurement with the aid of a parametric amplifier and applying it to the squeezed state generated by a silicon nitride (SiN) microring resonator. In our scheme, two matched SiN micro-rings are sequentially constructed. The first ring generates a squeezed state, whereas the second ring acts as a high-gain parametric amplifier (PA) that measures the squeezed state before the light experiences significant off-chip loss. This architecture is inherently loss-tolerant: the amplifier elevates the quantum noise well above the vacuum level, making the measurement insensitive to downstream losses. We directly observe a quantum noise reduction of 4.6 dB from the first ring, despite a chip-to-fiber coupling loss exceeding 5 dB. This work also demonstrates the first monolithic SU(1,1) interferometer with an estimated 5 dB signal-to-noise enhancement compared to traditional linear interferometers, and thus establishes a practical pathway for chip-based quantum sensors.

We investigate the geometric structure of the set of spectra of bipartite absolute separable states ($\mathrm{ASEP}_{m,n}$) and absolute positive partial transpose states ($\mathrm{APPT}_{m,n}$), i.e., bipartite quantum states that remain separable or PPT respectively, under all global unitary transformations. First, we establish general geometric properties of absolute convex sets of matrices, their spectra and extreme points. Regarding absolute separability, we present a permutation-symmetric reformulation of the absolute PPT criterion and use it to demonstrate that $\mathrm{APPT}_{m,n}$ is a spectrahedron for all $m\leq n$: in particular, all its faces are exposed. In contrast, while $\mathrm{ASEP}_{2,n}$ is also a spectrahedron, we prove that in general $\mathrm{ASEP}_{m,n}$ is a semialgebraic set for all $m\leq n$. Furthermore, we provide a complete characterization of the faces and extreme points of $\mathrm{APPT}_{m,n}$ and demonstrate that the dimension of a face is determined by the rank of a certain matrix, with maximal proper faces having dimension $(mn-m-1)$. In the quantitative setting, we provide a rigorous lower bound on the maximal attainable purity of $\mathrm{APPT}_{m,n}$ via an inscribed polytope $\mathcal{P}_{m,n}$ and conjecture that the maximal purity of $\mathrm{APPT}_{m,n}$ (along with its spectra) coincides with the polytope for arbitrary dimensions except when $m=n=2$. Additionally, we also provide a rigorous upper bound on the minimal von Neumann entropy of $\mathrm{APPT}_{m,n}$ and demonstrate numerically that the minimum entropy eventually coincides with the polytope $\mathcal{P}_{m,n}$ as the local system dimension $n$ increases. Finally, we show that the relative spectral volume of $\mathrm{APPT}_{m,n}$ decays exponentially in $n$ by a constant multiplicative factor of the relative volume of the inscribed polytope $\mathcal{P}_{m,n}$.

Protected superconducting qubits such as the $0$-$π$ qubit promise to substantially suppress error rates, facilitating fault-tolerant quantum computing with fewer qubits. Measuring these qubits is challenging due to their protected nature, and thus far no concrete proposal exists for how to measure them without breaking their protection. Here we show how to perform protected measurements of the $0$-$π$ qubit in two orthogonal bases. The protection of these measurements is facilitated by their quantum non-demolition nature, allowing faults on ancillary measurement qubits to be tolerated. As experimental progress pushes protected qubits further into the low error-rate regime, our techniques will be crucial for fault-tolerant universal control.

Fault-tolerant quantum processors based on topological codes execute programs through lattice surgery, where operations must be mapped, routed, and supplied with magic states across a 2D grid of physical patches. Non-Clifford operations require these magic states, produced either by distillation factories or by cultivation, each trading footprint against preparation latency, and delivering a magic state to the data patches that consume it requires routing through the same shared layout as every other operation. Yet placement, routing, scheduling, and magic-state supply cannot be optimized in isolation: two operations with no circuit-level dependency can still contend for the same ports, routes, or magic-state terminals once placed, so a compiler that decouples instruction scheduling from magic-state generation, or hard-codes a single generation protocol, is forced to trade execution time against layout footprint instead of co-optimizing both across protocols. We present Harvest, a resource-aware compilation approach for lattice-surgery that co-optimizes magic-state consumption with circuit-aware placement and congestion-aware routing under a protocol-agnostic resource model, then reclaims unused layout footprint after scheduling. Across standard benchmark suites (QAOA, QFT, QASMBench), Harvest achieves an average speedup of $4.83\times$ (up to $17.8\times$) over sequential execution, improves schedule length by up to $1.35\times$ through circuit-aware placement, and reclaims up to $72.0\%$ of unused magic-state patches and $33.9\%$ of unused routing patches.

We identify enhanced strong coherent Surface-Enhanced Raman Scattering (SERS) interactions facilitated by hybridized metallo-dielectric cavities with a resonant fluorescent molecule. By illuminating a detuned electronic transition near saturation via a narrowband hybrid plasmonic mode, we observe enhanced splittings in the Stokes and anti-Stokes spectra, revealing strong optomechanical coupling and nonlinear vibrational modifications at intensities far below irreversible SERS damage thresholds. We compute the second-order photon correlations that allows identifying the nonclassical character associated to these strong optomechanical interactions and SERS configurations that enables them to optically characterize the anharmonic character of the vibrational modes.

Recently, a DC magnetometry protocol utilizing $N$-spin-ensemble superradiance was proposed. This method physically amplifies the acquired signal, suppressing estimation errors from measurement noise and achieving $\mathcal{O}(1/N)$ precision scaling when measurement noise dominates quantum fluctuations. However, quantum metrology is generally vulnerable to independent Markovian pure dephasing. For instance, the scaling of Greenberger-Horne-Zeilinger (GHZ) state-based magnetometry deteriorates from $\mathcal{O}(1/N)$ to $\mathcal{O}(1/\sqrt{N})$. Although pure dephasing likely degrades superradiant sensing, its quantitative impact remains unclear. Here, we investigate the effect of independent Markovian pure dephasing on this protocol using numerical simulations and mean-field analysis. We demonstrate that, in the large-$N$ limit, the estimation error increase is limited to a constant factor. This sharply contrasts with GHZ-state-based sensing, where the error increases by a factor of $\sqrt{N}$. Our analytical solutions elucidate the physical origin of this robustness qualitatively. These findings establish the high robustness of superradiance-based DC magnetometry against independent Markovian pure dephasing.

The implementation of quantum circuits is currently very expensive, especially due to the usage of large Toffoli gates. Therefore, it is critical to optimize circuit costs by factoring expressions as they become more complex. In the proposed algorithms to factor ESOP expressions, each product term is converted into a cell in a 2D matrix, and optimal factored AND/EXOR solutions are determined using Disjoint and Even-Odd Rectangle covering methods. Two Python programs implementing these algorithms were tested and evaluated using well-known benchmarks. The results showed that both the literal counts used in classical logic circuits as well as the Maslov cost used in quantum circuits was reduced by 20%-95% depending on expression size.

We introduce a novel multipartite entanglement-assisted classical communication task, referred to as dense coding swapping, in which legitimate parties collaboratively swap the dense codeability from one communication channel to another through suitable joint unitary operations. Due to the dense coding (DC) exclusion principle, the scheme enhances the dense codeability of a target pair while simultaneously reducing it for a non-target branch in the network. This swapping capability has broader implications, as it may be viewed as a form of process swapping, distinct from resource swapping, while also providing a prevention measure when one of the receivers is compromised. We derive necessary and sufficient conditions, expressed in terms of the Schmidt coefficients, for three-qubit pure states to support DC swapping, while we obtain a sufficient criterion for mixed states using their Bloch correlation parameters. Furthermore, we identify the optimal two-qubit unitary operators capable of realizing the swapping of dense codeability between communication channels. We further examine the tolerance of these eligible states against both colored and white noise, demonstrating the resilience of the proposed task under environmental perturbations. We also show that multipartite states supporting DC swapping require only a small amount of genuine multipartite entanglement and that this requirement decreases with increasing system size.

Multi-phonon resonance conditions underpin kinetic theories of phonon transport and lattice thermalization. We show that exact resonance matching, nonzero interaction coefficients, and network connectivity do not guarantee persistent energy diffusion. Symmetry-enforced balance relations drive exact-resonant collision currents to nonthermal zero-flux states, producing kinetic arrest from individual resonant sets to connected networks. Complete energy spreading is sustained by quasi-resonances. The thermodynamic and weak-nonlinearity limits do not commute: the leading kinetic behavior is recovered in the former, whereas at fixed finite size the thermalization time diverges through higher-order crossovers as the nonlinearity vanishes. Exact-resonance existence and connectivity are therefore kinematic, not sufficient dynamical, criteria for phonon energy diffusion.

Monitored random Clifford circuit is a paradigmatic platform for exploring non-equilibrium quantum many-body dynamics using quantum-information methods. It is well-known for exhibiting a measurement-induced phase transition (MIPT) between volume-law and area-law phases of bipartite entanglement. In this Article, we develop a graph-state based framework that grants direct access to the typical output states of monitored random Clifford circuits. We first show that, in the large-$N$ limit, where $N$ denotes qubit number, the graph representations of random stabilizer states converge to the Erdős--Rényi random graph ensemble $G(N,1/2)$. This observation allows us to resolve the open problem of Greenberger--Horne--Zeilinger (GHZ) entanglement in random stabilizer states. We derive analytically the mean GHZ content, $\langle g_3\rangle=1.204$ for even $N$ and $1.325$ for odd $N$. For monitored one dimensional (1D) circuits in the volume-law phase, we uncover an emergent dense subgraph of the form $G(N_{\mathrm{sub}},1/2)$ in the output-state graphs. This implies that the output state of a monitored circuit is equivalent to an output of a unitary circuit on $N_{\mathrm{sub}}$ qubits, weakly perturbed by the remaining $N-N_{\mathrm{sub}}$ qubits carrying little entanglement. This result directly accounts for the quantum error-correcting capability of the volume-law phase. We further identify a clustering effect in the spatial distribution of the dense subgraph along the 1D qubit chain, and reproduce it with an infection-recovery toy model that exhibits a measurement-induced absorbing-state phase transition. Finally, we locate the critical point of the MIPT at $p_c = 0.1608$ through a mean-field argument on the graph, in excellent agreement with the numerical result $p_c\approx 0.16$.

Optically addressable spin defects in hexagonal boron nitride (hBN) are well suited for near-surface quantum sensing. They offer bright, wavelength-tunable single-photon emission with high optically detected magnetic resonance (ODMR) contrast at room temperature. Here we controllably synthesise a high density of spin-complex defects in carbon-doped hBN flakes. We find that the zero-field splitting parameter D is directly correlated with the zero-phonon line of an emitter, while the ODMR contrast shows no such correlation. We further analyse an individual narrowband defect showing 68% ODMR contrast and enhance its photon collection by ~40% using a solid immersion lens. By advancing both the practical synthesis of the spin complexes and the understanding of their microscopic origin, our results move us toward the deterministic creation of ODMR-active quantum emitters

The most subradiant eigenstate of a finite subwavelength atomic chain in free space, protected by strongly suppressed radiative decay, offers a powerful resource for photon storage, quantum sensing, and many-body quantum optics. Yet its optical preparation is hindered by the simultaneous need to match a wave vector outside the light cone and a nonuniform envelope. Here, we show that a free electron can overcome these constraints: its velocity sets the imprinted wave vector, while the trajectory of the diffracting wave packet shapes the excitation envelope. This simultaneous momentum and envelope matching enables heralded preparation with near-unity conditional fidelity ($F>99.5\%$) even in a deeply subwavelength regime that is difficult to access with propagating free-space photons. We further show that a path-superposed free electron can excite an antisymmetric state in two closely spaced parallel chains, whose interchain destructive interference yields stronger subradiance than a single chain with the same total number of atoms. These results establish free electrons as quantum writers for collective excitations that are difficult to access with propagating optical fields.

Quantum algorithms based on linear-system approaches for solving differential equations demand qubit and precision resources beyond near-term capabilities. To address these challenges, this work proposes a physics-informed quantum machine learning (PIQML) framework with hard constraint embedding, specifically designed for NISQ era. Within this framework, parameterized quantum circuits serve as machine learning models, where the input variable is encoded into a high-dimensional feature space via a Fourier feature map. Subsequently, to eliminate approximation errors in critical physical conditions, the solution is constructed through a rigorously designed function mapper that analytically enforces initial conditions as hard constraints. Crucially, we compute derivatives with respect to the input variable using the parameter-shift rule---a quantum native gradient evaluation technique that avoids classical discretization. Unlike generic loss functions that target abstract data patterns, our loss function focuses on the differential equation residual and reference data. This design ensures that the trained model not only approximates the data but also intrinsically satisfies the physical constraint expressed by the DE itself. Our method is validated on several differential equations, including highly oscillatory ones, demonstrating its capability to tackle challenging nonlinear dynamics. Results demonstrate that our quantum model successfully learns the solution, showing close agreement with a high-precision classical numerical benchmark.

Photonic multi-qubit entanglement is key to optical quantum information processing, particularly universal quantum computing. Yet multi-photon sources suffer from low emission efficiency, making single-photon high-dimensional encoding an appealing alternative. Here we propose an explicit and resource-efficient high-dimensional encoding approach to achieve the target multi-qubit quantum state. The technically challenging preparation of multi-photon quantum states is replaced by single-photon operations involving high-dimensional expansion, routing, and multi-layered quantum measurement. Besides, each photon in the resource multi-photon quantum state can be used to encode multiple qubits in a distributed manner, and a larger entangled state will be constructed. We demonstrate this approach using programmable photonic integrated circuits, where multi-qubit graph states--including the Greenberger-Horne-Zeilinger state and the cluster state--are generated and characterized. We additionally demonstrate the Grover search algorithm using the single-photon cluster state. Our findings unlock a novel route towards diverse entangled state generation with photons and advance large-scale and universal photonic quantum information processing.

In this paper, we present a unified framework for proving lower bounds for estimating functionals of quantum states. We therefore resolve several open problems by establishing lower bounds that match known upper bounds: we show that it requires $\widetildeΩ(N^2)$ samples to estimate the Uhlmann fidelity, trace distance, and von Neumann entropy. Moreover, they immediately imply matching query lower bounds of $\widetildeΩ(N)$ by quantum sample-to-query lifting. These lower bounds imply the near-optimality of a dozen quantum algorithms since 2016.

We develop an argmax principle for analyzing sum-of-squares relaxations of optimization problems over the unit sphere. Given a feasible pseudo-expectation, we form a polynomial of high-order pseudo-moments, such as $Φ_k(u)=\widetilde{\mathbb E}\langle x,u\rangle^{2k}$. Our guiding principle is that its maximizers are rounding candidates: their local and global optimality conditions reveal the reweighed pseudo-expectation inequalities governing SoS convergence. This viewpoint unifies several problems previously analyzed by rather different techniques. We obtain three results. First, for Best Separable State, we give a degree-$O(\sqrt{n/ε})$ SoS analysis for approximating $h_{\mathrm{sep}}(P)$ in the perfect-completeness regime, improving and simplifying Barak, Kothari and Steurer (STOC'17). The dependence is essentially tight for inverse-linear gap under the Exponential-Time Hypothesis, matching hardness from $\mathrm{QMA}(2)$ protocols. Second, for the matrix $2\to4$ norm, degree-$O(\sqrt n/ε)$ SoS gives a multiplicative $(1+ε)$ approximation. Barak et al. (STOC'12) previously gave a comparable-time constant-gap decision algorithm; our result gives a multiplicative guarantee and extends to a family of $p\to q$ norms with even $q$. Finally, for degree-$d$ polynomial optimization, we recover the convergence theorem of Bhattiprolu et al. (FOCS'17) with a shorter, more direct proof: degree-$k$ SoS gives approximation ratio $O_d((n/k)^{d/2-1})$. The paper introduces no new relaxation. Instead, the high-moment argmax gives a common way to read an SoS solution, unifying previously separate convergence analyses and yielding sharper bounds or simpler proofs.

We prove optimal finite quantum de Finetti upper bounds. Given a bosonic state $ρ_N\in D(\mathrm{Sym}^N(\mathbb C^d))$, there is a probability measure $ν$ on the unit sphere such that \[ \left\| ρ_N^{(2)}-\int |u\rangle\langle u|^{\otimes 2}\,dν(u) \right\|_1 \le \frac{\sqrt{d-1}}{N-1}. \] By purification, the bosonic theorem also gives the optimal $O(d/N)$ upper bound for arbitrary exchangeable states. These results settle the dimension dependence left open by Christandl, König, Mitchison, and Renner (CMP 2007). The proof casts de Finetti approximation as sum-of-squares rounding and applies the argmax method of Jeronimo, Wu, and Xu (manuscript 2026). More generally, $t$-site marginals satisfy $O(t\sqrt d/N)$ bosonic and $O(td/N)$ permutation-invariant bounds. Our proof formulates de Finetti approximation as the integrality gap of a symmetric-extension semidefinite program and rounds an optimum by the argmax principle. The sharp bounds have several consequences. For every fixed $\varepsilon\in(0,1)$, we construct a channel with input dimension $D=\exp(O_\varepsilon(\sqrt d\log d))=\exp(o(d))$ whose outputs are $\varepsilon$-close to separable states of local dimension $d$ and whose image contains every such separable state, thereby refuting Watrous's disentangler conjecture. We also obtain deterministic $\exp(\widetilde O(\sqrt d/\varepsilon))$-time algorithms for explicit Best Separable State without perfect completeness and for trace-distance separability testing. Finally, spectral truncation gives the first dimension-free bosonic de Finetti theorem in Hilbert--Schmidt distance, with the optimal rate $Θ(N^{-1/2})$ when the dimension may grow.

The mysterious nature of entanglement, one of the most prominent exquisitely quantum phenomena, is reflected in its intricate operational structure, with a hierarchy of classes of free operations that enable its manipulation at different levels of effectiveness. Here we use the class of 'flower states', parametrised by their (even) local dimension $2k$, to shine light on some aspects of this varied landscape. We compute all the main entanglement measures for flower states, uncovering a large gap between all forms of distillable entanglement, equal to 1 ebit independently of the local dimension, and the entanglement cost under local operations and classical communication (LOCC), known to be equal to $\log\big(2\sqrt{k}\big)$. Even under the strictly more powerful class of non-entangling (NE) operations, we show that their cost is still equal to $\log\big(1+\sqrt{k}\big)$, only about an ebit less than for LOCCs. This result, which we prove by calculating the recently introduced tempered entanglement negativity for these states, demonstrates the largest known 'irreversibility gap', i.e. the difference between distillable entanglement and entanglement cost, under NE operations, equal to $Θ\big(\frac12 \log d\big)$, with $d$ being the local dimension. A notable consequence is that the celebrated squashed entanglement is not a monotone under NE operations. Finally, we compute the exact cost under LOCC operations for flower states; this is given by the Schmidt number, which turns out to be additive over multiple copies and equal to $\min_{r|k} \log\left( r + \frac{k}{r} \right)$; for prime $k$ this reduces to $\log(k+1)$, about twice the standard LOCC cost. These last results leverage the uncertainty relations over cyclic groups proved by Tao and Meshulam.

We investigate a quantum Otto engine (QOE) constructed from the two-qubit quantum Rabi model, operating within a cavity quantum electrodynamics (QED) architecture. The engine operates with two qubits as the working substance and a single non-Markovian hot thermal bath, modeled via the hierarchical equations of motion (HEOM) formalism. In place of a conventional cold thermal reservoir, the cooling stroke is realized through a projective measurement protocol on the cavity mode, which acts as an ancillary subsystem and effectively mimics a cold bath for the qubit working medium via measurement back-action. A squeezing drive applied to the cavity mode serves as a quantum fuel. We demonstrate that cavity squeezing systematically enhances both the power output and operational efficiency of the engine - the work extracted per unit of heat drawn from the hot bath-driving it above the standard quantum Otto limit. In the limit-cycle regime, the efficiency, while remaining above the Otto bound throughout, asymptotically converges to it from above. This identifies squeezing as a controllable quantum resource for thermodynamic optimization. Our results reveal that the interplay between qubit-cavity coupling, measurement-induced cooling, and non-equilibrium squeezing gives rise to a multi-resource thermodynamic architecture with performance characteristics inaccessible to conventional two-bath quantum Otto engines, thereby providing a concrete route toward experimentally realizable quantum heat engines in cavity QED platforms.

Pseudomode approaches allow for an exact and unapproximated description of a quantum system interacting arbitrarily strongly with a bath. In general, a system coupled to pseudomodes will not thermalize to the system's Gibbs state: This is to be expected when the system-bath coupling is non-perturbative, but conflicts with common thermodynamic intuition when the system-bath coupling is asymptotically weak. We explore under which circumstances pseudomode models satisfy detailed balance (and subsequently thermalize to the system Gibbs state) and how specific choices of parameters can force "weak" detailed balance that is restricted to a limited frequency range. A combination of Hermitian and non-Hermitian pseudomodes that yields a flat effective-temperature profile is also considered. The results and criteria established here are relevant for the construction of pseudomode models in contexts where thermodynamic consistency is required.

We compare two popular models applicable to analyzing heat transport by thermal microwave photons in quantum circuits. The first model is derived from a weak-coupling Lindblad master equation, with transition rates determined by Fermi's golden rule induced by thermal dissipation sources. The second approach employs a circuit model, where thermal Johnson-Nyquist noise generated by dissipative elements introduces currents, and consequently Joule power, in other parts of the circuit. This leads to a Landauer type expression of heat transport where the transmission coefficient is proportional to the transconductance in the circuit. We find that the two models yield identical results in a linear circuit in the weak coupling limit with an analytic expression of power in an archetypal circuit of a cavity mediating heat between two baths. Our analysis yields a quantitative assessment of the range of validity of the weak coupling assumption in a circuit. Due to the correspondence of the two results, we feel confident in applying the weak coupling Lindblad model also for analyzing heat transport in quantum circuits consisting, e.g. of qubits and/or non-linear resonators.

The goal of quantum process tomography is to fully characterize an operation performed on a quantum state. By considering high-dimensional quantum states (qudit), we show that it is possible to fully reconstruct an arbitrary operation without performing any measurement on the transformed qudit. Our method is interferometric and conceptually different from existing techniques of quantum process tomography that must perform a measurement on the transformed qudit.

Tensor-network methods have opened a powerful route for the study of dynamical spectral functions in two-dimensional quantum systems. However, existing approaches within the framework of infinite projected entangled-pair states construct the required renormalization tensors solely from the ground-state environment and can suffer from severe numerical instability. We identify the origin of this instability and introduce an excitation-tailored corner-transfer-matrix renormalization-group (ET-CTMRG) method to resolve it. By incorporating excitation tensors into the renormalization procedure, the method constructs a substantially more accurate effective Hamiltonian matrix and thereby yields reliable and well-converged excitation spectra. For Heisenberg antiferromagnets, it reduces truncation errors by orders of magnitude and for the particularly complex case of the supersolid phase in the triangular-lattice XXZ magnet $\mathrm{K_2Co(SeO_3)_2}$, it achieves excellent quantitative agreement with inelastic neutron-scattering measurements. ET-CTMRG therefore provides a robust framework for investigating the dynamical properties of strongly correlated quantum systems.

Pendulums are attractive for macroscopic quantum control because gravity dilution reduces mechanical loss, while the $1/f$ force-noise spectrum associated with structural damping allows nearly lossless trapping to suppress the thermal noise sampled at an upward-shifted resonance. The same $1/f$ spectrum, however, produces a low-frequency tail that penalizes entanglement. With $10\%$ detection loss, we find that this tail raises the required back-action-to-thermal force-noise ratio by about $50\%$, corresponding to a required suspension gain $G_{\rm req}=1.49$. To overcome this structural-noise penalty, we realize a $7$-mg pendulum suspended by a stepped fused-silica fiber, with an energy-decay rate $Γ/2π=361(39)$ nHz ($Q\equivω_0/Γ=7.3(8)\times10^6$) at $ω_0/2π=2.63$ Hz. The reduction in $ω_0Γ$ yields a measured gain $G_q\simeq2.5$ relative to the previous monolithic device, exceeding the requirement.

We investigate the spread complexity of quantum quenches in generalized and long-range Aubry-Andre-Harper (AAH) models, encompassing regimes with and without mobility edges. In particular, in the generalized AAH models supporting energy-dependent mobility edges, we demonstrate that the long-time averaged spread complexity exhibits nonanalytic behavior when the post-quench quasiperiodic potential crosses the mobility edge associated with the energy of the initial eigenstate, thereby accurately identifying the mobility-edge transition. Such a behavior is supported by the spreading of local density of states. We further derive analytical expressions for the moments and the corresponding Lanczos coefficients for quenches between the limits of vanishing and strong quasiperiodic potentials. The Lanczos coefficients display qualitatively distinct behavior depending on the presence of mobility edges - they exhibit an initial plateau followed by a decay with the Krylov basis index, in contrast to the nearly constant behavior of the conventional AAH model without mobility edges. For LR hopping, the coefficients decay with the Krylov basis index for quenches from the localized to the extended phase, while they coincide with the AAH results for quenches in the opposite direction.

The standard benchmark for high-dimensional entanglement is the number of dimensions in which entanglement must be present in order to generate the state. This is called the Schmidt number and its detection is usually based on implementing an appropriate set of local basis measurements. However, as quantum technology brings increasingly large physical dimensions within reach, the implementation of such measurements typically becomes more costly. Here, we develop a scheme for detecting Schmidt numbers based only on sequences of single-qubit observables. These measurements are simpler to implement as they require only low-depth quantum circuits. Using up to sixteen-dimensional photonic spatial mode entanglement and multi-plane light conversion technology, we demonstrate how it simplifies setup complexity and successfully detects the maximal (or close-to-maximal) Schmidt number. Our results reveal that simple and more scalable measurements are sufficient to detect high-dimensional entanglement properties.

We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic with the semiclassical Pearcey function built on the cusp catastrophe lines. We also quantify the amount of superenergy exhibited in these solutions - regions of space where the local energy exceeds the largest constituent energy eigenvalue. We give a complimentary description of the caustic and superenergy behavior using the Madelung/Bohm trajectories, which gives additional insight about the energy of the trajectories and how they traverse the phase singularity chains.

We report precise measurements of inter-level interactions in a bosonic optical lattice clock based on $^{88}$Sr atoms. We observe a nonlinear density dependence of the clock shift, even without reaching quantum degeneracy. In a 2D lattice, the Rabi line shape exhibits an interaction sideband consistent with a collective spin model, while in a 1D lattice the shift is modified by density-induced dephasing. These findings, combined with a careful choice of interrogation detuning and atomic density, can enable operation at a net-zero systematic density shift in $^{88}$Sr lattice clocks. We discuss the implications of these findings in many-body physics, quantum simulation, and precision isotope shift measurements, which provide a powerful probe for new physics beyond the Standard Model.

Entanglement generation is a fundamental dynamical capability in quantum information science and underpins many quantum advantages. While quantum theory enables it through unitary dynamics, boxworld, a generalized probabilistic theory admitting Popescu--Rohrlich boxes with supraquantum correlations, has no reversible transformation capable of generating entanglement. We show that this no-go picture changes fundamentally once reversibility is relaxed to pure-state preservation. We construct a pure-state-preserving transformation that maps every uncorrelated pure state to a Popescu--Rohrlich box and completely classify all pure-state-preserving entangling transformations in the simplest bipartite boxworld. Our results provide the first explicit mechanism for generating beyond-quantum entanglement without introducing mixing and demonstrate a physical distinction between reversibility and pure-state preservation that is obscured by the structure of quantum theory.

Nitrogen-vacancy (NV) centers in chemical-vapor-deposition (CVD) diamond can form preferentially oriented ensembles with high sensing performance and low densities of lattice defects. Thin films of this material are a cornerstone of various imaging modalities. However, nitrogen injection needed to produce such films can transiently drive growth out of equilibrium, generating interfacial strain and spin defects that degrade NV coherence. Here, we investigate this disorder in $^{12}\text{C}$-enriched, preferentially oriented NV layers grown on (111) diamond using two nitrogen-injection procedures, combined with nanometer-scale selective plasma etching and NV spin-coherence measurements. Pulsed nitrogen injection produces a pronounced nitrogen overshoot within a 60--80 nm interfacial region, generating excessive amounts of defects. By contrast, smooth nitrogen delivery through mass flow controllers substantially suppresses interfacial disorder, yielding coherence properties close to the theoretical limit imposed by spin-bath noise. A 50-nm NV layer is used to demonstrate proton nuclear magnetic resonance detection. This work reveals the role of interfacial disorder associated with the nitrogen-doping procedure and provides a route to growing high-quality, thin NV-doped layers for quantum-sensing applications.

Readable error records can protect quantum sensing because they prevent physically distinct noise trajectories from being irreversibly mixed. A finite detector or ancilla, however, can retain only finitely many syndrome values, and a general criterion for deciding which records may be merged without losing metrological information is absent. We formulate the problem for a fixed fine-grained classical-quantum record and parameter-independent compression into at most $M$ flags. We prove an exact identity expressing the lost symmetric-logarithmic-derivative quantum Fisher information (SLD QFI) as a sum of state-weighted squared distances between fine and coarse SLD scores. Consequently, optimal finite-syndrome design is exactly an operator-valued clustering problem, and zero loss is characterized by a support-resolved common-SLD condition. We extend the identity to the full multiparameter SLD QFI matrix and distinguish local QFI preservation from recovery of an entire statistical model. For exact recovery of a quantum code, we separately show that, when each fine error is individually correctable, the minimum number of readable syndromes is the chromatic number of a Knill-Laflamme incompatibility graph. For qubit random-unitary noise we obtain a finite partition formula. A planar random-Pauli model admits a conditional-variance representation and, for a uniform error axis, the exact optimum $F_M^{\star}=[M\sin(π/M)/π]^2$, with deficit $π^2/(3M^2)+O(M^{-4})$. These results identify the information-theoretic cost of finite syndrome resolution while making explicit the side-information assumptions required for any passive noise-to-erasure interpretation.

Quantum resource theory has sharpened our understanding of the intrinsic complexity of quantum systems, particularly their classical simulability. However, it remains unclear which quantum resource governs the classical learnability of quantum circuits, especially beyond the regime of efficient classical simulation. Here we close this knowledge gap by studying the expectation-value functions of families of tunable quantum circuits, with many applications in digital quantum simulation, quantum metrology, and quantum-system characterization. Specifically, we introduce a new resource measure, the dynamical stabilizer entropy (\DSE), which quantifies how broadly an expectation-value function is distributed across its frequency modes. By relating \DSE to operator stabilizer entropy, we establish a computational phase diagram that compares classical simulators with quantum-data-assisted classical surrogates. We first determine the \DSE-dependent learnability boundary of this diagram by deriving bounds on the sample complexity and runtime of classical surrogates, and by developing a \DSE-guided surrogate. We then complete the diagram by proving, under standard complexity-theoretic assumptions, the existence of circuit families that can be efficiently learned by this surrogate but cannot be efficiently emulated from their circuit descriptions alone. Numerical experiments on random and structured circuits with up to 80 qubits support the predicted \DSE-dependent computational landscape. These results establish a quantitative resource-theoretic framework for delineating the boundary between classical simulation and learning, motivate resource measures linking quantum resources to learnability, and guide the design of learning-based algorithms for scalable quantum systems beyond the reach of direct classical simulation.

We introduce a quantum stochastic resetting protocol with uniform memory, in which each resetting event returns the system to a state visited at a time chosen uniformly from its entire history. The resulting dynamics is nonunitary, non-Markovian and a direct quantum generalization of the classical preferential relocation model. Working in the energy eigenbasis, we derive the exact evolution of every density-matrix element for an arbitrary time-independent Hamiltonian and show that the Hamiltonian enters the dynamics only through the corresponding Bohr frequencies. This leads to a natural distinction between two classes of quantum systems: gapped and gapless. In \emph{gapped systems} (systems with a discrete energy spectrum), while the diagonal elements remain unchanged, the off-diagonal elements of the density matrix in the energy eigenbasis decay algebraically with a continuously varying exponent and with an amplitude that oscillates periodically in $\log t$. The system therefore approaches a stationary state that is independent of the resetting rate and retains a strong memory of the initial state. In \emph{gapless systems} (systems with a continuous energy spectrum), arbitrarily small Bohr frequencies prevent stationarity. Instead, the position distribution spreads on the universal (ultra-slow) scale $\log(rt)/r$, independently of the initial state and of the details of the Hamiltonian. We illustrate these results with a two-level system, a harmonic oscillator, and a free quantum particle, and contrast them with their classical counterparts.

Two-dimensional (2D) spectroscopy is a powerful pump-pump-probe technique for revealing couplings between quantum states and disentangling the different contributions to the optical response of a system. We present an efficient method for 2D spectroscopy simulations in the Markovian limit for the environment, capable of handling arbitrary pulse shapes and reproducing time-ordering and overlapping pulse effects, while maintaining a computational cost that scales linearly with the number of sampling points. We leverage this framework to investigate how 2D spectra are affected by spectral phase distortions and highly non-Gaussian pulse shapes, such as those produced experimentally by hollow-core fibers or non-collinear optical amplifiers. We show that realistic pulses can induce the appearance of additional spectral features, lineshape distortions and oscillating contributions in the system's dynamics. Notably, even weak temporal pulse tails arising from uncorrected high-order spectral phase terms cause visible changes in the 2D spectra. We also find that homodyne detection schemes employed in experiments can mitigate the presence of such pulse effects. These results emphasize the importance of including realistic pulses in 2D spectroscopy simulations to identify pulse-induced effects and minimize ambiguities in the interpretation of experimental data.

Phase fluctuations between optical inputs limit programmable photonic processors because their output powers depend on coherent interference. We study the phase-drift penalty that arises when sine and cosine quadratures are measured sequentially rather than simultaneously. The analysis is motivated by measurements from an eight-mode programmable photonic processor, including 35 free-running recordings of 300 s acquired at approximately 125 samples per second per channel. These recordings provide an empirical route for estimating the phase-increment variance at a selected reconfiguration interval. The estimate is defined at the time of the second measurement. For fixed quadrature order, perturbation of the atan2 reconstruction gives $e_{C\to S}=-δ_τ\sin^2φ_0+O(δ_τ^2)$ and $e_{S\to C}=-δ_τ\cos^2φ_0+O(δ_τ^2)$. Writing $Q_τ=\operatorname{Var}(δ_τ)$, uniform phase averaging gives the first-order drift mean-square error $3Q_τ/8$. A phase-predicted ordering rule measures the locally less informative quadrature first and the more informative quadrature second. Its uniform first-order penalty is $(3/8-1/π)Q_τ$, which is 84.9 percent below the fixed-order value. We also derive an increment-aware estimator from a local state-space model. Marginalizing the unknown phase increment increases the variance of a stale phase observation by $Q_τ$, reducing its Fisher information from $I$ to $I/(1+IQ_τ)$. For ideal balanced Poisson detection, the Fisher information of each quadrature equals its detected signal-photon number. This yields dimensionless architecture boundaries in spatial information and phase-increment variance. Nonlinear Monte Carlo simulations validate the perturbative laws, quantify robustness to prediction error, and compare simultaneous, fixed-order, increment-aware, and adaptive receivers under a common noise model.

Many-body localization (MBL) is a dynamical phenomenon that describes the non-ergodicity of isolated quantum many-body systems. In contrast to thermalization, this phenomenon leads to a long-lived memory of initial states of local systems and slow growth of entanglement. In this work, we study Stark MBL in a 12-qubit correlated fermionic system described by the one-dimensional Fermi-Hubbard model using Hamiltonian simulation on an IBM superconducting qubit quantum computer. To enable such a computation on current-day noisy hardware, we combine a series of compilation steps, including the use of the spin-resolved Jordan-Wigner transformation, employing SWAP networks, and integrating a tensor-network-based quantum circuit optimization routine on top of a standard circuit optimization pipeline. As a result, there is approximately an 88$\%$ and 87$\%$ reduction in two-qubit gate count and circuit depth, respectively. Through such simulations of the real-time dynamics using Trotterized quantum circuits, we exhibit a crossover from thermalizing dynamics of the system at a weak tilt of the field to a strongly localized behavior at large tilt with short evolution times. We also benchmark our obtained results with respect to those from exact simulations.

Ever since the proposal of delayed choice quantum erasure and subsequent realization in the experiment by Kim et al., the interpretation and implications of delayed-choice experiments have remained a subject of intense foundational debate. This paper resolves the apparent paradox attached to the experiment using standard quantum mechanics. Using an extended Mach-Zehnder interferometer which captures every operational feature of the original experiment, we show that choosing between which-path and erasure detectors is simply a choice of measurement bases, which does not rewrite a photon's past. Furthermore, by mapping the experiment to a two-way Stern-Gerlach framework, we prove that quantum erasure is an expected result of measuring entangled states, not a physical anomaly. Ultimately, through a pedagogical game, we illustrate that the illusion of retrocausality arises from asking illegitimate questions, and that a forward-in-time description is entirely sufficient to explain the logic.

Most recently proposed quantum algorithms for solving linear and nonlinear partial differential equations rely on non-unitary operations. These operations are typically implemented probabilistically, requiring postselection and thus increasing the computational cost. We show that quantum lattice gas algorithms enable unconditionally successful quantum simulation of nonlinearities, yielding, to our knowledge, the first quantum algorithm for Burgers equation whose time steps can be concatenated without probabilistic failure. The key idea is to exploit the correspondence between the stochasticity of quantum measurement in the linear combination of unitaries framework and the intrinsic randomness of the classical lattice gas algorithm. In doing so, we identify general properties that characterize probabilistic classical algorithms amenable to this time-marching formulation, and illustrate the approach with an additional application.

In spite of recent advances, quantum computers are expected to be sufficiently noisy in the coming few years to the extent of limiting quantum chemical calculations to relatively small number of orbitals. However, even with reasonable quality single particle basis sets, small active spaces with limited orbitals can result in a significant fraction of correlation energy being lost, motivating the design of moderate quality qubit-efficient basis sets for quantum algorithms. We begin by reoptimizing the existing minimal basis sets using a genetic algorithm-inspired approach in conjunction with aggressive refinement strategies, and generate modified minimal basis sets (MSTO-kG basis; k = 2-11) for atoms from H through F. The ground state energies of H through F using our MSTO bases at FCI level of theory yield ground state energies that are comparable or sometimes even lower than those obtained using 6-31G basis sets. In the case of Li, the MSTO bases surpass the performance of cc-pVQZ bases. Thus, we obtain better atomic energies with same number of qubits relative to STO bases, and better/comparable energies with fewer qubits relative to higher quality bases. In the case of molecules, H2 performs poorly; a finding that is consistent with an earlier work in literature. For other molecules, Li2, C2, LiH, BeH and BeH2, the FCI results (except C2 for which we employ CISD) from our bases are comparable to/outperform those from 6-31G basis. Finally, we compare the resources required between different bases and find that MSTO bases yield better energies than the competing basis sets while incurring fewer qubits and two-qubit gates with VQE, QPE, and HHL. The logical T-gate counts are also found to be considerably lower for QPE and HHL respectively. Overall, our work paves way for more accurate yet less qubit-hungry quantum chemical calculations using near-term quantum computers.

Free-space Aharonov--Bohm (AB) Bessel modes are known to carry a flux-dependent azimuthal Schrödinger probability current and kinetic orbital angular momentum. We extend this response to the spin-resolved conserved Dirac current of a core-excluded finite-wall annular guide and show that confinement converts its surviving orbital component into a transverse Aharonov--Bohm (TAB) propagation phase for a straight traveling mode whose centroid path has zero projection onto $\mathbf A$. The radial-gradient current reverses under spin reversal; retaining the complete evanescent tail closes it as a boundary contribution, leaving a spin-independent orbital phase $Δφ_{ln}\propto lΦL_{\rm int}\langleρ^{-2}\rangle_{ln}/v_z$. Opposite-winding modes $|\pm l\rangle$ form a same-path qubit implementing $R_z(2δ_l)$ with differential readout and common-mode phase rejection, while direct first-order crosstalk requires the angular harmonic $m=\pm2l$. For a $100\,μ\mathrm{m}$ section with $a=20\,\mathrm{nm}$, $R=30\,\mathrm{nm}$, $E_z=10\,\mathrm{meV}$, and $|l|=10$, the sensitivity is $0.1885\,\mathrm{mrad/mG}$ and $R_z(π)$ occurs at $16.67\,\mathrm{G}$. Finite-wall confinement thus turns intrinsic azimuthal Dirac current into a guided field-free phase operation.

Parasitic two-level-system (TLS) defects are a major source of energy relaxation and temporal instability in superconducting quantum processors. Our sub-second adaptive spectroscopy reveals telegraphic switching of TLSs with a characteristic timescale of a few seconds and spectral diffusion with diffusivity $D \approx 0.9~\mathrm{MHz}^2/\mathrm{s}$. These timescales are about $3 \times 10^2$ times faster than what is observed in conventional nonadaptive spectroscopy, which typically requires hours of measurement time. We resolve such fast dynamics on a field-programmable gate array (FPGA)-based controller that enables measurement of frequency- and time-resolved relaxations with sub-second temporal resolution in flux-tunable superconducting qubits. We observe similar defect dynamics across multiple qubits in independently fabricated devices measured in different laboratories. We correlate TLS-induced fluctuations with gate-level errors using randomized benchmarking. Our results reveal a previously inaccessible regime of frequency-resolved TLS dynamics and redefine the timescales relevant to TLS-aware characterization and calibration of superconducting quantum processors.

Near-term quantum devices are limited by noise and hardware constraints, motivating algorithmic approaches that trade circuit complexity for increased sampling overhead. Quasi-probability decompositions (QPDs), for example, allow replacing non-local operations by multiple circuits with local operations, but the associated sampling overhead generally scales exponentially and limits their practicality. In this work, we introduce a reweighting strategy for QPDs for circuits with the same variational structure across parameter settings, reusing samples and thereby reducing the sampling overhead. We first demonstrate this approach by estimating fidelities between parameterized quantum states, a key primitive in variational time evolution and quantum kernel methods. Importantly, this setup allows controlling the exponential QPD sampling overhead while preserving the structure of the state-encoding ansatz. We then apply the method to estimate the real part of the quantum geometric tensor using the simultaneous perturbation stochastic approximation and find that, in the presence of realistic hardware noise, our method outperforms other standard estimation techniques. These results highlight the potential of reweighting strategies to extend the applicability of QPD-based methods in variational quantum algorithms.

Magnetometry with nitrogen-vacancy (NV) centers in diamond has shown great promise in recent years. In particular, absorption-based magnetometry techniques, employing a cavity to enhance the absorption length, can improve the contrast and sensitivity compared to conventional techniques based on reading out the NV$^-$ triplet fluorescence. The absorption techniques rely on magnetic-field-dependent absorption at the NV$^-$ singlet zero phonon line at 1042$\,$nm and its phonon sideband. In a cavity-enhanced spectroscopy approach, we study pump-laser- and microwave-induced cavity signal changes at room temperature over a spectral range of 680-1050$\,$nm. Through normalization, we eliminate the cavity-enhancement effect and provide quasi-single-pass values for the absorption and optically detected magnetic resonance (ODMR) contrast. The highest contrast is found at 1042$\,$nm, but multiple points of high contrast are found at the peaks of the phonon sideband. Additionally, cavity-enhanced ODMR contrasts in the range of 50-80$\,\%$ are presented. We further measure the broadband singlet absorption cross section at room temperature with a novel method through microwave-induced signal changes. This method is insensitive to pump-laser-induced signal changes by other defects and quantifies the room-temperature absorption strength of the singlet transition and its entire phonon sideband. We determine the absorption cross section at 1042$\,$nm to be $σ^{\,\bigstar}_{1042}=(0.89\pm0.14)\cdot 10^{-21}\,\text{m}^2$ or $σ^{\,\blacktriangle}_{1042}=(2.9\pm0.5)\cdot 10^{-21}\,\text{m}^2$. depending on the employed 532$\,$nm NV$^-$ absorption cross section.

Here, we investigate the motion of a thin circular quantum vortex filament near the infinite planar surface. The fluid surrounding this surface moves with a non-zero velocity $\bf{v}$, which is parallel to the surface. We study the specific features of this quantum system and show that they are quite suitable for the boundary layer theory. The developed model allows us to calculate the vortex energy spectrum, $E = E({\bf p})$, where ${\bf p}$ is the total momentum of a vortex ring. We have demonstrated that this function has complex non-trivial dependence on the velocity $\bf{v}$. It is stated that the inverse effective mass of a vortex under consideration is of a tensorial nature. In certain quantum states, the system shows the possibility of both negative and positive effective mass existing. This study employs a novel quantization method for classical closed vortex filaments, developed by the author earlier.

The dynamics of an open quantum system in the high-temperature regime of the Caldeira-Leggett model using a Bohmian language is investigated. By expressing the density matrix in polar form, generalized continuity and Hamilton-Jacobi equations are obtained. Thermal effects appear explicitly in the former, while they influence the latter only indirectly through an effective potential. Remarkably, the effective potential does not vanish in the classical limit and cannot, in general, be decomposed into simple additive quantum and thermal contributions. Instead, it retains a nontrivial structure leading to a residual temperature dependence in the resulting dynamics. As a consequence, the resulting temperature-dependent-classical trajectories remain deterministic even in the presence of a thermal environment. This behavior contrasts with the stochastic dynamics observed in the Langevin description and reflects the ensemble-based nature of the present approach. To further explore the quantum-to-classical transition, a scaled version of the Caldeira-Leggett equation is introduced by scaling both the density matrix and Planck constant through a quantumness parameter. This parameter takes the value one in the fully quantum regime and smoothly approaches zero in the classical limit. Applications to Gaussian states demonstrate a gradual suppression of coherence and interference, governed jointly by thermal effects and the transition parameter.

Bosonic quantum systems provide a hardware-efficient platform for quantum information processing but remain challenging to characterise due to their large Hilbert space and the high measurement cost of state tomography. Existing approaches estimate the fidelity with respect to a single target state, making them unsuitable for applications in which physically equivalent states differ by phase space translations, rotations, or other transformations. Here, we introduce an adaptive reconstruction technique that estimates the fidelity with respect to a family of bosonic states while reconstructing the underlying Wigner function from a small number of measurements. The method combines a physics-informed parametric model with Bayesian inference, bootstrap, and active learning to iteratively select the most informative phase space sampling points. We implement the approach on a circuit quantum electrodynamics platform and benchmark it on Schrödinger cat states with amplitudes $α\in[1,3]$. The reconstruction yields reproducible fidelity estimates within a few minutes, remains robust to substantial displacements and rotations in phase space despite using a mismatched prior, and is sensitive to subtle state imperfections. We further compare the adaptive strategy with existing Wigner function sampling protocols experimentally, demonstrating the advantage of adaptive sampling for measurement-efficient fidelity estimation with respect to a family of cat states. Finally, we incorporate the reconstructed fidelity into the figure of merit used in a proof-of-principle closed-loop quantum optimal control experiment, demonstrating the applicability of the method to autonomous optimisation of bosonic quantum states.

Integrated HPC/QC systems aim to combine classical high-performance computing with quantum processors, but cannot be reduced to mechanisms for dispatching quantum kernels. An integrated architecture must support aspects such as observability, which cannot be implemented using QPUs alone, as well as fallback execution and cost-aware decisions on whether to replace quantum tasks with classical surrogates. Such mechanisms must be approximate or benefit from problem structure to soften the inescapable exponential classical worst-case complexity. In this work, we study tensor-network ground-state search, as such a surrogate, for optimisation problems. This combines key quantum primitives with advanced classical simulation. It provides initial empirical indicators for surrogate selection criteria, and exposes end-to-end toolchain effects that may be missed when transformation steps are studied in isolation. We compare a native polynomial unconstrained optimisation to-higher-order-Ising and a quadratised quadratic unconstrained binary optimization to-quadratic-Ising formulation for Max-3-SAT. Both are encoded as matrix product operator and optimised using density matrix renormalisation group approaches, with simulated annealing (SA) as classical performance baseline. Our results show that quadratisation is not a neutral transformation step: auxiliary variables and pairwise couplings substantially degrade solution quality relative to the native higher-order representation, while SA matches or outperforms DMRG across all tested instances. Since the optima of Boolean satisfiability (SAT)-derived problems are classical product states, DMRGs advantages dont materialise here. These findings suggest that surrogate selection in HPC/QC runtimes must be encoding- and instance-aware and provide empirical groundwork for informed decisions on fallback strategies and architecture co-design.

Recent progress in fully quantum Markov chain Monte Carlo methods enables efficient Gibbs-state sampling on quantum computers [Chen et al., Nature 646, 561 (2025)]. Although rigorous worst-case bounds on mixing times remain largely inaccessible for classically intractable systems, experience from classical Monte Carlo suggests that convergence of relevant observables may nevertheless be rapid. This raises the practical question of how to diagnose convergence efficiently, i.e., with at most polynomial overhead. We propose a low-cost criterion for convergence monitoring that exploits the weak measurements inherent in quantum Gibbs samplers and their qubit-efficient variants [Ding et al., arXiv:2508.05703 (2025)]. Our approach is based on the observation that, at thermal equilibrium, the net energy flow between system and environment vanishes and energy-exchange statistics satisfy a balance condition. This condition appears in the distribution of (quasi-)frequencies extracted from the weak-measurement record and we use it to construct a Hamiltonian-agnostic stopping criterion based solely on data already generated by the sampler. We provide a statistical analysis, along with numerical and analytical studies to understand its performance, assumptions, and limitations.

Fault-tolerant quantum computing requires classical decoders that keep pace with the underlying hardware, translating syndrome measurements into corrections fast enough to avoid an exponential backlog. To meet this real-time constraint, pre-decoders have emerged as part of a hierarchical decoding approach to resolve simple, local errors before passing a sparser residual syndrome to a strong decoder. While pre-decoding should, in theory, speed up the strong decoder, in practice, the speedup is only marginal, since existing strong decoders are designed to decode dense syndromes and cannot exploit the sparsity provided by pre-decoders. To address this, we present Zero-G, a strong decoder designed for use alongside pre-decoders. As a stochastic approximate minimum-weight perfect matching (MWPM) decoder, Zero-G exploits sparse residual syndromes, dynamically trading latency for accuracy rather than relying on an all-or-nothing runtime-accuracy trade-off. By decoupling hardware control from the decoding core itself, we enable heterogeneous deployment across both FPGAs and CPUs without maintaining separate implementations. Zero-G achieves a $10\times$ latency improvement over existing strong decoders at matching accuracy, with worst-case sub-350ns decoding at code distances up to d=15, while scaling to 640 logical qubits on a single 128-core CPU and 32 logical qubits on a single AMD Versal V80 FPGA.

A conservation-law-guided classification framework is developed for the execution of coarse-graining operations in quantum field theory. Coarse-graining produces a selection at the level of Feynman diagrams. Diagrams with nonzero momentum transfer are suppressed by oscillatory factors, zero-momentum-transfer ladder diagrams can accumulate through geometric series resummation to produce a spectral pole, and single-bubble topologies contribute only to the continuum. Conservation laws govern this classification. For operators protected by a Ward identity, the matrix element at zero momentum is guaranteed to be nonvanishing. For operators protected by BRST symmetry, the Slavnov-Taylor identities provide no mandatory suppression. The two cases differ in the strength of the algebraic guarantee. For unprotected operators the injection term vanishes and the spectral function remains continuous. The sign of the single-bubble contribution is determined by spin statistics. A positive sign leads to amplificative feedback in the ladder resummation, a negative sign leads to suppressive feedback. These two attributes, the nonvanishing of the injection term and the sign of the single-bubble contribution, are the defining criteria of the classification. As a direct application, a general classification of local operators is established within the emergence framework and verified on eight physical channels and three known solvable systems. The framework indicates which emergence paths are possible for each operator; whether the critical condition is reached is left for independent nonperturbative computation. The logical structure of this classification is parallel to the strategy used in deriving fluid equations from molecular kinetic theory in classical statistical physics.

Quantum error correction (QEC) is the most promising route toward fault-tolerant quantum computing and, thus, useful quantum computers. QEC operates as a continuous measure-decode-correct cycle: ancilla qubits are read out, a decoder infers errors from the resulting syndromes, and corrections are applied before the next round begins. Within this loop, readout occupies a uniquely critical role, as it is the sole source of ground truth available to the decoder. Yet readout is also the slowest and most error-prone operation in the stack, with characteristics that vary across qubits and drift over time; This complexity propagates directly to the classical control hardware, and in particular to the FPGA-hosted machine-learning (ML) discriminator that must classify each analog signal into a binary syndrome outcome. Despite this central role, QEC performance has not yet been studied in depth from the perspective of readout characteristics, readout length, and their co-design with an ML discriminator. We introduce Oraqle, an end-to-end benchmarking framework that evaluates qubit-state readout and its impact on QEC performance across real experimentally extracted qubit-state-readout datasets, state-of-the-art ML discriminators, multiple QEC codes, and hardware regimes spanning current to projected devices. Our study reveals three asymmetric findings: The measurement duration can be significantly reduced with nearly no penalty to the logical error rate; The discriminator complexity barely affects the QEC performance, as residual errors are written into device physics rather than the model; and the impact of qubit-state readout on the logical error rate is conditional on where the hardware sits in the QEC landscape, a window that widens as devices mature.

We report a measurement of the optical frequency ratio between the $^2\mathrm{S}_{1/2}(F=0)$--${^2\mathrm{F}_{7/2}(F=3)}$ electric-octupole (E3) transition of $^{171}$Yb$^{+}$ and the $^1\mathrm{S}_0$--${^3\mathrm{P}_0}$ transition of $^{87}$Sr, $ν_{\mathrm{Yb}^{+}}/ν_\mathrm{Sr} = 1.495\,991\,618\,544\,900\,588\,1(65)$. Reaching a fractional uncertainty of $4.3 \times 10^{-18}$, this result improves upon the previous best by more than a factor of three and is among the few that meet the requirements for interspecies clock comparisons specified by the roadmap towards the redefinition of the SI second. The comparison is between a transportable optical lattice clock and a stationary single-ion clock. It spans a period of nearly two years, during which the transportable clock was intermittently operated off-campus. The ratio was reproducibly measured during four separate campaigns, which are consistent within their statistical uncertainties. The results demonstrate reproducible $10^{-18}$ level operation of the transportable clock and thus validate its application for chronometric geodesy and as a transfer standard for inter-institute clock comparisons, e.g., in the absence of optical fiber links.

We prove that the entanglement of formation of every two-mode Gaussian state coincides with its Gaussian restriction, solving a longstanding open problem in continuous variable quantum information theory. The key result is a sharp affine relation between entanglement and a generalized Einstein-Podolsky-Rosen observable, valid for arbitrary pure two-mode states, including non-Gaussian ones. Our result extends to bisymmetric multimode Gaussian states, and also provides a measurable lower bound on the entanglement of formation of arbitrary non-Gaussian states.

We introduce Pangaea, a fault-tolerant quantum architecture that uses a quantum bus to mediate logical operations between remote patches of two-dimensional topological codes. The bus is an auxiliary gauge-code strip whose measurements reconstruct joint logical operators while preserving nearest-neighbor physical connectivity. Enabling native heterogeneous topological codes and multi-qubit Pauli operations, the quantum bus can be interpreted as a three-dimensional generalization of lattice surgery. We require only $O(dN_L)$ physical qubits to implement multi-qubit interactions for $N_L$ distance-$d$ logical qubits, compared to $O(d^2N_L)$ of traditional two-dimensional architectures. At the 50-logical-qubit scale, Pangaea uses up to $10\times$ fewer physical qubits than planar surface-code architectures at matched logical error rates. We verify fault-tolerance of long-range measurement-based CNOT primitives for both surface--surface and surface--color joint parity measurements using pseudo-threshold simulations. We use this protocol to construct a native heterogeneous 15-to-1 magic-state distillation module using the quantum bus. These results establish Pangaea as a scalable architecture for three-dimensional fault-tolerant quantum computing that resolves the routing bottleneck of planar lattice surgery.

We present a reinforcement learning-optimized Rydberg electrometer based on the asymmetric blockade effect and achieve high-sensitivity electric field sensing in Rydberg arrays. Microwave dressing induces asymmetric blockade to suppress interactions between target atoms, while keeping the coupling between the central control atom and target atoms field-tunable near Förster resonance. The field-regulated blockade radius affects the detectable atomic population signals, thereby enabling electric field sensing via state-selective readout. In planar atomic arrays, classical Fisher information exhibits near-quadratic scaling with atom number and approaches the Heisenberg limit. Reinforcement learning-designed composite pulses greatly enhance quantum Fisher information by up to one order of magnitude compared with single $π$ pulses. We further establish a compact six-atom spherical configuration for vector electrometry, in which field orientation is extracted from calibrated axial populations, and weak bias fields eliminate dipole-dipole-induced sign and magic-angle ambiguities. Numerical tests against Rabi frequency deviation, positional error, residual inter-target coupling and projection noise demonstrate the reliability of this scheme. This work provides an experimentally viable approach to realize high-precision three-dimensional Rydberg electric field sensing.

We establish a general symmetry-projection framework for multiparameter quantum sensing. Decomposing encoding generators into subspace-preserving and subspace-changing components relative to a symmetry sector identically eliminates all cross-sector elements of the quantum Fisher information matrix (QFIM) and the mean symmetric logarithmic derivative (SLD) commutator matrix. When projected subspace-changing generators act as a scalar within the occupied subspace, the corresponding QFIM block reduces to four times the symmetrized covariance matrix, regardless of probe state purity. For parity-protected collective $\mathrm{SU}(2)$ spin systems, this renders the transverse QFIM directly certifiable via spin fluctuations, with the optimal axis aligned with the anti-squeezed quadrature. Applied to a dissipative one-axis-twisting system, our framework reveals that highly mixed transient states can exhibit nearly balanced, Heisenberg-scaled QFIM components for transverse--longitudinal parameter pairs $(θ_y,θ_z)$ over a broad time window. Furthermore, while the steady state retains an isotropic transverse QFIM scaling as $N^2/3$, weak compatibility for transverse parameter pairs $(θ_x,θ_y)$ exhibits a sharp parity dependence---failing for odd $N$ but restored for even $N$. The resulting symmetry protection eliminates the Uhlmann curvature for transverse--longitudinal pairs, enabling simultaneous saturation of the multi-parameter quantum Cramér-Rao bound in the asymptotic limit.

We introduce a validation process that harnesses engineered many-body relaxation to control and calibrate quantum hardware. On two independently developed neutral-atom processors, we realize the many-body quantum Mpemba effect in an open system for the first time. Initial-state engineering creates fast and slow relaxation pathways: the fast pathway opens access to unreachable mixed-state physics before hardware noise obscures the target dynamics, whereas the slow pathway amplifies hidden imperfections in preparation and control. Computational-basis measurements directly and independently benchmark dynamical reliability, revealing each processor's actual operating window as a many-body simulator. The processors are thus judged by the very dynamics they are built to reproduce. Complementary responses disentangle control errors and drive an adaptive, time-resolved scheme that supplies hardware developers directly actionable corrections, enhancing faithful reproduction of the target dynamics. These results establish many-body relaxation as a transferable validation and calibration tool for programmable quantum processors.