Quantum Physics Paper Analysis

We consider the problem of purifying noisy qubit unitary channels. Given the ability to apply an unknown qubit unitary channel followed by depolarizing noise, we aim to construct a superchannel that purifies the noisy unitary back to the original unknown unitary. We first provide numerical evidence that sequential strategies can strictly outperform parallel strategies when the number of channel uses is finite, highlighting the fundamental distinction from state purification. We then provide a concrete $\mathrm{U}(2)$-covariant parallel protocol based on a novel entanglement-assisted quantum error-correcting code that suppresses the first-order noise strength as $O(1/n)$ with $n$ channel uses and show this scaling is asymptotically optimal in the low-noise regime, even when sequential strategies are allowed.

The Ising framework maps the decoding problem in quantum error correction onto ground-state optimization of a classical Hamiltonian, in which $X$-$Z$ error correlations enter as cross terms. Under phenomenological depolarizing noise, the exact joint formulation contains up to 8-body interactions for the toric code and 10-body for the $6.6.6$ color code. These high-order terms degrade solver convergence, inflate runtime, and raise the auxiliary spin overhead when embedding into native 2-body Ising hardware. In this work, we propose the iterative low-order decoding (ILOD) algorithm, which alternates between $X$- and $Z$-type sub-Hamiltonians, approximating cross-type correlations through Bayesian priors that reweight each type's couplings using the other type's inferred error configuration. This halves the maximum body count of interaction terms in the Hamiltonian, accelerating the solver, restoring convergence at larger code distances, and reducing the total spin count for 2-body embedding by a factor of $2.5$. For the toric code, ILOD attains a threshold of $4.73%$ versus $4.83%$ for the joint formulation, with the empirical runtime ratio scaling as $(0.81)^d$. For the $6.6.6$ color code, their thresholds agree within statistical uncertainty for small code distances, and ILOD remains convergent for larger distances where the joint formulation fails to converge despite a larger annealing budget.

The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires: mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a $4 \times 4$ rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold $p^\star \approx 0.034$. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.

Grover's algorithm achieves a quadratic speedup for unstructured search given a global oracle for the target set. In many applications, however, the target set is specified as the intersection of multiple constraint sets. Constructing a global oracle for the intersection can be costly, whereas the individual constraint oracles are often much simpler to implement. We study a randomized Grover search algorithm that directly uses these constraint oracles. At each iteration, one of the corresponding Grover operators is selected at random. For the two-operator case with uniform sampling, we prove that the success probability approaches one after \[ Θ\left(\frac\pi4\sqrt{\frac{N}{r}}\right) \] iterations, where $r$ is the size of the intersection. Thus, the algorithm achieves the same asymptotic query complexity as standard Grover search but without requiring a global oracle. We then generalize the analysis to arbitrary sampling distributions and an arbitrary number of Grover operators through an auxiliary operator that approximates the expected Grover evolution, while retaining the same asymptotic complexity. We further show that highly biased sampling distributions can still achieve near-unit success probability, enabling cheaper Grover operators to be used more frequently. Finally, we prove asymptotic optimality and support the theoretical results with numerical simulations.

Reliable large-scale quantum computation relies on fault-tolerant architectures, where quantum error correction (QEC) continuously extracts and decodes error syndromes in real time. A critical component in QEC is the decoder, a classical subsystem that must simultaneously deliver high logical accuracy and ultra-low latency. This paper presents a novel algorithm-hardware co-design that improves the accuracy-latency trade-off over existing approaches such as vanilla Minimum-Weight Perfect Matching (MWPM) and Union-Find (UF) decoders. At the algorithmic level, we introduce coset ensemble decoding, which improves UF decoding by explicitly exploiting logically equivalent cosets. Our method performs ensemble forest exploration to generate multiple coset-consistent candidates and aggregates them to approximate coset-level maximum-likelihood decoding. We further reduce computational and memory complexity via reverse-order elimination and lossless graph compression, without sacrificing accuracy. At the hardware level, we design a domain-specific architecture that temporally reuses resources, avoiding the code-distance-proportional resource growth in prior spatial architectures. Several optimizations, such as multi-bank memory hashing and hierarchical ID mapping, are proposed to mitigate pipeline stalls and memory conflicts under highly concurrent access patterns. Under a circuit-level depolarizing noise model, our co-design approach achieves a better accuracy-latency trade-off than prior MWPM- and UF-based decoders, while reducing FPGA LUT consumption by up to 8.2 times compared with reported UF-based decoder resources. The tunable candidate number further exposes a flexible design knob, enabling users to tailor decoding performance to the requirements of different fault-tolerant workloads. Our implementation is publicly available at https://github.com/IMSeonL/coset-ensemble-decoder.

Bosonic codes offer hardware-efficient approaches to quantum error correction, with the best encodings offering effective protection of idle quantum information against loss and dephasing - particularly rotation-symmetric codes, which include the cat and binomial code families. However, rotation-symmetric codes are only naturally endowed with a single logical Pauli gate, while other logical gates require the use of non-linear operations, obstructing the utility of these codes for realizing quantum algorithms. Here, we balance error protection with controllability by introducing bosonic cyclic codes: a generalization of rotation-symmetric codes that enable the measured tradeoff of error protection properties for fault-tolerant logical phase gates. Through our general construction, we find that sacrificing the detectability of a single photon loss relative to a rotation-symmetric code can yield a number of logical phase gates commensurate with the original rotation symmetry order of the code, all achievable via passive Gaussian rotations. Giving the corresponding generalizations of cat and binomial codes - which we dub cyclic cat and Vandermonde codes, respectively - we further find that many of the desirable properties of these codes transfer to the bosonic cyclic code setting. We go on to discuss the larger $SU(2)$ symmetry and rotation gates of the codes, which yield additional stabilizers and logical Pauli gates, as well as new non-Clifford gates for the smallest `kitten' binomial code, and provide a new error detection protocol. Finally, we introduce a general paradigm for converting higher-order stabilizers to logical gates, as in our generalization of rotation-symmetric codes, and apply it to several multimode bosonic codes.

Crosstalk refers to unwanted qubit addressing. This is particularly detrimental when scaling up quantum information systems because unintended interactions limit their overall performance. For superconducting qubits, tunable couplings and frequency tunability achieved through externally applied magnetic fluxes enable high-fidelity entangling gates; however, they also introduce crosstalk through unintended flux coupling. In this work, we investigate the impact of time-dependent external magnetic fluxes in quantized circuits on superconducting qubit couplings. We find that non-trivial cross-voltage driving emerges between capacitively linked qubits when the magnetic flux threading the SQUID loop of a qubit varies in time, in a manner analogous to Faraday's law of induction. Crucially, we show that this effect enables fast single qubit control through the coupler element in standard tunable-coupler architectures, potentially eliminating the need for individual microwave $XY$ control lines.

We present fast algorithms $\unicode{x2013}$ under the depolarizing noise assumption, often made in fault-tolerant quantum computations $\unicode{x2013}$ to test its strength. Our optimal algorithms answer the following question: is the quantum channel implemented by a given black box identical to a target unitary or $\varepsilon$-far from it in the diamond distance, assuming that the deviation is a depolarizing channel with unknown parameter? Our algorithm has a query complexity of $Θ(1/\varepsilon).$ The query complexity of the relaxed problem of testing whether the black-box channel is $\varepsilon_1$-close to a target unitary or $\varepsilon_2$-far in the diamond distance is $Θ\bigl(\varepsilon_2/(\varepsilon_2 - \varepsilon_1)^2\bigr).$ In both cases, we provide matching lower bounds that hold even for adaptive, ancilla-assisted protocols with multi-outcome incoherent measurements.

Superconducting resonators are central to superconducting quantum information technologies and essential for bosonic qubit architectures, where long-lived storage modes enable hardware-efficient error correction. Achieving ultra-high quality factors in scalable planar circuits is challenging because multiple dissipation channels contribute to the total loss. Here we report planar $α$-Ta resonators fabricated on 300 mm ultra-high-resistivity ($>10$ k$Ω$ cm) intrinsic silicon using industrial processes, achieving median internal Q factors exceeding 40 million and maxima above 60 million. Energy-participation-ratio analysis identifies a dominant participation-controlled interface loss mechanism and places conservative upper bounds on substrate-associated dissipation. For the best-performing substrate, the inferred substrate loss tangent is below $1.0 \times 10^{-8}$, establishing industrial MCZ silicon among the lowest-loss substrate platforms reported for superconducting resonators. At the same time, the exceptionally low losses show no clear correlation with commonly cited silicon substrate metrics such as room-temperature resistivity or impurity concentrations. More broadly, these studies establish industrial 300 mm processing, careful interface engineering, and 300 mm MCZ silicon substrates as a promising platform for resonator-heavy superconducting quantum architectures with ultra-high quality factors.

Recently, experimental and theoretical quantum error correction methodology has seen remarkable breakthroughs. In particular, magic state cultivation has been shown to simplify magic-state preparation and make it feasible for near-term devices. However, recent research on magic state cultivation has focused primarily on the cultivation of $T\left| + \right>_L$. Only a few other magic state cultivation methods beyond $T\left| + \right>_L$ have been investigated. Here, we generalize phase kickback checks for magic states at arbitrary Clifford hierarchy levels in specific codes. We provide an example of cultivation of $\sqrt{T}\left| + \right>_L$ in the doubled color code and the corresponding escape strategy using lattice surgery from the color code to large rotated surface codes. Using state vector simulation for un-grown cultivation, we observe a strong consistence between $S\left| + \right>_L$ and $\sqrt{T}\left| + \right>_L$ cultivation's performance on the doubled color code. Finally, we discuss the application of the corresponding $\sqrt{T}\left| + \right>_L$ cultivation, incorporating the STAR architecture and $T$ gates, for early fault-tolerant quantum computing and its potential to shorten gate synthesis in the fully fault-tolerant quantum computing era.

Uniform permutation generation is a fundamental task in both classical and quantum computation, with applications ranging from cryptography to quantum optimization and quantum error correction. Existing exact quantum constructions typically require all-to-all qubit connectivity and quadratic circuit depth. We develop a variational quantum circuit framework for uniform permutation generation under connectivity constraints, in which the circuit architecture is determined by the underlying interaction graph and the variational parameters are optimized to enforce the target permutation statistics. In particular, we present explicit controlled-SWAP-based unitary constructions that achieve exact uniformity with quadratic circuit size and linear depth \(O(n)\) on linear nearest-neighbor topologies. Our approach, therefore, removes the need for all-to-all connectivity while improving the depth of previous exact constructions by a factor. We further prove that a quantum Beneš-like architecture is intrinsically non-uniform. Despite its logarithmic depth and ability to realize any permutation it cannot generate a uniform distribution over permutations for any choice of variational parameters. These results clarify the role of circuit topology in exact permutation generation and identify variational quantum circuits as a natural framework for hardware-constrained uniform sampling. More broadly, this work suggests that exact uniform permutation generation is a strictly stronger requirement than mere permutation realizability, and lays the groundwork for a formal complexity separation between the two.

Scaling superconducting quantum computers toward thousands of qubits remains a difficult control hardware problem. It requires hardware that reduces room-temperature to cryogenic wiring and cryogenic power while preserving in-fridge programmability for microwave pulse generation. This work develops a 4 K hybrid photonic/CMOS control architecture in which optical fibers distribute shared shaped pulse templates, while local cryogenic CMOS (Cryo-CMOS) circuits provide transmission control, amplitude programming, sample-and-hold envelope shaping, LO-tone and phase selection, and microwave upconversion, enabling both single-qubit and two-qubit gate generation within the same control path. Compared with fully Cryo-CMOS controllers, this architecture reduces per-channel active dissipation by moving high-speed sampled RF/IF waveform synthesis and waveform-memory access out of each cryogenic channel. Compared with purely photonic-link qubit-control approaches, it adds local 4 K programmability for pulse selection, amplitude scaling, timing updates, and LO-phase control, while remaining compatible with room-temperature real-time feedback and quantum error correction (QEC) workflows. We present architecture-level first-order models for 4 K power dissipation, waveform-memory scaling, and controller-induced fidelity limits, and cross-check the dominant fidelity terms using a three-level transmon simulation. The analysis shows that shared optical pulse template distribution with local 4 K envelope programming is a feasible path toward scalable superconducting qubit control.

Fault-tolerant quantum memories depend on the syndrome extraction circuit as much as on the underlying code. Ancilla-free or dynamic circuits are an effective way to improve this circuit layer. For the 6.6.6 honeycomb Floquet code, making the circuit dynamic raises the threshold and lowers the qubit overhead, but at the cost of halving the spatial code distance. A dynamic construction for the 4.8.8 lattice layout was conjectured to preserve full distance. I confirm this and give a dynamic measurement circuit for the CSS 4.8.8 Floquet code. To benchmark it, I construct and compare four circuit-level implementations on a torus, including two dynamic variants (with and without mid-circuit resets), the standard ancilla-based circuit, and a pipelined ancilla-based circuit. Under circuit-level depolarising noise, the reset dynamic circuit reaches a per-round threshold of $0.463\%$ $(0.490\%)$ with MWPM (BP+matching), while the no-reset variant reaches the highest threshold of all four circuits at $0.512\%$ $(0.574\%)$. The standard ancilla-based circuit only achieves $0.228\%$ $(0.240\%)$, but the pipelined schedule reaches $0.478\%$ $(0.489\%)$. The reset dynamic circuit also has a faster-growing timelike distance, with $2\le d_t/n_{\mathrm{qec}}\le 3$ asymptotically against a tight $3/2$ for the other three, and running it for fewer rounds gives the smallest spacetime volume in the fast-reset regime, while the no-reset variant is smallest in the slow-reset regime. The 4.8.8 dynamic circuits therefore see the expected threshold gain and overhead reduction without the spatial-distance cost, demonstrating the advantage of dynamic syndrome extraction in Floquet codes.

Entanglement-assisted (EA) stabilizer codes enhance the rate of error correction in relation to codes with no pre-shared entanglement. Meanwhile, bosonic error-correcting codes, such as the Gottesman-Kitaev-Preskill (GKP) code, can be concatenated with qubit stabilizer codes to significantly reduce the logical failure probability of those stabilizer codes. First, we combine the above two concepts to propose an EA version of the qubit-into-oscillators concatenated code that chains an EA-stabilizer (outer) code with a GKP (inner) code. As an example we present a three-qubit EA-repetition concatenated with a GKP code. Second, we propose an EA version of the non-Gaussian oscillator-into-oscillators concatenated code that chains a GKP (outer) code with an EA-stabilizer (inner) code. As an example we present a GKP code concatenated with a three-qubit EA repetition code that uses two maximally entangled modes (emodes) and suppresses the variances of both position and momentum quadrature errors of a data mode. Furthermore, we generalize the latter example to a family of GKP code concatenated with a $n$-qubit EA repetition code that uses ${n-1}$ emodes and suppresses the variances of both position and momentum quadrature errors of a data mode by a factor ${1/n}$.

Quantum Key Distribution (QKD) has emerged as a fundamentally secure approach to communication in the era of quantum computing, offering protection against threats posed to classical cryptographic schemes such as RSA and Diffie-Hellman. This thesis presents a comprehensive performance analysis of satellite-based QKD protocols, focusing on both prepare-and-measure and entanglement-based schemes under realistic atmospheric and operational conditions. The study begins by introducing the theoretical foundations of quantum communication, including qubits, entanglement, and quantum entropy, and motivates the need for satellite-based QKD to overcome the distance limitations of fiber-based systems. Subsequently, the thesis evaluates four prominent QKD protocols-BB84, B92, BBM92, and E91-using a circular beam propagation model that incorporates atmospheric effects such as diffraction, turbulence, attenuation, and pointing errors, along with environmental noise contributions for uplink and downlink. Comparative numerical simulations reveal that protocol performance is strongly influenced by channel asymmetries, beam propagation characteristics, and noise, providing guidance on optimal protocol selection for low Earth orbit (LEO) satellite links. The research further investigates high-dimensional (HD) QKD protocols, specifically HD-BB84 and HD-Extended B92, using the elliptic-beam approximation to account for turbulence-induced distortions for both uplink and downlink. Simulations under vary ing system dimensions, weather conditions, and zenith angles demonstrate that HD-BB84 achieves higher key rates, superior noise tolerance, and more favorable probability distributions of the key rate compared to HD-Extended B92, highlighting the advantages of high-dimensional encoding for robust satellite-based QKD.

As quantum networks evolve from experimental testbeds to fault-tolerant systems, the primary performance metric shifts from physical link fidelity to end-to-end logical error rate. However, current control planes remain ill-equipped for this transition: routing decisions are typically decoupled from Quantum Error Correction (QEC) strategies, relying on topology or scalar fidelity metrics that fail to predict how specific physical noise structures interact with logical codes. Optimizing this coupled route-and-code performance requires precise, real-time visibility into network error biases, yet traditional active tomography is operationally prohibitive due to throughput collapse and service interruption. We present SCOPE (Syndrome-based COntrol PlanE), a network-layer architecture that enables joint routing and coding optimization using purely passive telemetry. Instead of injecting probes, SCOPE harvests error syndromes -- the parity-check outcomes naturally generated by QEC decoders during user service. By aggregating these signals, SCOPE's inference engine reconstructs the network's time-varying error map, capturing complex, context-dependent noise correlations. This visibility drives a decision engine that proactively pushes optimal route-and-code configurations to source nodes. NetSquid and IBM-calibrated simulations show that SCOPE reduces estimation error by more than 60% relative to a standard EM baseline. In large-scale networks, this precision reduces logical error rates by 30-35% (up to 65%) against topology-aware baselines.

We relate the properties of bivariate-bicycle-surface (BBS) codes, constructed from a pair of bivariate polynomials over a finite field, to the number and location of their common roots in the extension field. The number of roots $(x,y)$ with finite, non-zero coordinates -- counted with algebraic multiplicity -- determines the dimension of the codes. This dimension is invariant under monomial automorphisms of the Laurent polynomial ring. Conversely, roots with zero or infinite $x$- or $y$-coordinates indicate that specialized generators are required near the corresponding boundary (e.g., the left or right boundary for a root where $x$ is zero or infinite, respectively). These roots can appear or disappear under monomial transformations, which reveals the structure of tilted boundaries. Based on these results, we formulate a prescription for constructing BBS codes that works for regions with rectangular, diagonal, and arbitrarily tilted boundaries. A key advantage of this approach is that no corner corrections are needed, provided the polynomials satisfy orientation-specific edge conditions.

Fractional quantum Hall states are a cornerstone of topological physics, hosting fractionally charged quasiparticles with exotic statistics that promise to enable topologically protected quantum information processing. Among these, the Pfaffian state introduced by Moore and Read implements a p-wave pairing structure that supports excitations with non-Abelian exchange statistics. Despite extensive study in electronic systems, direct access to its pairing structure has remained limited. Here we realize a three-particle bosonic Pfaffian state of ultracold $^{87}\mathrm{Rb}$ atoms in an optical lattice subject to a Floquet-engineered synthetic magnetic field. Using a Bayesian-optimized adiabatic protocol, we prepare a state exhibiting Pfaffian pairing correlations. Site-resolved measurements of multi-point density correlations reveal a pronounced suppression of short-range three-body coincidences, reflecting the underlying pairing structure. We further probe the state's transport response through Hall drift measurements. Our results establish a bottom-up approach to engineering non-Abelian topological order and lay the groundwork for future explorations of anyonic braiding in synthetic matter.

Neutrino evolution in dense astrophysical environments is typically described either within a quantum kinetic framework, which neglects the build-up of multi-body correlations, or through simplified many-body calculations that allow significant entanglement to develop. In this work, we compare these two approaches in a simple neutrino-gas configuration, with particular emphasis on the role of non-forward scattering processes. These effects are incorporated either through a collision term in the kinetic description, or by considering the full neutrino-neutrino many-body Hamiltonian. We highlight differences between the two descriptions in both their characteristic timescales and asymptotic behavior. Motivated by the natural suitability of quantum computing for many-body calculations, we further investigate the non-classicality of neutrino evolution, discussing Trotter error scaling, along with the associated costs of constructing quantum circuits in terms of entangling gates and non-Clifford gates. We find that the resources needed for neutrino many-body evolution are on the low end of typical high-energy physics problems and on the mid to high end with respect to quantum chemistry problems. For the full Hamiltonian, resource requirements increase relative to the truncated version. We emphasize the importance of efficient fermion-to-qubit encodings, which are essential for reducing the substantial computational resources required for such simulations.

The stabilizer fragment of the ZX calculus is amongst the most important fragments of the theory. The closely related Clifford+T fragment is approximately universal (arXiv:1705.11151). Additionally, the stabilizer calculus can be described by a small collection of rewrites, most of which have been shown to be necessary (arXiv:1709.08903). However, two rules, describing the red/green compact-structure coincidence and the important bialgebra law, had not been shown to be necessary. We present a countermodel-style argument showing that both of these rules are individually necessary relative to the connectivity meta-rule of Backens--Perdrix--Wang (arXiv:1709.08903), and hence establish that the rule set presented in arXiv:1709.08903 has no redundant rewrite rule.

Bell's theorem shows that entangled quantum particles can exhibit correlations that classical particles cannot reproduce without an additional nonlocal resource, such as communication. In this sense, quantum particles are fundamentally more nonlocal than classical ones, and entanglement becomes unavoidable in physics. Here we prove the analogous result within quantum theory itself: indistinguishable fermions transmitted through a quantum network can generate correlations that distinguishable particles or indistinguishable bosons cannot reproduce without additional communication. In the same sense, fermions are fundamentally more nonlocal than bosons or distinguishable particles, motivating fermionic anticommutation and indistinguishability as unavoidable operational resources. Our result further implies that fermions can strictly surpass all qubit-based protocols for certain distributed computing tasks, demonstrating that a complete understanding of information processing requires going beyond qubits to fermionic information carriers - febits.

We theoretically investigate spin- and valley-resolved quantum transport in monolayer tungsten diselenide (WSe$_2$) described by an effective massive Dirac Hamiltonian. Particular attention is devoted to a finite barrier region characterized by simultaneously modulated Fermi velocity and scalar potential. The barrier velocity $v_2$ is related to the external velocity $v_1$ through a velocity ratio $ξ=v_2/v_1$, motivated by an optical analogy with the Snell-Descartes law. The exact refraction condition depends on the full spin- and valley-resolved dispersion, and the simple ratio $ξ=v_2/v_1$ is recovered only in the massless, symmetric limit. The interplay of intrinsic spin-orbit coupling in the conduction and valence bands, quantified by $λ_c$ and $λ_v$, with spin- and valley-dependent Zeeman fields, $M_s$ and $M_v$, gives rise to substantial changes in the quasiparticle dispersion, leading to pronounced modifications of the transport characteristics. By solving the Dirac equation and enforcing current-conserving matching conditions at the interfaces, we compute the spin- and valley-dependent transmission probability and conductance. Our results demonstrate that the barrier velocity, scalar potential, incidence angle, incident energy, and barrier width serve as effective control parameters for transport, giving rise to strong anisotropy and resonant tunneling features. Furthermore, we show that both the magnitude and orientation of spin- and valley-polarized currents can be continuously tuned via velocity and potential modulation. These findings establish combined velocity and potential engineering as a powerful theoretical framework for controlling spin-valley physics in two-dimensional transition-metal dichalcogenides.

We consider a movable conducting plate of finite mass, between two fixed ones, whose mechanical degrees of freedom are treated quantum-mechanically and bound to its equilibrium position by a harmonic potential. The movable wall is thus subjected to quantum fluctuations of its position. This creates a system of two sub-cavities separated by the movable fluctuating plate, and two massless one-dimensional scalar fields, one in each sub-cavity. This system is described by an appropriate generalization of the Law Hamiltonian. The presence of the movable wall yields an effective plate-fields interaction, as well as an effective interaction between the field modes. We obtain, at the second order in perturbation theory, the ground state of the interacting system and the reduced density operator of the fields in each sub-cavity by tracing out the wall's degrees of freedom. We calculate the entanglement between two field modes, one in each cavity, by evaluating analytically the negativity; we then evaluate numerically also the total multimode negativity. Our results show that in both cases the fields in the two sub-cavities are entangled, in contrast to the case in which the wall is fixed in space. We discuss the amount of the field entanglement present as a function of relevant physical parameters of the system such as the mass and oscillation frequency of the movable wall, its distance from the fixed walls and the frequencies of the field modes considered.

A quantum repeater segment is a basic building block of a quantum repeater, generating buffered entanglement of quantum memories to connect quantum repeater cells. It also enables the connection between quantum computers. In the implementation we present here, photons emitted from two co-trapped free-space coupled $^{40}$Ca$^+$ ions are converted to the telecom-C band and interfered after transmission over 440$\,$m of optical fiber (220$\,$m per arm), where a photonic Bell measurement is performed to create entanglement between the memories. With this scheme we generate an entangled $\left|Ψ^+\right\rangle$ Bell state with $\ge 68(8)\,$% fidelity, highlighting trapped $^{40}$Ca$^+$ ions as a promising quantum repeater hardware platform.

The standard in Earth-observation tasks today is having near real-time access to surface images in response to changing conditions. For instance, as urban environments interface more with wildlands and wildfires become less predictable, their tracking with satellite resources becomes essential. This requires the coordination of increasingly large constellations of satellites, giving rise to challenging computational problems. With wildfire detection and tracking as a backdrop, we investigate the power of special purpose and novel computing paradigms to tackle the ensuing satellite scheduling problems, making a compelling case for quantum algorithms. We bring quantum scheduling algorithms closer to implementation by examining both the emerging iterative quantum algorithm framework, which comes with analytic guarantees compared to some classical algorithms, and distributed quantum computing methods whose relevance is on the rise as utility-scale problems begin to get solved with quantum computers. Drawing strength from several computing fronts, we develop a distributed/parallelization scheme in conjunction with the quantum algorithm design and apply these techniques to real-world datasets for wildfire detection. While our quantum subprocesses are currently too small to see significant quantum advantage, our results validate the utility of these techniques, and continue forging the path toward distributed quantum computing.

The asymmetric three-qubit W-class state $|\overline{W_3^L}\rangle$ defines an isosceles entanglement-network geometry, (a) two vertex-base (VB) links form stronger bipartite connections, (b) while the base-base (BB) link is weaker. This suggests that concentrating entanglement into a super-link may be advantageous for quantum-network tasks. Here, we show that this intuition is incomplete. We analytically compare the bipartite concurrence dynamics of the symmetric |W> state and the asymmetric $|\overline{W_3^L}\rangle$ state, which differ both in entanglement-network geometry and excitation sector under standard noise models. In the absence of noise, the concurrence hierarchy is C_{VB} > C_W > C_{BB}$. Under phase damping, this hierarchy is preserved for all noise strengths and no entanglement sudden death occurs. Under amplitude damping, however, the hierarchy is reordered. The symmetric |W> state becomes the most robust, while the base-base concurrence of $|\overline{W_3^L}\rangle$ vanishes at the finite threshold of parameter $γ$. We term this reordering as the \textit{Super-Link Fragility Effect}. The same structural asymmetry that produces a stronger vertex-base link also makes it more vulnerable to energy dissipation when coupled with multi-excitation amplitudes. Under depolarization, the asymmetry advantage is erased, with $C_W$ and $C_{VB}$ sharing the same sudden-death threshold for some value of the parameter p, while $C_{BB}$ disappears earlier at some other value of the parameter p. The generalized amplitude damping channel continuously connects the damping-dominated regime to the pure-excitation limit, where the initial hierarchy is restored. These results show that entanglement robustness in $W$-class resources is controlled not by initial concurrence alone, but by the joint structure of entanglement-network geometry, excitation sector, and noise symmetry.

The origin of cosmic acceleration remains a central problem in cosmology, commonly attributed to a cosmological constant within the $Λ$CDM model or to dynamical dark energy. Here, we develop an alternative approach in which acceleration emerges from quantum post-selection, a standard feature of quantum theory that is not usually incorporated into cosmological modelling. While quantum theory admits both pre-selected and post-selected ensembles, quantum cosmological models are almost exclusively formulated in terms of initial conditions. Building on previous work on post-selected quasiclassical dynamics, we construct a minimal predictive cosmological model in which post-selection and coarse-graining generate effective late-time acceleration without introducing a cosmological constant, dark energy, or modifications of general relativity. The resulting expansion history is highly constrained theoretically and depends on at most two parameters beyond standard Friedmann evolution. Confrontation with type Ia supernova and cosmic chronometer data yields statistically competitive fits while naturally avoiding the coincidence problem. The model also reproduces the standard radiation- and matter-dominated behaviour at early times and predicts a present-day jerk parameter significantly different from the $Λ$CDM value. These results suggest that cosmic acceleration may arise as a macroscopic quantum cosmological effect rather than from additional cosmological fluids or modified gravitational dynamics.

Reference frame mismatch among communication parties introduces errors in quantum cryptographic protocols. As the number of participants increases, aligning reference frames becomes increasingly difficult, complicating multipartite quantum cryptographic implementations. Here, we theoretically and experimentally investigate multipartite reference-frame-independent (RFI) quantum cryptographic communication using Greenberger-Horne-Zeilinger (GHZ) states. We generalize the bipartite RFI security parameter $C$ to an $N$-party parameter $C_N$ and derive the asymptotic secret key rate expressed solely in terms of experimentally accessible quantities. We analyze the key rate under global and local depolarizing noise models and find that increasing the number of parties $N$ enhances robustness against global depolarizing noise while increasing vulnerability to local channel noise. We also present a proof-of-principle experimental demonstration of four-party RFI quantum cryptographic communication using four-photon GHZ states, confirming the reference-frame invariance of both the $C_4$ parameter and the secret key rate under various reference frame rotations.

Characterization of time-frequency (TF) quantum states requires reliable reconstruction of their TF distributions. However, imperfect transmission or measurement channels can distort reconstructed joint spectral intensities (JSIs), especially when the underlying perturbation mechanism is unknown. Here, we experimentally demonstrate a reconstruction and correction framework that uses a TF grid state as an intrinsic frequency-domain reference. By analyzing the displacement of the grid points, a Gaussian process regression model is employed to reconstruct a correction mapping for the nonlinear coordinate deformation without assuming a prior physical model of the distortion. The learned mapping reduces the residual coordinate deviation of the TF grid state by approximately a factor of 11 and, when applied to an independent frequency-entangled test state, improves the Gaussian-shape fidelity from 76.2\% to 90.0\%. These results establish TF grid states as practical metrological resources for diagnosing and correcting distortions in TF quantum systems, providing a pathway toward distortion-resilient quantum communication and high-dimensional quantum information processing.

A central principle in quantum machine learning is that an ansatz should be expressive enough to represent the quantum data of interest. Yet, the expressibility is statistically meaningful only insofar as it can be learned from finitely many copies of an unknown quantum state. In this work, we develop an information-theoretic Occam theory for quantum data generated by finite-size quantum circuits. For the class $S_{n,G}$ of $n$-qubit pure states preparable with at most $G$ two-qubit gates, a metric-entropy argument gives the realizable sample law $\widetildeΘ(G/ε^2)$ in the circuit-limited regime. For an arbitrary source $\hatρ$, we introduce the best $G$-gate approximation error $d_G(\hatρ)$ and the approximate circuit complexity $C_η(\hatρ)$. We prove an agnostic quantum Occam theorem: with $M$ copies, one can learn up to the best $G$-gate approximation error plus a statistical penalty $\widetilde{O}(\sqrt{G/M})$. We then remove the need to know $G$ in advance through an adaptive model-selection theorem whose oracle inequality selects the circuit complexity justified by the data. Matching lower bounds yield a sample-supported expressibility law: at trace-distance accuracy $ε$, $M$ samples can support only $G_{\rm supported} \simeq Mε^2$ gates, up to logarithmic factors and tomography saturation at $2^n$. Thus, the circuit complexity becomes an adaptive statistical resource rather than a static promise. Our framework turns bounded circuit complexity into a model-selection principle for quantum machine learning.

Single-wall carbon nanotubes (SWCNTs) are narrow ribbons of graphene with atomically precise edges and a single quantum transport channel, at experimentally-relevant dopings. This makes them ideal systems to harness quantum transport straintronics (QTS), i.e. using mechanical strain to control accurately quantum transport. We present QTS data from three single-wall carbon nanotube quantum dot (SWCNT-QD) transistors over a broad range of in-situ tunable and reversible uniaxial strain ($Δ\varepsilon_\text{mech}\approx$ 0 to 3 %). We first present the nanofabrication of the suspended SWCNT transistors whose channel lengths are $\approx$ 30 nm. The channels are strained by moving gold clamps holding firmly the nanotubes. We present detailed charge transport data, $dI/dV_{\text{B}} - V_{\text{B}} - V_{\text{G}}$ and $dI/dV_{\text{B}} - V_{\text{B}} - Δ\varepsilon_\text{mech}$, showing a large mechanical-gating effect of the SWCNT-QDs. The precise reversibility of the data, and their agreement with QTS theory, confirms that the tubes are strained elastically. We demonstrate that the mechanical control of the QD doping is not due to capacitive-gating effects, but to quantitatively predictable bandstructure changes including a strain-tunable bandgap. This precise mechanical control of the doping and bandgap of SWCNT-QDs could find applications in qubits, condensed matter physics, and homojunction molecular transistors.

Randomness amplification, the task of extracting uniform private bits from biased seeds that may be partly known by a malicious third party, is of central importance in cryptography. The highest security in this task is provided by a class of quantum protocols known as device-independent, which however are challenging to integrate into scalable devices. Semi-device-independent (SDI) protocols are a promising alternative that guarantees security under few natural assumptions, such as bounds on the amount of energy used by the devices. Here, we provide the first demonstration of SDI randomness amplification on an integrated silicon photonic chip, achieving a throughput rate of 20 Mbps suitable for practical applications. This rate is achieved through a novel technique for SDI entropy certification, which delivers strictly tighter von Neumann entropy bounds compared to existing methods and remains valid even if the preparation and measurement devices share quantum correlations. Overall, the methods developed in this work enable the integration of SDI technology into portable telecom devices, opening up a new generation of quantum cryptographic hardware.

Fiber optical cavities offer small mode volumes and correspondingly strong light-matter interactions in an open Fabry-Perot geometry. However, existing fabrication techniques do not reliably produce substrates with surface profiles amenable to high mode matching between the cavity mode and fiber core, thereby limiting the achievable collection efficiency. Here we present a technique to fabricate fiber mirror substrates while using $\textit{in situ}$ reflectometry to constrain the achievable mode matching prior to coating. By measuring the back-reflection from freshly cleaved fiber tips, we pre-select 138 fibers compatible with 96.5-99.5% mode matching, and after a single CO$_2$ laser ablation pulse, these fibers remained compatible with 95.3-99.2\%. This simple technique provides rapid feedback during each stage of substrate fabrication, greatly enhancing the yield of viable fiber mirror substrates prior to (expensive) coating runs.

In this chapter we review some results describing the high-frequency eigenmodes of the Laplacian on compact manifolds, or Euclidean domains, for which the geodesic flow is chaotic. We focus on the macroscopic distribution of these eigenmodes, which is described by the concept of semiclassical measure. The main result on the question is the Quantum Ergodicity theorem, originally due to Schnirelman. We provide the detailed proof of this theorem, including the adjustments necessary to treat the case of manifolds with boundary. We also discuss the Quantum Unique Ergodicity conjecture, and some progress towards this conjecture for strongly chaotic (Anosov) systems. In particular, we describe the constraints on admissible semiclassical measures, in terms of their Kolmogorov-Sinai entropy, as well as more recent delocalization results.

Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. For the case where this set consists of only products of Pauli operators, known as Pauli strings, we provide a necessary and sufficient condition for it to generate $\mathfrak{su}(2^n)$, i.e., to be universal for quantum computation on $n$ qubits. When combining Pauli strings with a general Hamiltonian, we show a sufficient (and in certain circumstances even necessary) condition for universality based on the Pauli-basis expansion of the Hamiltonian. As an application of these results, we prove two corollaries: (i) a necessary and sufficient condition for the universality of a general Hamiltonian given arbitrary single-qubit control on all qubits, and (ii) the universality of an XYZ Heisenberg Hamiltonian with local control of just two adjacent qubits.

Non-Hermitian systems can evade Anderson localization and exhibit delocalized states even in one dimension. Here, we show that such non-Hermitian delocalized states under periodic boundary conditions (PBC) are intrinsically critical, realizing the universality class of one-dimensional random Dirac fermions. By linking spectral winding to topological Anderson transitions via Hermitization, we demonstrate that the delocalized PBC states exhibit a Dirac-type criticality with universal algebraic correlations. In contrast to Hermitian systems, where this criticality occurs only at fine-tuned transition points, it emerges generically in non-Hermitian systems as a consequence of spectral topology. These results identify a universal mechanism by which non-Hermiticity promotes criticality, providing a unified description of non-Hermitian delocalization in one dimension.

We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped Quesne oscillator potential. Our investigation is based on a finite-difference version of relativistic quantum mechanics. So-called relativistic configurational r-space is a key concept here. We show that the radial wavefunctions and angular wavefunctions are expressed through the continuous dual Hahn polynomials and Jacobi polynomials, respectively. A discrete energy spectrum has been found. The radial wave functions and energy spectrum have the correct nonrelativistic limit. We also build a dynamical symmetry group SU (1, 1) for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

In quantum mechanics, a measurement applied to a state in general produces some amount of intrinsic randomness. This is not only a fundamental feature of the theory, but is also at the basis of any quantum process to generate random numbers. The simplest of such processes consists of a single, fully charaterized, measurement acting on a single, fully characterized, state. Unfortunately, no general method to estimate the intrinsic randomness produced in such setups is known. In this work, we address this issue by presenting a semidefinite programming formulation of the maximum probability with which an adversary, Eve, can guess the outcomes of characterized but untrusted prepare-and-measure setups. We then present several applications of this construction. First, we apply our method to a variety of specific setups, allowing us both to benchmark the approach and, more importantly, to determine the exact amount of certifiable randomness in scenarios where only upper bounds were previously available. Then, we show that the presence of entanglement between the device preparing the state and the measurement strictly increases Eve's predictive power, already in the most elementary setup of a binary measurement acting on a qubit state.

The harmonic oscillator is considered within generalized frameworks using complex and quaternionic numbers. The classical oscillator is considered in terms of a complex position function, and quantum oscillators are examined in terms of complex wave functions, and in terms of quaternionic wave functions as well. Both of the quantum solutions are obtained within the real Hilbert space formalism. The results reveal the complex and quaternionic descriptions as suitable frameworks for non-stationary processes, including damped oscillations, forced oscillations, and additionally self-interacting processes that cannot be appropriately described otherwise.

Entanglement is a key bottleneck limiting the efficiency of tensor-network and quantum simulations of molecular electronic structures. Here, we systematically assess and extend Clifford disentanglers as a structure-preserving approach to entanglement reduction: they can modify the entanglement structure of qubit wavefunctions while retaining the Pauli-string form of qubit Hamiltonians. To enable a practical search over Clifford transformations, we classify Clifford operators by their action on the Schmidt spectrum across a bipartition, reducing the two- and four-qubit search spaces to 20 and 91392 representatives, respectively. Embedded in an iterative Clifford-augmented matrix product state framework, these transformations reduce the energy errors at fixed bond dimension for the molecular test cases studied and mitigate the dependence on orbital orderings and fermion-to-qubit mappings. We further show that Clifford disentanglers can also benefit quantum simulations such as the shallow-circuit variational quantum eigensolver calculations. Together, these results establish Clifford disentanglers as a useful structure-preserving entanglement-engineering tool for tensor-network and quantum simulations of molecular electronic structure, while also clarifying their correlation dependence and motivating future developments.

We introduce a geometrically constrained hidden-variable framework that generates a family of correlations parametrized by a boundary function, within which the quantum singlet correlation appears as a particular member. Exact expressions for the correlation function are derived. Several structural results are established, including admissibility conditions, symmetry properties, a universal stationary point of the associated CHSH function, and an exact relation between the CHSH value at $ν=π/4$ and a geometric contrast measure defined on the underlying hidden-variable distributions. Rather than treating the quantum singlet correlation as an isolated target to be reproduced, the present framework places it within a broader geometric structure of correlations. These results suggest the existence of a nontrivial geometric structure underlying the family of correlations and motivate the search for a principle capable of selecting the quantum singlet solution from within that family.

Characterizing quantum processes is essential for hardware benchmarking, error diagnosis, and algorithm verification. While recent work [PRX QUANTUM \textbf{4}, 040337 (2023)] extended classical shadows from quantum state to quantum process, enabling efficient single-channel $\mathcal{E}$ property prediction, its applicability to composite processes $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$ remains unexplored. We introduce shadow engineering, a framework encoding the classical shadows of processes into sparse transfer matrices to predict $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$ properties with proven polynomial sample complexity, matching single-channel efficiency while exponentially lower than quantum process tomography. Crucially, this approach repurposes existing $\mathcal{E}_m$-shadow data without physical execution of $f(\mathcal{E}_1, \mathcal{E}_2,\cdots, \mathcal{E}_k)$, enabling flexible quantum process characterization with minimal hardware overhead. We demonstrate the framework's effectiveness and practicality on a superconducting quantum processor for typical applications such as error mitigation and Hamiltonian dynamical simulation. This framework unlocks new capabilities for predicting complex quantum behaviors without physical re-execution, with immediate applications in near-term device calibration and quantum simulation.

The quantum information lost in open evolutions cannot be fully recovered, but partial recovery is possible. The Petz recovery map guarantees almost optimal recovery, notably if the chosen reference state is close to the real one. This map has been widely used in theoretical studies, but has been the object of only a handful of experimental realisations, typically under a single fixed noise model. In this work, we describe and implement the Petz recovery map for a versatile class of qubit channels with tunable decoherence and dissipation. The setup we realize is also the first experimental example of ``tabletop reversibility'': for a good range of choices of the reference state, the Petz recovery map can be implemented with the same devices as the forward dissipative evolution, whose effect it is partially undoing. Our results demonstrate that the Petz recovery map can be resource-efficiently realized without requiring complex ancillary resources, providing a feasible pathway for mitigating information loss in quantum systems.

Quantum systems face a fundamental trade-off: they must remain decoupled from the environment to maintain long coherence times, yet they require interactions with the environment to be accessible for measurement. As a prime example, emitter arrays coupled to waveguides facilitate collective modes that, owing to interference, can suppress radiation into the waveguide. While complete destructive interference creates perfectly dark states with infinite lifetimes, their inherent decoupling makes them unmeasurable in standard waveguide quantum electrodynamics. Consequently, current approaches must rely on system non-idealities that permit measurement but limit the coherence times. In this work, we lift this limitation by proposing the use of weakly squeezed light generated in \{chi}(2) nonlinear waveguides for the spectroscopy of completely dark states. We show that the fluorescence spectrum probes transitions between the dressed dark states of the emitter array. This work paves the way towards the measurement and control of dark states, with applications for robust quantum memories, computation, and communication.

We explore an array of quantum emitters as non-equilibrium probes, coupled to a one-dimensional photonic waveguide, aiming to estimate its properties such as wave number which encodes the waveguide frequency and dispersive characteristics. By considering transient dynamics following initial excitation, we show that the quantum Fisher information (QFI) can be significantly enhanced through careful emitter positioning. For two-emitter probes, optimal spacing stabilizes populations and coherences in the single-excitation subspace, suppressing super radiant decay and extending both the magnitude and longevity of QFI. Randomized emitter configurations also reveal that vanishing waveguide-mediated cross decay maximizes both achievable sensitivity and the temporal duration over which information about the parameter remains accessible. Extending to multipartite probes, we demonstrate that the maximum QFI and its temporal integral scale with system size, exceeding the Heisenberg limit for all positioning strategies. Our results highlight the potential of waveguide-coupled emitter arrays as versatile quantum sensors, where collective radiative dynamics can be harnessed to achieve tunable, long-lived, and enhanced precision.

Molecular rare-earth-ion complexes offer unique opportunities for quantum technologies by combining the intrinsic coherence properties of rare-earth ions with chemically tunable molecular environments. A crucial capability is the realization of multi-qubit architectures with defined qubit couplings to enable two-qubit quantum gates. Here, we investigate the optical coherence properties and excitation-induced interactions of two Eu$^{3+}$-based molecular complexes, comparing a mononuclear reference system with a dinuclear analogue in which two Eu$^{3+}$ ions are positioned at a well-defined intramolecular distance of about 7 Angstrom. Using cryogenic ensemble spectroscopy, including spectral hole burning, free-induction decay, and photon echo measurements at temperatures down to 100 mK, we demonstrate long optical coherence times $T_{2,\text{o}}$ of up to 9 $μ$s. As a key step toward scalable multi-qubit architectures, a control-target sequence was implemented to probe conditional ion-ion interactions, revealing a stronger interaction-induced dephasing in the dinuclear complex. Finally, we show the integration of the dinuclear complex into a fiber-based optical microcavity, and observe an 380-fold emission enhancement of the $\mathrm{}^5\mathrm{D}_0\rightarrow\mathrm{}^7\mathrm{F}_0$ transition. Together, these results position molecular rare-earth complexes as versatile and chemically tunable building blocks for scalable quantum technologies.

Trace norms are fundamental to quantum information theory, yet in many-body systems their evaluation remains a major computational bottleneck, as it generally requires diagonalizing exponentially large operators. Here, we overcome this bottleneck by introducing a controlled tensor-network algorithm for estimating the trace norm of matrix product operators without full diagonalization. The key idea is to combine Zolotarev's rational approximation to the sign function with a variational formulation solved using a density-matrix-renormalization-group-like algorithm. The resulting approximation is systematically improvable, with its accuracy controlled by the rational approximation parameters and the spectral weight near zero. Beyond the reach of exact diagonalization, we demonstrate controlled trace-norm calculations for entanglement negativity, quantum fidelity and quantum Fisher information, achieving substantially improved accuracy over polynomial-based Lanczos approaches. Our results establish trace-norm-based quantities as practical tensor-network observables, opening a route toward tensor-network studies of quantum information in mixed states.

The Traveling Salesman Problem (TSP) is a classical NP-hard problem in combinatorial optimization, where determining the shortest route among a set of cities becomes computationally prohibitive as the problem size increases. This work explores quantum computing as an alternative approach to address this complexity. Unlike existing methods that primarily rely on quantum annealing, we propose a quantum iterative framework integrating Quantum Phase Estimation (QPE) and Grover's search algorithm. Route costs are encoded as quantum phases, enabling QPE to efficiently evaluate them, while Amplitude Amplification, implemented via the Grover-Long algorithm, iteratively refines the solution space toward the optimal route. A proof-of-concept case study on a small-scale TSP instance demonstrates the feasibility of this approach and its potential for scaling to larger optimization problems. Furthermore, under an expectation-based analysis, the algorithm exhibits an expected computational complexity of $O(\frac{m^2\log_2(m)\log_2(1/ε)}{\sqrtε})$ which depends on the error tolerance parameter $ε$. This estimation omits the initialization term, which we expect future refinements to render subdominant to Phase Estimation.

We study statistics of atypical measurement outcomes in the steady states of driven open quantum systems. In equilibrium, the probability distribution over the phase space, as encoded in, e.g., the Wigner function, is analytic in the phase-space coordinates. We show that this property is generically lost in driven dissipative systems: their {\it large-deviation function} develops lines and surfaces across which its derivatives are discontinuous. As an illustrative example, we consider a parametrically driven Kerr oscillator coupled linearly and/or nonlinearly to a dissipative bath. Rare fluctuations in the amplitude and phase of the induced oscillations are governed by semiclassical instanton trajectories of the corresponding Keldysh-Lindblad action. We demonstrate that a given fluctuation can be realized through multiple distinct instanton trajectories. The competition between these trajectories leads to abrupt switching of the dominant instanton and, consequently, to non-analytic features in the large-deviation function.

Machine-learning approaches to quantum state tomography can achieve high reconstruction fidelity, but the physical structure used by the trained model often remains implicit. Here we ask whether a sparsified Kolmogorov-Arnold Network (KAN) can be used not only as a regressor, but also as an inspectable reconstruction rule whose internal organization can be checked against known Pauli structure. We study a controlled three-qubit GHZ-family benchmark in which all 63 non-identity Pauli expectation values are used to reconstruct three GHZ-subspace variables: the population imbalance $z$, the real off-diagonal component $c$, and the imaginary off-diagonal component $s$. Under finite-shot sampling and depolarizing noise, external ablation identifies the extended 12-channel GHZ-relevant Pauli set from the 63 measurements, with exact top-12 recovery across the tested shot counts and depolarizing-noise strengths. These support patterns remain stable across multi-seed random-initialization and noise-level analyses, and collapse under random-label controls. The dominant pruned input-hidden-output pathways organize Z-type population observables and X/Y off-diagonal observables in a pattern consistent with the analytic GHZ Pauli grouping, and sparse formula recovery recovers the canonical signed Pauli relations. The contribution of the KAN is therefore pathway-level structural interpretability within a neural reconstruction model, rather than superior sparse regression. Together with negative controls, these probes provide a consistency chain for auditing learned reconstruction rules against known physical structure.

We establish a rigorous mathematical bridge from quantum many-body path integrals to the cusp catastrophe model by Lyapunov-Schmidt reduction, which provides a theoretical foundation for analyzing superconducting phase transition using the catastrophe theory. First, it is proved that, near the critical point the infinite-dimensional effective action is diffeomorphic to a finite-dimensional catastrophe. Secondly, starting from Ginzburg-Landau free energy functional, the Euler-Lagrange partial differential equation can be reduced to the cusp catastrophe model. Thirdly, the fermionic imaginary-time path integral to the cusp catastrophe is derived through the Hubbard-Stratonovich transformation, Matsubara frequency expansion, and Grassmann algebra. Furthermore, we connect this framework with the adsorption potential theory we proposed, elucidating the catastrophic topological nature of the electron pairing mechanism in high-temperature superconductivity. The precise microscopic derivation of the adsorption potential from first-principles electronic structure calculations would strengthen the predictive power of the theory.

In closed quantum systems, local information spreads throughout the entire system and becomes highly complex under unitary evolution. In contrast, when the system is embedded in an environment, system-environment coupling can transfer information from the system into the environment, thereby reducing the rate of complexity growth within the system. This leads to the environment-induced scrambling transition established in previous works. In this work, we identify entropy injection from the environment as a different physical process that instead enhances many-body chaos. Our setup consists of coupling a system that is already in equilibrium with one environment to another environment, which serves as an entropy reservoir and drives the system into a non-equilibrium state. When entropy flows into the system through either heat transfer or particle transfer, the effective Hilbert space explored by the system enlarges, a mechanism that can enhance many-body chaos. We explicitly demonstrate this idea by constructing a solvable complex Brownian SYK model, in which both the relaxation toward the steady state and the steady-state quantum Lyapunov exponent can be computed analytically. Our results provide a controllable mechanism for tuning quantum scrambling through entropy flow in quantum many-body systems coupled to environments.

We study the dynamics of quantum correlations in the hydrogen hyperfine spin system subject to Markovian phase noise. Treating the electron and proton spin degrees of freedom as an open two-qubit system governed by an isotropic hyperfine Hamiltonian and local dephasing, we obtain the exact time-dependent density matrix and derive analytical expressions for the full X-state family. We compute concurrence($C$), trace-distance measurement-induced nonlocality (Trace MIN--$\mathcal{N}_1$), and average steering coherence (ASC) in closed form and establish their strict ordering $ C(t)\leq \mathcal{N}_1(t)\leq \mathrm{ASC}(t) $ at all times. Entanglement is identified as the most fragile resource, undergoing sudden death at a finite time. Trace MIN exhibits dephasing-immune freezing for states with nonzero population imbalance, while ASC is the most robust quantity, persisting longest in every scenario studied.We additionally demonstrate that the dephased thermal hyperfine state serves as a resource for quantum teleportation, deriving a closed-form expression for the average fidelity and establishing that the teleportation advantage window coincides exactly with the entanglement survival interval, $\mathcal{F}_A > 2/3 \Longleftrightarrow \mathcal{C} > 0$, for the full X-state family with maximally mixed marginals. We identify four distinct dynamical regimes and map all three correlation measures onto directly measurable Pauli spin correlators, enabling experimental reconstruction of the full hierarchy without full state tomography.

The position operator plays a central role in condensed-matter observables such as velocity, orbital moment, and electric polarization. In solid-state physics, the evaluation of operators incorporating the position operator has not reached a consensus, as observed in the operator-level discrepancy between the local circulation of Wannier functions and the self-rotation of wave packets. Here, to achieve a consistent evaluation of such operators, we propose three rules for evaluating operators involving the position operator in the Bloch representation. The rules are devised to satisfy physical conditions: independence from the choice of unit cell, preservation of Hermitian conjugacy for the product of operators, and recovery of the correct intraband velocity. We further address the gauge dependence of the position operator and introduce a scheme termed gauge filtration, which systematically removes gauge-dependent contributions from the operators containing the position operator. This methodology ensures that the quantities obtained from the operator evaluation correspond to observable physical phenomena. By applying our framework, we reconcile the results concerning the self-rotation of the wave packet and the local circulation of the Wannier function. We expect our proposal to establish a consistent framework for evaluating operators involving the position operator.

Standard dot-product self-attention computes, in a single layer, only pairwise (order-2) interactions between tokens; representing a generic order-$k$ interaction is known to require either super-quadratic resources in one layer or composition across depth. We introduce \textbf{Quantum Higher-Order Attention (QHA)}, a shallow, hardware-realizable quantum attention head that, via data re-uploading and an all-to-all non-Clifford entangler, synthesizes order-$k$ token interactions inside the circuit and exposes them through a local single-qubit read-out. We prove (i) an expressivity separation: any single standard self-attention layer with embedding dimension $m$, $H$ heads and $p$-bit precision satisfying $mHp=o(N/\log\log N)$ cannot represent the order-$k$ correlation family that one QHA head represents with circuit depth $O(\log k)$ ($O(k)$ two-qubit gates); and (ii) a trainability guarantee for its local-design instantiation: with a local read-out and $O(\log n)$ depth the gradient variance is $Ω(1/\mathrm{poly}(n))$ (no barren plateau), which we confirm empirically -- while being explicit that the more expressive all-to-all instantiation we benchmark is trained empirically and shows exponentially decaying gradients. Empirically, at a $6.5\times$ smaller parameter budget, QHA generalizes hidden-subset parity of every order $k\le6$ from disjoint inputs, whereas the larger classical attention head collapses past order~2; consistent with theory, the size of the advantage tracks the target's Fourier degree - largest for parity and shrinking when low-order structure is present. As an application, QHA serves as a compact high-order interaction detector across three domains - genetic epistasis, learning-parity-with-noise, and graph triangle detection - reaching the noise ceiling at the smallest parameter budget where field-standard linear methods fail.

The appeal of adiabatic quantum computing lies in its intrinsic robustness against various technical imperfections, making it attractive for many quantum information applications. However, it faces a fundamental challenge: accelerating the adiabatic operations while preserving adiabaticity within the qubit coherence time. In this article, we propose an electromagnetically induced transparency-based adiabatic CNOT gate protocol which harnesses atomic hyperfine intermediate states (HISs) to speed up the adiabatic evolution. The HISs, naturally-existed in two-photon transitions, often need to be suppressed due to their significant decay errors. In contrast, this paper introduces a novel method that utilizes appropriately chosen HISs not only to enhance the adiabaticity in STAY pathway but also to accelerate the population transfer in TRANSFER pathway. Through pulse optimization, we achieve adiabatic gate fidelities exceeding 0.9991 within 0.3903 μs in realistic Cs atomic setups. To demonstrate the generality of protocol we further assess the impact of decays from multiple HIS and extend our model to arbitrary number of states, providing a practical route toward fast and robust adiabatic quantum gates in Rydberg-atom platforms.

Quantum cloud platforms are poised to deliver powerful computing capabilities, but users have no direct means to verify which physical device executes their workload. This lack of transparency enables hardware substitution attacks, where a malicious adversary could redirect a job to a substituted or inferior processor. We present a general authentication framework that addresses this problem by constructing multi-dimensional quantum fingerprints from raw measurement data. Without any curve fitting, we directly concatenate the raw statistics of complementary experiments into a high-dimensional feature vector that preserves subtle device-specific information. A Mahalanobis nearest-neighbor classifier achieves 100\% benign authentication accuracy on three superconducting processors over a three-week chronological split. The classifier naturally yields an authentication confidence $C_{\mathrm{claimed}}$ which reveals device-specific safety margins and motivates per-device alert thresholds. We assess the framework's robustness under two distinct scenarios. Under additive isotropic Gaussian noise, $C_{\mathrm{claimed}}$ decays predictably at a rate explained by inverse covariance traces, enabling an early warning mechanism. Against white-box adversarial perturbations, the same confidence threshold detects $L_2$ targeted attacks with near-perfect success and reveals device-dependent empirical thresholds for $L_\infty$ attacks, while untargeted and sparse attacks are ineffective. The proposed framework thus unifies fingerprint extraction, drift-resilient authentication, proactive health monitoring, and adversarial defense, offering a practical step toward trustworthy quantum cloud computing.

Approximate tensor-network simulators enable classical simulation of quantum circuits beyond the reach of exact methods, but selecting optimal approximation parameters -- such as bond dimension thresholds -- remains a costly trial-and-error process. We present a family-aware neural architecture that predicts both the minimum approximation threshold required to achieve target fidelity and the expected wall-clock runtime for quantum circuit simulation, given only the circuit's OpenQASM description and execution context. Our key insight is that quantum circuits from different algorithmic families (e.g., QFT, Grover, VQE) exhibit fundamentally distinct simulation cost profiles due to their differing entanglement structures. We employ family-conditioned residual corrections -- additive, family-specific adjustments atop a shared backbone, drawing on established conditional computation techniques -- enabling the model to capture both universal circuit properties and algorithmic nuances. The architecture incorporates a pretrained family classifier (97.5% accuracy) and domain-informed algorithm fingerprint features derived from gate-composition heuristics. Evaluated on circuits spanning 7--130 qubits across 10 algorithm families, our system achieves 79.5% exact threshold accuracy (91.2% within one rung) and $R^2 = 0.82$ runtime correlation, with inference completing in approximately 50 ms -- replacing trial-and-error simulation runs that may take minutes to hours. Ablation studies confirm that family-aware modeling provides the single largest performance improvement (+3.2 percentage points), validating the hypothesis that algorithm family is a first-class feature for simulation cost prediction.

We investigate the atomic transition probabilities in atom-mirror set-ups that are in circular motion. In one scenario, the atom is in circular motion inside a static cylindrical mirror. In the other scenario, the cylindrical mirror rotates around its central axis while the atom remains static. We report structural similarity in the atomic transition probabilities between these two cases -- these probabilities are equivalent upon interchanging the field frequencies between the two scenarios. We interpret such an observation as a semi-classical phenomenon analogous to the classical Mach's principle.

We study superspace concentration as a quantum resource, formalized through the focus measure F(\r{ho}) = λ_max(\r{ho}_super) - the largest eigenvalue of the reduced superspace state - which quantifies the capacity of a quantum system to concentrate informational weight into a preferred subspace of an extended degree-of-freedom space. We develop a complete resource-theoretic framework around this measure and validate its properties through GPU-accelerated numerical simulation. Analytic decoherence predictions are confirmed to machine precision (1.11 x 10^{-16}) for superspace dimensions dS in {2,4,8,16,32}. Focus monotonicity holds across 10,000 random states with zero violations under four focus-non-generating channels across six system configurations. Focused quantum states resist coherent unitary attacks with significantly greater resilience than standard fidelity predicts, with focus remaining above 0.9 at attack strength ε = 0.302 versus ε = 0.174 for fidelity. We further demonstrate that the focus measure and the U(dS)-asymmetry measure are operationally distinct: asymmetry remains near zero and provides no robustness signal under coherent and targeted attacks while focus tracks spectral concentration and remains robust until ε > 0.3. The connection between Grover's algorithm and superspace concentration is made explicit via the identity F(|ψ_k><ψ_k|) = P(marked), providing a resource-theoretic interpretation of oracle query complexity. Finally, we provide the first numerical characterization of the focus capacity gap ΔF, identifying a log_2(dS) scaling law confirmed for both product and correlated noise channels.

We present an approach based on tensor networks for distributed quantum computing simulation of chemical wavepacket dynamics in a continuous variable representation. The central idea is that the tensor-network representation of the multidimensional time-evolution operator naturally induces an elevated Hilbert space where the dynamics decomposes into a set of independent lower-dimensional propagations. This transformation converts an entangled quantum evolution into a set of parallel computational tasks that can be executed asynchronously across heterogeneous quantum and classical computing architectures. The resulting formalism establishes a direct connection between tensor-network decompositions, uniformly controlled quantum circuits, and asynchronous distributed quantum computing. The approach is developed with a goal towards hybrid quantum/classical implementation, and is appropriate for a general heterogeneous mixture of quantum hardware systems. The experimental realization of the asynchronously distributed quantum processes that arise from the tensor-network decomposition are carried out on the Sandia National Laboratories' trapped-ion quantum computer, where the circuits are compiled using native partial-entangling $XX(θ)$ gates, reducing the expected two-qubit gate infidelity by more than 30\% relative to conventional fully entangling decompositions. We demonstrate the methodology by quantum computing the vibrational spectra of a small protonated water cluster that shows critical quantum nuclear behavior. Such water cluster systems have been found to be challenging for experimental action spectroscopy and for theory, and here, for the first time, we provide results for vibrational spectroscopy that are in agreement with the respective classical results to within 4cm$^{-1}$, thus allowing for the potential for spectroscopic accuracy from quantum computations.

Participation entropy (PE) quantifies the spread of a many-body wavefunction across configuration space. While PE relaxes rapidly in generic chaotic systems, we show that $\mathrm{U}(1)$ conservation laws slow it down by imprinting with the slow hydrodynamic modes. Using a cluster expansion around equilibrium, we show that, after local density inhomogeneities decay, the leading PE deficit is dominated by squared connected density correlations. The long time relaxation is therefore controlled by diffusive correlation spreading, giving $ΔS(t)\sim t^{-1/2}$ in the hydrodynamic regime and crossing over to $\sim \exp[-O(t/L^2)]$ when $t\geq L^2$. We confirm this entropy correlation relation using exact computation and infinite system tensor network simulations in various quantum $\mathrm{U}(1)$ conserving circuits. Our results establish PE as a sensitive probe of hydrodynamic memory and suggest that slow relaxation is a generic consequence of conservation laws.

Quantum batteries provide a useful setting for exploring nonequilibrium many-body effects in energy storage. Here we investigate the optimization of a quantum battery based on the central-spin model. We identify two complementary structural indicators associated with the effective charging dynamics: one yields an upper bound on the average charging power, while the other characterizes the buildup of stored energy. We show that these two indicators are jointly optimized at a distinguished initial charger excitation number, which selects a particular Dicke sector of the model. At this common optimal point, the effective charging Hamiltonian becomes exactly mirror symmetric, suggesting mirror symmetry as a useful structural indicator for optimizing quantum batteries. We further show that the corresponding optimal dynamics can be closely approximated by product initial states, in particular by spin coherent states whose excitation-number distribution is centered at the symmetry-selected point. Our results establish a direct connection between charging performance, optimal-state structure, and emergent symmetry in the central-spin quantum battery, and suggest symmetry as a useful organizing principle for efficient charging in interacting many-body quantum systems.

Mesoscopic colliders provide an effective platform for probing the mutual statistics of quantum particles. Recent experiments have successfully extracted the mutual statistics of fermions, and more exotic anyons using quantum point contacts (QPCs). Coupling a point-like collider, such as a quantum point contact, to a two-level impurity or qubit can induce statistical transmutation of fermions, causing them to display boson-like bunching tendencies. Here, we extend the analysis to an extended collider. We investigate the scattering of two incoming fermionic and bosonic wave packets in the presence of post-selection on the impurity state, and systematically analyze the possible benchmarks used to characterize bunching and infer the underlying mutual statistics. We show that only a specific benchmark faithfully captures the mutual statistics of the colliding particles, while alternative choices can produce spurious statistical signatures. Hence, the correct benchmark for probing the quantum statistics depends on the intricate details of the mesoscopic collider.

A new type of Yang-Baxter equation (YBE) for $R$-matrices parameterized by three spectral parameters is constructed from the star-triangle and star-star relations for the chiral Potts model. As the $Z_N$ symmetric generalization to the Ising model, its Boltzmann weights are known to depend on two variables describing a curve with genus larger than one for $N>2$, except for the self-dual point corresponding to the Fateev-Zamolodchikov chain. This combined with the fact that the quantum Hamiltonians of edge models like Ising contain both nearest neighbor interaction and onsite potential terms results in the extra spectral parameter of the $R$-operator. My construction extends the recent unification of solvable edge and vertex models which recasts Onsager's star-triangle relation from a mere alternative form of the YBE for edge models to its underlying ingredient.

We investigate a minimal molecular model consisting of square planar plaquettes hosting multiple electrons, whose dynamics is governed by a tight-binding Hamiltonian supplemented by on-site Hubbard repulsion. By coupling this system to a spatially nonuniform cavity mode, we analyze the emergence of a magnetostatic instability, namely photon condensation, originating from the paramagnetic Van Vleck mechanism. The global behavior of the system is analyzed for different electronic filling factors, and we find that, except for the special cases of half-filling and single electron, where the transition, if it occurs, is necessarily a second order phase transition, the global system may also undergo a first order transition because of the action of the electron-electron interaction. The polaritonic excitation energies are analyzed, providing clear spectroscopic signatures of the magnetostatic instability and of its order.

We generalize the condition under which a quantum material exhibiting a pseudogap phase is a precursor to a superconducting (SC) dome. The result reveals the non-analytic T* as a function of doping. A well-known example is the high-Tc cuprates. Essentially, the SC dome is generated under two conditions: (1) that the pseudogap T* is a decreasing function of doping, due to the decrease in size of extended pairing of doped holes with doping, and most importantly, (2) that the rate of configurational-ordering parameter is an increasing function of doping as a result of the decrease in extended length of the disordered pairs. These two conditions are provided by the new entanglement and confinement pairing mechanism of high-Tc cuprates. This is a theory that has recently been discussed in the literature by Buot et al. It hinges on a novel strong entanglement and confinement hole pairing (ECHP) mechanism that unravels the microscopic features of the entire phase diagram of both electron and hole-doped high-Tc cuprates.

The Th-229 nuclear isomeric state has the lowest energy of all known nuclear excited states, placing it within the reach of current table-top laser technology. This extraordinary property has made this nuclear isomer an attractive candidate for a nuclear optical clock of incredibly high precision and accuracy, both as isolated trapped Th-229 ions and embedded into solid-state platforms. Activity around Th-229 has surged in recent years, driven by breakthroughs in its direct laser excitation. The underlying nuclear physics that gives rise to this unique isomer will be elucidated, as well as the nearly half-century of efforts that led to its direct excitation. The design and systematics of a Th-229 nuclear clock will be discussed, both in ion traps and in the solid-state. These systematics, such as frequency shifts and quenching channels, can be leveraged both to probe the local chemical environment, and as a control knob during clock operation. Finally, the nuclear clock's high sensitivity to the variations of fundamental constants will be discussed.

We discuss a theoretical approach to discriminate whether two states of a many-body quantum system belong or not to different topology classes. This approach is based on expressing a strange correlator - a recently established tool for quantum topology discrimination - between the states as a function of Kirkwood-Dirac quasiprobabilities (KDQs). KDQs provide a first-principles representation of two-time quantum correlators. The link between strange correlators and KDQs allows to establish that strange correlators are weak values of an observable converting an initial trivial state into a topologically non-trivial one. We thus propose a quantum topology witness that is achievable measuring the prior and subsequent effects on a many-body system of a sudden quench transformation that realizes the transition between trivial and topological phases. The witness is evaluated on a probe quantum state whose main features are detailed within the paper. Finally, directly exploiting schemes that allows for the complete reconstruction of KDQs, we address an interferometric protocol for topology discrimination, along with a general discussion of the main lines and challenges towards its implementation.

Asynchronous, event-based graph neural networks (AEGNNs) have recently emerged as an efficient paradigm for processing the sparse and high-temporal-resolution data from event cameras. In this paper, we propose quantum analog AEGNNs (QA-AEGNNs), a novel framework to implement an AEGNN on a neutral-atom quantum computer. Neutral-atom quantum processors offer a programmable analog quantum computing platform based on controllable Rydberg-atom interactions. To this end, we map the streaming event data to an array of trapped neutral atoms, where each atom represents a graph node (event) and is positioned such that geometric proximity reflects the spatio-temporal neighborhood of events. The native Rydberg Hamiltonian of the quantum processor is programmed to mirror the message-passing computations of the AEGNN, with atomic qubit states serving as node feature embeddings and inter-atom interactions realizing graph edges. Furthermore, we propose a hybrid quantum-classical training scheme in which the analog Hamiltonian parameters (e.g., laser pulse amplitudes and detunings) are optimized using classical feedback to learn the quantum AEGNN model from data. Our approach leverages the continuous Hamiltonian dynamics and massive parallelism of neutral-atom quantum systems to natively execute event-based graph computations with potential accuracy improvements

Estimating properties of unknown quantum states via quantum singular value transformation (QSVT) often requires high-degree polynomials to handle small eigenvalues of density matrices. Specifically, the existing approaches determine the polynomial degree by relying on overly conservative worst-case bounds based on the minimum non-zero eigenvalue or the rank of the density matrices. In this work, we propose a spectral cutoff method that truncates the negligible eigenvalue tail depending on the task, the target accuracy, and the state, which enables the use of significantly lower-degree polynomials. To implement this, we develop a two-stage algorithm to estimate nonlinear properties, particularly von Neumann entropy and R{é}nyi entropy. In the first stage, we execute a search algorithm to identify the spectral cutoff directly from the unknown quantum state. In the second stage, we estimate the nonlinear properties utilizing QSVT with the degree of polynomial adaptively determined by the cutoff. This two-stage algorithm significantly improves the overall estimation cost compared to known bounds, even without knowing the minimum eigenvalue or the rank.

Quantum sensing with high precision and sensitivity plays an important role in quantum technologies and quantum information processing. Here, we propose a nonreciprocal quantum metrological scheme for estimating rotational angular velocity in a hybrid light-matter platform, where the setup consists of a spinning ring cavity coupled to a two-level system and an auxiliary bosonic mode. Through the Sagnac effect, the angular velocity is converted into a direction-dependent detuning, which modifies the effective light-matter dressing of the hybrid system. As a result, the angular velocity is encoded not only into the renormalized hybrid-mode spectrum, but also into the virtual excitations generated by ultrastrong coupling. These virtual excitations modify the polaritonic frequency response to rotation and enhance the quantum Fisher information (QFI) associated with angular velocity estimation, without requiring direct extraction of virtual excitations. Moreover, since the Sagnac-Fizeau shift enters the virtual-transition energy denominators, the metrological response becomes intrinsically different for opposite driving directions, leading to a tunable nonreciprocal sensitivity contrast. In addition, we also discuss a readout scheme and show that bundle emission coincidence counting can serve as an auxiliary direction-dependent readout channel. Our results provide a route toward exploiting nonreciprocal light-matter dressing and virtual excitations as resources for quantum rotation sensing.

Self-testing refers to the strongest device-independent (DI) certification method that validates the nature of a quantum system and devices solely based on the observed statistics. We demonstrate the self-testing of state and measurements based on the Gisin Bell inequality (GBI) featuring arbitrary inputs for both parties. We introduce a systematic and elegant sum-of-squares (SOS) approach that enables the dimension-independent derivation of the optimal quantum violation of GBI. We derive the state and the interrelation between the local observables directly from the optimization condition. Since the practical experimental scenario involves inevitable noise and imperfection, we present a comprehensive strategy for robust self-testing.

We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.

Bell nonlocality provides the foundation for device-independent (DI) certification of quantum devices. We introduce a Bell inequality capable of identifying genuine multipartite nonlocality (GMNL) in an arbitrary m-partite scenario with an arbitrary odd number of measurements per party. Since the multi-setting nature of this inequality precludes the use of Jordan's Lemma, we construct an analytical sum-of-squares (SOS) decomposition to obtain the optimal quantum violation without assuming any bound on the Hilbert space dimension. This, in turn, enables self-testing of the shared entangled state and the corresponding measurement observables, up to local isometries, whose existence we confirm using a swap-based certification scheme. In addition, we show that our framework enables the extraction of maximal global DI randomness (m bits) at the optimal quantum violation, thereby exceeding previous limitations in the GMNL regime. Finally, we demonstrate that the architecture of our inequality yields improved robustness to noise as the number of measurement settings grows, ensuring experimental feasibility.

In quantum image processing, a fundamental step is encoding classical image data into quantum states. This can be achieved using methods such as Flexible Representation of Quantum Images (FRQI), Quantum Probability Image Encoding (QPIE), and Novel Enhanced Quantum Representation (NEQR). However, on real quantum hardware, these encodings can quickly lead to circuits with many gates, large circuit depth, and high qubit usage, which is a problem for Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we investigate whether low-rank state approximation, formulated via Schmidt decomposition, can help reduce this complexity. The method keeps only the most significant parts of a quantum state's entanglement structure, making state preparation more efficient while preserving most of the image information. We compare the three encoding techniques in their original form and with low-rank approximation, evaluating metrics such as circuit depth, CNOT count, MSE, and visual quality of reconstructed images. The results reveal meaningful trade-offs between accuracy and resource efficiency, with the FRQI model achieving a 97 percent reduction in circuit depth while maintaining a near-perfect reconstruction (MSE of about 0.27). This demonstrates the potential of low-rank techniques for advancing practical quantum image processing on near-term hardware.

Cameron, Montanaro, Newman, Severini and Winter gave a construction which shows that, for $n \in \{2,4,8\}$, any graph $G$ which admits a real $n$-dimensional orthogonal representation is quantumly $n$-colorable. This result can be recast as the statement that the real sphere $S^{n-1}$ is quantumly $n$-colorable for these values of $n$. We investigate possible extensions of their construction. We first show that their hypothesis that the orthogonal representation be real-valued is required by proving that there is no analogue of this for the complex spheres, which all have quantum chromatic number strictly bigger than the dimension except in two dimensions. We also provide candidate finitary witnesses of this and show for the first time that the real and complex orthogonal ranks are distinct as a byproduct. For the real case, we show that if $S^{n-1}$ is quantumly $n$-colorable, then either $n=2$ or $n$ is a multiple of 4, and show that the converse holds whenever a Hadamard matrix of order $n$ exists. Hence, assuming the Hadamard conjecture, this completely classifies the dimensions to which the CMNSW construction can be extended. Our method of proof involves showing the equivalence between the existence of such a construction and the existence of a maximal code space for Clifford-algebraic errors given a clean ancilla, and we believe that the representation-theoretic techniques we use for tackling the latter problem could be of independent interest. It also follows from this equivalence that $S^{n-1}$ admits a rank-one quantum $n$-coloring if and only if $n \in \{2,4,8\}$, thereby settling a conjecture of Zeng and Zhang, as does the fact that for all $m \geq 1$, there exists a catalytic zero-error remote state preparation protocol for real $m$-qubit states with $m$ bits of communication and which consumes $m$ ebits.

High-order exceptional points (EPs) emerging in non-Hermitian systems have attracted broad interest for their significantly enhanced sensitivity to perturbations. However, quantum sensing schemes based on high-order EPs remain scarce, due to the experimental challenge of fine-tuning the system to such an extremely sensitive isolated point. Here we propose a four-channel dissipative coupling model that supports both fourth-order exceptional surfaces and second-order exceptional volumes. This non-Hermitian model can be realized in a thermal atomic system, and its complex energy spectra can be determined via electromagnetically induced transparency spectroscopy. The proposed model exhibits a characteristic fourth-order response to multiple physical quantities such as the laser detuning and the distance between optical channels, significantly surpassing the response of second-order EPs. We further reveal the sensitivity-robustness trade-off under experimental noise. Our work opens a route toward high-performance sensing leveraging higher-order EPs.

In this work, we investigate controlled quantum teleportation in the presence of noisy channels acting on the three-qubit resource state. We employ a series of generalized noisy channels that bridge the dephasing channels and amplitude damping channels while encompassing extensive intermediate scenarios. We provide an in-depth analysis of the degradation of the maximal average fidelity and the optimal average fidelity in controlled quantum teleportation induced by such noisy channels by deriving the analytical expression and examining several special cases. The analytical expression shows that attaining the optimal average fidelity requires Charlie's cooperation in performing a measurement at suitably chosen angles, and is also related to the initial state and the channel parameters. Our analysis reveals that the optimal average fidelity does not always decrease monotonically with the evolution parameter, instead, it first decreases and then increases. This non-monotonic behavior depends on the entanglement of the initial resource state, as well as on the parameters of the channel traversed by the first qubit.

We study the pair creation phenomenon for a real scalar field $\varphi$ in the presence of a surface that undergoes time-dependent deformations, while imposing Dirichlet-like boundary conditions. Including terms up to fourth order in the departure of the surface from an infinite plane, we present results for the angular dependence of the emission rate for the vacuum-to-pair process as a function of the geometry and the dynamics of the surface, as well as of the momenta of the emitted pair. We check the consistency of the leading contribution with previous results obtained from the imaginary part of the effective action, and clarify how the relation between exclusive probabilities and the imaginary part of the effective action is modified at fourth order by the opening of a two-pair channel.

Noisy quantum channels degrade quantum resources such as coherence and entanglement and hence pose challenges for realizing quantum technologies. Coherent control of noisy channels allows us to minimize their effects on the quantum system. Here we achieve the cancellation of two noisy quantum channels by superposing their corresponding Stinespring dilation unitaries. We first arrive at conditions under which superposition of channels results in a valid quantum channel. We then consider superposing two dephasing channels and observe their destructive interference, thereby effectively recovering the quantum coherence. On superposing two zero-capacity depolarizing channels, we show superactivation of quantum capacity. We experimentally realize the cancellation of two dephasing channels using a three-qubit NMR register. Furthermore, using a five-qubit NMR register, we realize the cancellation of two depolarization channels and demonstrate superactivation of quantum capacity.

The distribution of quantum sensors on quantum networks is a key enabler of quantum technologies in interferometry, gravimetry, timekeeping, biological monitoring, and beyond. Yet, guaranteeing the security of these distributed sensors over noisy, insecure networks remains a formidable challenge. Previous efforts to combine quantum metrology and cryptography have encountered an apparently unavoidable tension, proposing bounds for security which are only loosely tied to the achievable measurement performance. Here we introduce a quantum remote sensing protocol that can rigorously certify privacy and integrity of the estimation. By employing offline bilateral Pauli-twirling, our approach forces the effective quantum channel into a Bell-diagonal form, independently of the attack. Surprisingly, this also preserves metrological sensitivity without introducing additional experimental overhead. Relying solely on public communication alongside an insecure quantum link, the protocol enables legitimate users to exactly quantify their estimation error relative to an eavesdropper controlling the channels. We experimentally demonstrate this framework by estimating an optical phase using entangled photons, observing that the users' precision consistently surpasses the eavesdropper's capabilities across a broad parameter regime. By unifying quantum cryptography and metrology, our results provide a practical pathway to achieve simultaneous quantum-limited precision and rigorous information security in real-world quantum networks.

Beyond the weak-coupling limit, open quantum systems equilibrate to a highly entangled thermal state. For continuous-variable systems, this state can be written explicitly as an imaginary-time phase-space path integral, in which the positions are directly entangled with the bath, and the momenta are correlated with the positions through a phase term. Here, we ask to what extent this state can be reached by propagating stochastic classical trajectories in path-integral phase space. Surprisingly, we find that the trajectories equilibrate to the exact quantum equilibrium state, recovering the purely imaginary momentum-position correlation in the phase term. The trajectories are generated using a recently derived Matsubara generalized Langevin equation, which produces the imaginary correlations by evolving the stochastic variables into the complex plane. This makes the dynamics numerically unstable, but we are nonetheless able to demonstrate the equilibration of a quartic oscillator coupled to a white-noise bath. These unexpected findings could lead to new approximate methodologies for simulating continuous-variable open quantum systems.

We investigate the thermodynamic properties of static, spherically symmetric Anti-de Sitter (AdS) black holes, focusing on the interplay between characteristic temperatures, as well as on the universality of Ruppeiner scalar curvature at the Hawking-Page (HP) phase transition. In particular, we study the relation between the minimum temperature and the HP phase transition temperature for static, spherically symmetric AdS black holes in pure Lovelock gravity. For the electromagnetically neutral case in Einstein gravity, the minimum temperature in $(d+1)$ dimensions coincides with the HP transition temperature in $d$ dimensions, while in higher pure Lovelock theories this relation is modified by a dimension- and order-dependent factor, reducing to the Einstein result in appropriate limits. For charged AdS black holes, in the grand canonical ensemble, in general relativity, the two temperatures differ by a simple dimension-dependent factor, whereas no universal relation persists in higher curvature pure Lovelock theories. We further analyze the normalized Ruppeiner scalar curvature at the HP transition and show that it is a universal constant depending only on the spacetime dimension for electromagnetically neutral black holes in pure Lovelock theories. The normalized scalar curvature remains a constant, under appropriate conditions, even for the charged static spherically symmetric black holes in the grand canonical ensemble for the Einstein theory case, whereas in general pure Lovelock theories it depends on thermodynamic parameters such as pressure and electrostatic potential, asymptotically approaching a constant in the large-pressure or simultaneous large-potential and large-pressure limits.

The manipulation of localization in quasiperiodic systems by mobility edges or localization transition holds significant physical importance. In this letter, we demonstrated that the dissipation can induce the emergence of anomalous mobility edges and extended-localized transition in emitter-cavity arrays controlled by quasiperiodic potentials. Specifically, we observe that the localization properties of emitters is governed by the nature of quantum bound states, either discrete or embedded in continuum, providing a unified mechanism linking the emitter-photon bound physics to quasiperiodic criticality. Depending on the bound state discrete or continuumlike, the induced effective excitation hopping exhibits either exponentially decaying or sinusoidally oscillating, giving rise to the formation of localized or critical states, respectively. Through a generalized duality transformation, we analytically determine the anomalous mobility edges and the critical strength of potential, enabling the construction of a full phase diagram. The study reveals that the physical characteristics of cavity exert a significant influence on excitation localization. Therefore, the manipulation of excitation localization can be achieved solely by adjusting the cavity fields.

We formulate an exact Green-function theory for non-Hermitian single-microwave-photon scattering by finite superconducting circuit subsystems embedded in an SSH waveguide. The structured SSH environment is integrated out exactly and enters the local scattering problem as an energy-dependent matrix self-energy, reducing the full open system to a finite-dimensional effective non-Hermitian Hamiltonian. This reduction places scattering amplitudes, exceptional-point diagnostics, coherent-perfect-absorption conditions, and lasing thresholds within one unified framework. Within this approach we analyze two superconducting devices. A flux-controlled two-qubit interferometric scatterer exhibits a broad bright branch and a narrow quasi-dark branch whose interference is reshaped by the SSH environment and changes qualitatively across the two dimerizations. A mediator-assisted two-qubit scatterer generates an additional energy-dependent complex coupling, reorganizes the dressed spectrum, and produces clearer dimerization-sensitive transparency-versus-absorption windows together with a pronounced separation between zero-like and pole-like scattering branches. In the active regime, near-exceptional-point hybridization enhances the pole-dominated response while deepening the singular-value valley associated with near-coherent perfect absorption. These results show how structured topological waveguides can be used not only to host scattering, but also to design non-Hermitian superconducting microwave functionalities.

We study interaction-driven ultrafast dynamics in finite graphene flakes following an optical pump quench in an interacting tight-binding model. By comparing exact real-time evolution with simulations restricted to particle-hole excitation subspaces, we assess when relaxation can be captured by low-order many-body processes and when this is not sufficient. The single-particle orbital entropy provides a compact diagnostic for dynamic correlation growth. For the systems studied here, periodic graphene flakes are well described by low-order excitations, whereas confined geometries require substantial higher-order contributions even for relatively small interaction strengths. The quench protocol combines simple initial-state preparation with strongly correlated dynamics, identifying a promising benchmark problem for future quantum-computing simulations.

We investigate precision scaling at the interface between unitary and non-unitary encoding under generalized noise including single-particle and collective dephasing and decay. Using linear response theory and the error propagation formula, we derive analytic precision expressions for both the unitary parameter $Ω$ and the dissipation strength $γ$. For unitary encoding, when the observable commutes with a Hermitian noise operator, the optimal encoding time is independent of $N$, yielding the Heisenberg limit $ΔΩ\propto 1 / N$; otherwise the precision degrades to the standard quantum limit or ceases to improve with $N$. For non-unitary encoding, when $[\hat{A}, \hat{O}] = 0$, the precision is insensitive to intrinsic dynamics and encoding time, scaling as $Δγ\propto \sqrt{γ/ \expval*{\hat{L}^\dagger \hat{L}}}$. Notably, for collective decay, the Dicke state reaches the Heisenberg limit $Δγ\propto 1 / N$, demonstrating that entanglement can enhance non-unitary estimation. Our results provide a unified framework and practical guidance for designing quantum metrology protocols in noisy environments.

We study single-photon scattering in a Su--Schrieffer--Heeger (SSH) photonic lattice locally coupled to a superconducting qubit with tunable loss or gain. Working in the single-excitation sector, we derive an explicit real-space scattering formulation for the full energy-dependent scattering matrix $S(E)$ and identify how its eigenvalues encode coherent perfect absorption, amplification, and spectral singular behavior. The analytical results are benchmarked against time-domain wave-packet simulations, which reproduce the stationary scattering probabilities with high accuracy. We show that the SSH dimerization, the qubit-induced non-Hermitian self-energy, and the synthetic gauge phase cooperate to reshape the reflection and transmission spectra in a highly selective way. In particular, changing the dimerization can switch the system between transmission-dominated and reflection-dominated regimes, while the flux provides a direct handle on interference and symmetry-controlled response. We also find a robust loss--gain correspondence in the reflection landscape and show that the linewidth broadening is governed predominantly by the magnitude $|γ|$ of the non-Hermitian coupling. These results establish a compact and experimentally relevant framework for topological scattering in superconducting quantum networks.

High-density nitrogen-vacancy (NV) ensembles are promising platforms for solid-state quantum sensing, but their performance is limited by dipolar interactions and inhomogeneous dephasing. Periodic decoupling sequences such as Waugh-Huber-Haeberlen (WAHUHA) can extend the observed stroboscopic decay time. However, it remains unclear that a longer effective dephasing time yield improved magnetic-field sensitivity. Here, we show that WAHUHA control increases the effective inhomogeneous dephasing time of a dense NV ensemble from $T_2^\ast$ of 0.9 $μ$s to $T_{2,eff}^\ast$ of 31 $μ$s, while producing little improvement in dc magnetic-field sensitivity. Using detuning-resolved stroboscopic spectroscopy and finite-pulse Floquet analysis, we show that the long-lived signal arises from phase wrapping and quasi-energy branch folding of the one-cycle unitary. These effects reshape the stroboscopic spectrum and suppress the detuning-to-phase transduction slope, $dΦ/dΔ$, which governs the dc magnetic-field response. Our results demonstrate that, under periodic driving, an extended effective dephasing time does not necessarily translate into enhanced dc sensitivity and establish finite-pulse Floquet analysis as a practical framework for evaluating coherence in spin ensembles.

This article presents a comprehensive analysis of two classes of quantum radars, including quantum direct-detection and quantum-entangled noise radars. In the first case, inspired by the well-established concept of single-photon LiDARs, we investigated the performance of single-photon radars, in which state-of-the-art single microwave-photon detectors are employed to enhance the detection sensitivity and enable the detection of weaker signals. We derived analytical expressions for the maximum detection range of both classes of quantum radars in terms of the Lambert W function, by considering all relevant system, target, and environmental parameters. Our formulation facilitates direct comparison of noise radars with direct-detection radars and suggests that a quantum-entangled noise radar can be regarded as an enhanced direct-detection radar with an effective threshold signal-to-noise ratio. Furthermore, we applied this framework to classical-correlated noise radars and defined the parameter range enhancement factor (REF) to quantify the superiority of quantum-entangled noise radars over their classical counterparts. Moreover, we introduced a rule-of-thumb for approximating the REF. We also examined the influence of limitations imposed by various microwave detection technologies. Our analysis shows that the conventional antennas limit the potential benefits of quantum-entangled noise radar systems. We also demonstrated that the optimal detection method for these radars is a microwave detector based on a quantum transducer combined with a single optical-photon detector. We showed that, with the current technology, implementing a quantum-entangled noise radar with the maximum detection range on the order of few kilometers is possible. Finally, we explored the potential applications of quantum-entangled noise radars.

We experimentally demonstrate the continuous-variable quantum approximate optimization algorithm (CV-QAOA) for multi-variable problems and multiple QAOA depths using a measurement-based CV quantum computing platform on a quad-rail lattice (QRL) cluster state. We propose a systematic method to map arbitrary quadratic cost functions onto the QRL architecture and examine the resulting construction in settings involving up to 100 modes. Using the programmable platform, we prepare the CV-QAOA ansatz and optimize the variational parameters via Bayesian optimization. We then investigate the performance on quadratic optimization problems and observe that increasing the depth from 1 to 2 improves performance, whereas further increases yield only limited gains. In contrast, numerical simulations under idealized conditions, assuming an infinite number of measurement shots and gradient-based optimization, indicate that the performance of CV-QAOA can improve with increasing depth, suggesting that the experimentally observed limitations primarily arise from noise accumulation and classical optimization challenges. This work provides an experimental demonstration of CV-QAOA on a programmable CV platform and establishes a foundation for future developments of variational quantum algorithms in CV systems.

Scalability is a key challenge in advancing quantum technologies such as quantum computing, communication, and metrology. Photonic systems offer a promising route to scalability by enabling the deterministic generation of large-scale entangled states. Homodyne detection is an essential quantum measurement to exploit such entangled states, enabling quantum-enhanced measurement, deterministic quantum teleportation, GKP-state breeding, and quantum error correction. Despite the recent progress in generating large-scale quantum states, realizing quantum measurement at scale remains a major challenge. Here we realize scalable and efficient homodyne detection by leveraging a large number of pixels in a charge-coupled-device (CCD) camera. Our approach enables shot-noise-limited quadrature measurements of 60 optical modes simultaneously, while requiring only nanowatt-level local oscillator power per mode -- a six-order-of-magnitude reduction compared to conventional methods. The system achieves clearance exceeding 24 dB for all modes with negligible crosstalk. We demonstrate its compatibility with a large-scale quantum state by directly observing squeezing and entanglement in 60 optical modes. Furthermore, we showcase applications in verifying multipartite entanglement and in the conditional preparation of multimode states. This work provides a scalable method for quantum measurement, paving the way for large-scale quantum information processing.

Quantum squeezing, a cornerstone of quantum optics and photonics, has played a key role in achieving ultra-precision sensing and realizing nonreciprocal engineering. However, the nonreciprocal multiquanta emission has remained largely unexplored by using directional quantum squeezing. Here, the one-way photon-photon bundle emission in a compound system consisted of two coupled optical resonators and a two-level atom is investigated. It is found that the directional quantum squeezing induces the asymmetric frequency detuning and photon hopping interaction between the two resonators, leading to the directional excitation of the two-photon super-Rabi oscillation. In particular, by harnessing intrinsic dissipation of the system, two types of two-photon bundle emission can be selectively induced for the probe field input from one direction while it is prohibited with the probe from the other direction. This finding bridges the broad fields ranging from nonreciprocal physics to quantum squeezing optics and multiquanta emission control through an all-optical approach, which can enable potential applications in chiral quantum emitters and backscattering-immune photonic communications.

We apply a deep-neural-network (DNN) ansatz to the symmetrized spectator vector of the subtracted three-body Faddeev integral equation for identical bosons near the Efimov limit. The network is trained by minimizing the residual of the discretized integral equation, while the positive binding scale associated with the three-body energy is treated as a trainable parameter. Deterministic diagonalization of the same discretized kernel is used only as an a posteriori numerical benchmark. As preliminary validation, the neural-solver strategy is tested on the analytically solvable hydrogen radial problem. At unitarity, the DNN reproduces the Efimov ground-state binding scale with a DNN--deterministic deviation of $0.022\%$, while the first excited state is recovered to $0.002\%$. The deterministic solver recovers the universal Efimov scaling ratio $e^{2π/s_0}\simeq 515.03$, and the neural method traces the bound-state branches as a function of the inverse scattering length $1/a$ by continuation from the unitary solution. These results indicate that DNN-based residual minimization can provide a compact and differentiable representation of a renormalized few-body integral-equation solution in a regime governed by discrete scale invariance.

We propose a scheme to realize tunable and strong nonreciprocal photon blockade (PB) in an asymmetric Fabry-Pérot cavity. The setup consists of a single-mode optical cavity trapping a two-level atom, with the cavity coherently driven by a laser and the atom pumped by an auxiliary control field of the same frequency. By engineering quantum interference between multiple excitation pathways by adjusting the amplitude and relative phase of the control laser, we identify two distinct optimal control conditions that enable directional suppression of two-photon states. Under optimal control conditions, strong nonreciprocal PB is achieved, with a nonreciprocal ratio exceeding 30 dB over a broad operational bandwidth. The proposed protocol requires only standard coherent laser sources and is compatible with current cavity QED experimental setups, offering a practical and scalable platform for nonreciprocal quantum photonics.

We demonstrate an optomechanical system with tunable dissipative and dispersive couplings using a Fabry-Perot cavity and a string mechanical resonator. By varying the diameter and material of the mechanical resonator, and the relative location between the mechanical resonator and the cavity, the relative strengths of dissipative and dispersive coupling could be tuned continuously from dissipation-dominated regime to dispersion-dominated regime. In our experiments, the dissipative-to-dispersive coupling ratios of 1.3 and 0.6 are achieved by using two different mechanical resonators, corresponding to a transition from dissipation-dominated to dispersion-dominated optomechanical system. Theoretically, the coupling ratio could be tuned from 25 to 0.02 by optimizing the mechanical resonator, spanning over three orders of magnitude. These two distinct coupling regimes are achieved with the same experimental platform. The capability to freely adjust the coupling ratio provides a versatile platform for exploring quantum effects of massive mechanical resonators and quantum-limited measurements.

Measurement-device-independent quantum key distribution (MDI-QKD) is designed to eliminate detector side-channel vulnerabilities. However, its practical deployment remains experimentally demanding because it requires two-photon interference (TPI) between mutually phase-randomized optical states. In this study, we demonstrate a reconfigurable platform that supports both polarization encoded MDI-QKD and BB84 measurements utilizing the same optical hardware over 20 km optical fiber channels. Two mutually phase-randomized weak coherent states (WCSs) are generated from a shared continuous-wave (CW) laser via electro-optic phase modulation and subsequent etalon-based first-order sideband filtering. Channel indistinguishability is verified through Hong-Ou-Mandel (HOM) interference, combining time-resolved coincidence measurements and polarization mismatch scans, confirming a high degree of indistinguishability that robustly approaches the classical upper limit of 0.5 for WCSs. The transmitted states go through partial Bell-state measurement (BSM) to implement MDI-QKD. Here, the sytem can be directly reconfigured for BB84 simply by rotatinga single half-wave plate (HWP) by 22.5 degree in one arm of the module. This seamless reconfiguration drastically reduces hardware redundancy and enhances operational flexibility in dynamic network environments. These results indicate that EOM-based frequency engineering using a shared CW laser offers a highly practical route toward scalable and reconfigurable quantum communication systems.

For nearly a century, a recrossing-free dividing surface in quantum mechanics has been thought impossible. One-way reactive flux seems to require simultaneous trajectory-level knowledge of position and momentum -- an apparent conflict with the uncertainty principle. We show that this obstruction is not fundamental. The exact quantum flow can admit stable and unstable invariant manifolds whose intersection defines a unique bounded trajectory. This trajectory anchors a moving dividing surface that reactive quantum characteristics cross exactly once, producing a one-way flux of the standard quantum probability current. The geometric framework underlying classical reaction dynamics therefore carries over to the exact quantum flow, in a fundamentally quantum form.

Quantum Circuit Born Machines (QCBMs) offer a natural approach to generative machine learning by leveraging the Born rule. Recent work has provided a method to classically train QCBMs with Instantaneous Quantum Polynomial (IQP) circuits via the Maximum Mean Discrepancy (MMD) loss. Despite the assumed intractability of sampling from IQP circuits classically, their expectation values can be computed classically, enabling training of these IQP QCBMs. However, quantum machine learning (QML) models have various other challenges, including trainability issues caused by exponential concentration or barren plateaus. While these issues have been explored for parameters sampled from a uniform distribution, little work has been done to rigorously treat the use of arbitrary Gaussian initialization schemes. This work leverages Stein's lemma and Lipschitz concentration bounds for Gaussian random variables to provide an analytical lower bound of the variance of the gradient and a probabilistic concentration bound of the deviation of the gradient from its mean. It discusses strategies to either avoid or encourage exponential concentration, as well as the conditions under which barren plateaus are more likely to occur.

In this work, we investigate the use of a quantum circuit as a binary classification model in the context of quantum machine learning. We call this model, binary quantum classifier. First, we describe fundamental concepts of quantum computing and introduce the computational tool used: Qibo, an open-source framework for efficient quantum simulations and quantum hardware control. Then, we describe how to design a binary quantum classifier for the classification of images and small arrays of variables by showing how to input data in the circuit, defining a quantum circuit model Ansatz with trainable parameters and a loss function, and implementing multiple minimizers. We test our quantum classifier with two data sets. The first one is the MNIST data set which is composed of handwritten digits (reduced to only handwritten zeros and handwritten ones for binary classification). We study the behavior of different minimizers by increasing the number of layers of the Ansatz. The second data set represents two different high energy collisions that can occur at colliders such as LHC (CERN). Due to in-time proton-proton interactions known as pile-up, we distinguish two different data sets: "without pile-up" and "with pile-up". These collisions can be represented by images of size 32x32 or by six high-level variables that we call features. By increasing the size of the training data set and the number of layers of the Ansatz, we search for the best minimizer. Splitting the data set in training set and test set, we compute: ROC curve, AUC score, confusion matrices and test set accuracy. For "with pile-up" images, we compare the results obtained with the quantum classifier with a small convolutional neural network. We conclude that is possible to build a binary quantum classifier with a quantum circuit and we highlight its performances and limitations in comparison with classical technologies.

We use the exactly-solvable t Hooft model of 1+1D large-N_c QCD as a rigorous laboratory for the breakdown of analyticity of a causal response function, the meson two-point function. A PT-symmetric deformation i gamma(x-1/2) of the light-cone meson operator, the analogue of an imaginary chemical potential, drives the lowest two mesons to an exceptional point (EP) at gamma_c. Recasting the resolvent as a Jacobi continued fraction yields gamma_c in closed form: 2 pi g^2 N_c at the two-pole level, converging to 7.966 g^2 N_c by depth five -- an analytic, not numerical, threshold. The square-root exponent nu=1/2 is fixed by the 2x2 Jordan form and confirmed by finite-size scaling to N=1999. The breakdown has an unambiguous time-domain signature: the propagator norm is bounded for gamma < gamma_c, grows linearly at gamma_c (the Jordan secular law), and exponentially beyond -- observable, since the deformed operator is a non-Hermitian Wannier-Stark ladder, in photonic and topolectrical analogues. The threshold is locked to confinement, gamma_c propto g^2 N_c, and recurs as a uniform EP cascade; a second, non-reciprocal deformation yields an exactly-exponential non-Hermitian skin effect. This is the first analytically-controlled instance of exceptional-point analyticity breakdown in a confining gauge theory.

Variational quantum algorithms are increasingly explored for optimization problems at scales relevant to near-term quantum devices. Their practical performance depends strongly on design choices such as the sampling objective, classical optimizer, and ansatz layout before and after hardware transpilation. We study these factors for dynamic portfolio optimization, a multi-period financial problem balancing return, risk, transaction costs, cash-interest effects, and constraints. Using a sampling-based VQA framework on a 150-qubit dynamic portfolio instance, we evaluate several components of the optimization workflow. We propose a specific adaptive CVaR schedule that gradually tightens the sampled tail used for optimization, together with a two-stage optimizer combining global exploration with Particle Swarm Optimization and local refinement with the Nakanishi-Fujii-Todo optimizer. We also study ansatz depth and sequential growth strategies. Finally, we introduce two hardware-aware ansatz-layout modifications: a data-guided colored layout that assigns correlated variables to qubits connected by entangling gates, and a heavy-hex-native deep-chain layout designed to increase native two-qubit interaction depth without additional routing overhead after transpilation. Simulator studies select CVaR, optimizer, and depth configurations, while the ansatz comparison is performed on the ibm_quebec QPU. The results show that sampling strategy, optimizer scheduling, and hardware-aware layout design materially affect performance. In the reported QPU layout comparison, the proposed heavy-hex-native deep-chain layout achieves the best final objective value and CVaR-tail performance among the tested layouts. Although we do not observe quantum advantage over a state-of-the-art exact classical solver, our results provide practical guidance for improving VQA performance on near-term hardware.

For a system with a large number of identical Bosons, it is common to claim, often without any additional justifications, that, when the mean occupation number in a single particle state is sufficiently large, classical field description will be applicable. This is why e.g. for ultra-light dark matter, the classical field equations are used to compute its dynamics. In this work, we test the validity and robustness of this assumption based on the criterion $2 σ_\varphi < |\langle \varphi \rangle| $ for classical field behaviour and applying it to aribtrary quantum states. We find that an arbitrary state with large occupation number doesn't behave classically while imposing some restrictions on the state vectors can improve the classical behavior. Since coherent states are known to have quasi-classical behaviour, we also ask how much deviation from coherent state can spoil the classical behaviour. Based on this analysis, we find that it is the proximity of the state to a large occupation coherent state rather than large occupation number itself which ensures validity of classical description. Implications of this for ultra light dark matter are discussed.

We establish a universal scaling law for collective charging of quantum batteries, independent of microscopic details. We prove that the ergotropy-to-energy ratio approaches unity at least as fast as $\sim N^{-1}$ with the number of batteries $N$, implying generic asymptotic freedom. We further show how the universal $1/N$ scaling can be overcome: when the battery state becomes asymptotically pure, the convergence can be substantially faster, including $\sim N^{-b}$ with $b>1$ and even exponential scaling in $N^2$. Rigorous finite-$N$ upper and lower bounds on the ergotropy-to-energy ratio are further derived, providing nonasymptotic guarantees for the universal $1/N$ scaling.

To explore the pathways toward establishing a global quantum network, we investigate several link architectures for transatlantic quantum entanglement distribution over a 6,500 km ground distance. We define free-space link configurations involving satellites and stratospheric high altitude platforms (HAPs), using today's technology and without relying on quantum memories and repeaters. Considering link budgets, space radiation, orbital characteristics, and system complexity we find that a hybrid architecture consisting of an entangled photon source located on a low Earth orbit (LEO) satellite supported by two passive optical relays located on HAPs provides the overall highest entanglement distribution rate. In addition, the satellite HAP architecture offers practical advantages in payload design and launch requirements, and the ability to lower the weather-related link interruptions assuming some maneuverability of HAPs. Overall, this hybrid configuration yields on the order of 5X10^6 secure key bits per year using 30 cm aperture ground receivers, nearly two orders of magnitude higher than achievable with a single MEO satellite and 1 m aperture ground receivers. Our results highlight the major benefits of hybrid satellite HAP architectures by reducing system complexity while enabling scalable and more accessible long-range quantum communication networks.

The Mpemba effect refers to faster relaxation of states that are initially farther from equilibrium, yet its characterization is often tied to a chosen distance or resource measure. We introduce resource-Markovianity, an extended concept of quantum Markovianity to quantum resource theories, and formulate the resource Mpemba effect operationally as the breaking of resource-Markovianity by a relaxation operation. This yields a measure-independent operational characterization of resource Mpemba effects in general resource theories, together with quantitative characterizations based on resource-non-Markovianity measures. We illustrate the framework with the Mpemba effect for distinguishability of states, due to its relation to quantum Markovianity, and with the thermomajorization Mpemba effect from an operational perspective. These results reveal a deep interplay between quantum resources, non-Markovianity, and the Mpemba effect.

We develop a general framework for investigating the influence of topological defects on the local characteristics of a quantum scalar field in a warped geometry background. The Ricci tensor and curvature scalar are decomposed into contributions from the warp factor, the radial geometry and the angular defect structure. For an arbitrary curvature coupling parameter, the field equation is separated into independent radial, angular and warp-coordinate parts. A complete set of normalized mode functions is obtained for general values of the angular deficit parameters. The general formalism is applied to several specific cases, such as conformally flat warped spacetimes, generalized cosmic strings, global monopoles and anti-de Sitter (AdS)-type warped geometries. The Hadamard two-point function is then evaluated for a global monopole in AdS spacetime using the obtained mode functions.

Hard safety filters are increasingly placed downstream of learned controllers to guarantee constraint satisfaction at run time. Yet a filtered controller that never violates a constraint may still have learned nothing about safety: the filter can silently repair an incompetent upstream policy, so that post-filter success measures the filter, not the policy. We argue that safe policy learning should ask who earns the safety - the policy or its protective layers - and we make this question measurable. We introduce Intervention-Aware Variational Quantum Differentiable Predictive Control (IA-VQC-DPC), which (i) trains a compact variational quantum circuit (VQC) policy under a primal-dual intervention budget that penalizes reliance on a differentiable Control-Barrier-Function (CBF) projection, and (ii) is evaluated with a safety-attribution protocol that decomposes the executed-trajectory correction into a CBF term and a deployment runtime-guard term, and stress-tests the policy with guard-off evaluation. On closed-loop, high-fidelity BOPTEST building-control emulators (5 seeds, 60 episodes per method), intervention-aware training significantly lowers the quantum policy's raw pre-filter violation and total safety-layer reliance (both p < 10^-4) with no significant energy regression; at an equal approximately 400-parameter budget the quantum policy is significantly safer and more comfortable than a matched classical policy. Guard-off evaluation confirms the improvement is policy-level and exposes a valuable negative result: a learned differentiable energy head is only safe when paired with a distribution-aware runtime guard. The attribution protocol is general beyond quantum policies and buildings.

Understanding the dynamical properties of quantum systems is an essential task in quantum computing, quantum control, and many-body physics. Tools such as representation theory and Lie theory provide crucial information on reachability and computational power. However, this information can be difficult to access exactly or compute efficiently for arbitrary generating sets. Here we focus on the setting of Pauli strings, which satisfy numerous exceptional properties that simplify the problem. We find deep connections between Pauli Lie algebras and certain subgroups of the Clifford group generated by transvections, through the symplectic properties of the Pauli strings. This allows us to give an invariant-based perspective on these objects and their reachability, in the language of Pauli orbits, symmetries, and invariant subspaces. The invariant-based approach provides efficient algorithms for identifying Lie algebras and orbits, as well as a simple framework for analyzing structured Pauli generating sets. We also show in an elementary way that Clifford subgroups generated by transvections provide 3-designs for the corresponding Pauli Lie groups. We illustrate the framework through structured examples from variational quantum algorithms, restricted quantum computation, many-body systems, and random circuits.

Observing the physical world is a foundational pursuit in science. In the quantum realm, however, observation necessitates a fundamental quantum-to-classical conversion: destructive measurements irreversibly project quantum states into classical data, inevitably incurring a loss of information. What physical principles govern this information loss, and how can we construct optimal measurements to maximize the readout? Here, we address these questions by establishing an intrinsic relationship between readout capability--quantified by the ratio of accessible classical Fisher information to the total quantum Fisher information (QFI), and measurement complexity--defined as the quantum circuit depth required prior to projection. Remarkably, we uncover a sudden emergence of observability: a sharp hidden-to-visible transition driven entirely by measurement complexity. We rigorously prove that below critical depth thresholds--$Θ((\log n)^{1/δ})$ for $δ$-dimensional architectures and $Θ(\log\log n)$ for all-to-all connectivity--readout capability decays exponentially with system size $n$, rendering the quantum information fundamentally inaccessible. Surprisingly, immediately above this threshold, the system enters a visible regime: we demonstrate that randomized measurements universally recover a constant fraction of the QFI using approximate unitary 3-designs, for which we explicitly develop optimal-depth circuit constructions tailored to finite-dimensional architectures. By unveiling the fundamental scaling laws and transitions that govern quantum observation, our results delineate definitive resource boundaries for quantum learning, state certification, and quantum metrology.

Rydberg atoms possess strong electric dipole transitions and tunable energy levels, making them promising candidates for microwave to optical conversion on integrated superconducting atom chips. Achieving strong coupling of the atoms to e.g. the microwave field of an on-chip resonator requires placing the atoms within tens of micrometers from the chip surface. However, inhomogeneous stray electric fields originating from the surface can induce position-dependent Stark forces, resulting in atomic motion and leading to time-dependent shifts of the Rydberg energy levels. We experimentally investigate these effects using time-of-flight and spectroscopic techniques, observing substantial level shifts and signal loss attributable to field-induced atomic motion. A theoretical model incorporating an exponentially decaying surface field with a superimposed bias accurately reproduces the observed dynamics. To mitigate the level shift, we introduce a Stark echo sequence that dynamically reverses the force. This approach suppresses the atomic motion and maintains the atomic resonance. The method relies solely on global field control and is compatible with atom-resonator coupling architectures, providing a robust strategy for preserving coherence of Rydberg atoms in inhomogeneous electric fields near surfaces.

Training parameterised quantum circuits (PQCs) on quantum hardware is bottlenecked by the measurement cost of gradient estimation, which under the parameter-shift rule scales linearly in the number of trainable parameters and dominates the total shot budget of training at scale. In this work, we propose a framework of forward gradient estimators for PQCs, based on the forward mode of automatic differentiation, that yields an unbiased estimator of the gradient by averaging a freely tunable number of random directional derivatives and recovers SPSA, random coordinate descent, and the parameter-shift rule as limiting cases, with no ancilla qubits or controlled-gate overhead. We prove that stochastic quantum forward gradient descent converges under standard assumptions, with an explicit second-moment expansion that interpolates between the single-direction extreme of SPSA and the full-gradient extreme of parameter-shift. Within this framework we derive QUIVER (Quantum Iterative V-adaptive Estimator Rule), an adaptive optimiser for parameterised circuits whose update rule follows from a closed-form minimum measurement-cost allocation. We show numerically that forward gradients train Hamming-weight-preserving orthogonal quantum neural networks with up to 60 qubits and 1770 parameters on the ECG5000 and MNIST datasets orders of magnitude more efficiently than the parameter-shift rule. We also demonstrate that our proposed QUIVER optimiser can outperform iCANS and gCANS measurement-frugal optimisers on optimisation problems using the quantum approximate optimisation algorithm and quantum simulation with the variational quantum eigensolver.

In this paper, we continue a line of research initiated by Basu, Brakensiek, and Putterman [2026] studying the sparsifiability of Hamiltonians. We focus particularly on the sparsifiability of the widely-studied Quantum Cut (QC) Hamiltonians. Our main result is that in an $n$-qubit system, any $n$-qubit QC Hamiltonian can be sparsified to $\widetilde{O}(n /\varepsilon^2)$ many terms while preserving the energy of every state up to a factor of $1 \pm \varepsilon$. Our result can be interpreted as giving an importance sampling scheme for the edges of an arbitrary graph $G$ such that the \emph{Kikuchi} graph at level $\ell$ of the sampled graph is a spectral approximation to the Kikuchi graph of $G$. Importantly, the \emph{same} sampling scheme works simultaneously for all $\ell$. The natural approach of leverage score sampling, analyzed via matrix concentration inequalities, yields a polynomially worse bound in our setting because the underlying matrices have dimension $\sim 2^n$. Instead, our approach relies on decomposing the action of these matrices into invariant subspaces. Then, by using an operator-valued inequality of Alon and Kozma [Ann. Henri Poincaré, 2020], itself building on an \emph{octopus inequality} of Caputo, Liggett, and Richthammer [J. AMS, 2010], we extend our sparsification technique to all expander graphs. We then invoke expander decomposition to extend our sparsifier to all graphs.

We study driven and open quantum systems described by a time-periodic Lindblad master equation. In closed systems, the stroboscopic dynamics can always be described by an effective time-independent Floquet Hamiltonian; this idea is the basis of Floquet engineering. However, in the presence of dissipation, the existence of an effective time-independent Floquet Lindbladian is not guaranteed due to the non-unitary nature of the evolution. Using Floquet theory, we construct a well-defined time-independent Floquet Lindbladian in an extended Sambe-Liouville space, transforming the initial time-dependent problem to a static and non-Hermitian eigenvalue problem. For harmonic driving, we introduce a matrix continued fraction method to nonperturbatively resum multiphoton processes and construct an effective Floquet Lindbladian acting only on the physical Liouville space. Compared to other high-frequency expansions, this method has the advantage of providing the whole infinite series expansion at once. Using a resolvent formalism, we show how to obtain a spectral Floquet representation of correlation functions of an open quantum system. As an application, we consider a dissipating two-level system in a linearly polarized field and calculate its resonance fluorescence spectrum. Furthermore, we consider a parametrically driven quantum dot with pump and loss for which we calculate its spectral function and current-voltage characteristics.

Bidirectional quantum key distribution (QKD) protocols face persistent challenges related to classical disclosure, confinement of the signal space to predictable subspaces, and limited detectability under substitution or entanglement-swapping attacks. In this work, we present a Bell-state extension of the Loop-Back QKD architecture that improves efficiency and detectability while preserving its defining feature of a simplified, measurement-free remote terminal. The protocol employs entangled Bell states together with deterministic local Pauli encoding at the remote node. A central element is that Alice privately prepares and knows the initial Bell state, which serves as a hidden reference enabling her to interpret the Bell-state transition induced by Bob, while preventing an adversary from reconstructing the encoding without access to this reference. By exploiting both intra- and inter-family Bell transitions, the scheme expands the effective signal space beyond the subspace restrictions of earlier two-way protocols. Alice performs a Bell-state measurement to deterministically infer Bob's operation without any basis sifting. Although the traveling subsystem remains locally maximally mixed, concealing the initial Bell family amplifies disturbance under separable substitution strategies, yielding an intrinsic detection probability of approximately 3/4 per round. From an efficiency perspective, the protocol lifts the intrinsic post-selection limitation of single-qubit Loop-Back schemes: the effective throughput is bounded only by the Bell-state measurement success probability, reaching up to 50% in linear-optical implementations. These features make the proposed scheme particularly suitable for mobile or edge-based QKD scenarios, where passive remote nodes must operate under high loss and limited interaction times.

Superconducting resonators coupled to semiconductor quantum dots provide a powerful platform to investigate light-matter interaction and decoherence mechanisms in solid-state quantum systems. Here we study a hybrid circuit quantum electrodynamics architecture consisting of a GaAs double-quantum-dot charge qubit capacitively coupled to a high-impedance, frequency-tunable SQUID-array resonator. By tuning the qubit transition frequency over the range $ω_\mathrm{q}/2π\sim 3$-$6$ GHz, we perform frequency-resolved decoherence spectroscopy of the charge qubit across a broad energy window. Time-resolved measurements enable us to disentangle relaxation and pure dephasing processes and to identify distinct decoherence regimes as a function of qubit frequency. We find that at lower frequencies ($\leq 4.5$ GHz) dephasing dominates the qubit linewidth, whereas at higher frequencies energy relaxation becomes the leading contribution. The measured frequency dependence of the relaxation rate exhibits a cubic scaling, consistent with charge-qubit decay dominated by coupling to a piezoelectric phonon bath and providing frequency-resolved access to the corresponding phonon-induced spectral density. Our results show that hybrid semiconductor--superconducting circuits can serve as sensitive spectroscopic tools to probe microscopic decoherence mechanisms relevant for a wide range of hybrid quantum devices.

We show that strongly amplified dynamical responses in cavity optomechanical systems can be harnessed for enhanced quantum sensing. By tuning the optomechanical interaction to a regime of enhanced susceptibility, weak perturbations produce disproportionately large changes in the system response, leading to substantially improved estimation precision. Using Gaussian estimation theory, we demonstrate that the quantum Fisher information exhibits a divergent scaling as the perturbation strength decreases, implying a corresponding suppression of the estimation error. We further show that heterodyne detection of the output cavity field yields the classical Fisher information with the same asymptotic scaling as the quantum Fisher information, demonstrating that the enhanced sensitivity is accessible with a standard measurement protocol. These results identify amplified optomechanical dynamics as a controllable resource for quantum enhanced sensing and metrology.

We propose an analog quantum simulation of chiral magnetic dynamics using ultracold atoms in an optical superlattice. The massive Schwinger model in the zero gauge coupling limit maps onto the Rice-Mele model, with the fermion mass and topological angle encoded in the superlattice parameters. We study the real-time dynamics of the vector current following two quench protocols that drive continuous chirality injection and chirality relaxation. Simulations with realistic superlattice parameters and experimental noise demonstrates clear mass dependence of the current dynamics in both protocols, robust against experimental imperfections. The vector current may be directly measurable via single-bond-resolved detection, establishing cold atom superlattices as a viable platform for probing non-equilibrium chiral phenomena.

Diabatic quantum annealing with variationally optimized schedules can exhibit exponential speedups over conventional adiabatic quantum annealing, as was demonstrated numerically for a frustrated Ising ring model by C{ô}t{é} et al. Here we identify Landau-Zener-St{ü}ckelberg interference as the underlying mechanism for this speedup, and based on this insight we propose a variational schedule ansatz with far fewer parameters. This simplified ansatz allows us to show analytically that the classical optimization of the schedule parameters can be done in polynomial time and discuss conditions when we expect this type of mechanism to provide speedups over adiabatic annealing. Furthermore, we provide an analytical argument that coherence is an essential resource for this mechanism, which we verify numerically. We perform extensive numerical tests of the proposed ansatz and observe substantial improvements over adiabatic annealing and competitive performance in particularly challenging problem instances, including a well-studied MAXCUT instance commonly used for benchmarking. Our work shows that explicitly leveraging physical mechanisms can lead to more effective designs of variational annealing algorithms.

Solution-state molecular nuclear spin networks are promising quantum simulators because their scalar-coupling Hamiltonians are chemically programmable, precisely measurable, and coherent at room temperature. Their main limitation for quantum information science is initialization: thermal Boltzmann polarization produces highly mixed, high-entropy states. Here, we use parahydrogen-based Signal Amplification by Reversible Exchange (SABRE) at hypogeomagnetic fields (i.e., magnetic fields below Earth field) to hyperpolarize the chemically engineered 12-spin chain [U-13C,15N]-butyronitrile. SABRE generates percent-level 13C and 15N polarization and prepares non-equilibrium multi-spin orders across the network. A von Neumann entropy analysis of such a hyperpolarized system shows that, at the optimal transfer field of 0.52 uT, the full spin system could reach S/k = 8.274, compared with S/k = 8.318 for the unpolarized reference, giving (S-Sth)/k = -0.043. Experimentally, nuclear spin temperatures of 52 mK and 257 mK are achieved for 15N and 13C subensembles, respectively. The larger entropy deficit of the full network than of individual subsystems indicates correlated multi-spin order beyond single-spin polarizations. Rapid field cycling to 9.4 T enables site-resolved NMR readout, while the precisely determined coupling network provides an experimentally benchmarked Hamiltonian for testing quantum-simulation, quantum-control, and Hamiltonian-learning protocols.

Double microwave shielding employs $σ^{+}$- and $π$-polarized microwave fields, tuned close to the lowest rotational transition, to engineer a long-range repulsive barrier between polar molecules. By preventing molecules from reaching the short range, this technique suppresses detrimental two-body losses and recently enabled the realization of molecular Bose-Einstein condensates and self-bound droplets. Yet, the optimal operating regimes of the shielding mechanism remain largely unexplored. Here, by leveraging the underlying universality of the scattering problem, we systematically map the four-dimensional microwave parameter space-spanned by the detunings and intensities of the two fields-to identify configurations that maximize both shielding efficiency and interaction tunability. We define optimal operating regimes as configurations that are strictly free of field-linked bound states while sufficiently suppressing two-body losses to exceed typical lifetimes of ultracold samples. In these regimes, we evaluate the elastic-to-inelastic collision ratios required for efficient evaporative cooling and explore the accessible tuning range of the effective dipolar interactions. Finally, to identify the best platforms for future quantum simulation experiments, we conduct a global survey of candidate molecular species under realistic field constraints. We identify heavy, strongly dipolar molecules as the most promising candidates, demonstrating that they can achieve extreme loss suppression alongside robust interaction tunability using only moderate field strengths.

We compare phase-only control with phase-and-amplitude control when designing shaped pulses using the GRAPE algorithm, and explain why phase-only control has significant advantages. Trotterisation can be used to simulate amplitude modulation with phase modulation, indicating that the two approaches are fundamentally equivalent. Pulses designed by either method can be interconverted, but phase-only optimization is faster and simpler. The resulting pulses can then be converted into phase-and-amplitude form for more robust implementation if desired.

Modulated circulant matrices form a special class of N-parametric circulant matrices, recently introduced in the literature, with a structured spectral decomposition based on a Vandermonde type basis. Motivated by this definition, in this work we define the Modulated Quantum Fourier Transform (MQFT), a quantum primitive tailored to this matrix family.

The river-crossing problem, also known as Zermelo's navigation problem, is a classic example of an optimization problem with practical relevance and a scalable degree of complexity. It asks for the optimal trajectory of a vessel moving through a water flow field and provides a setting in which physics, variational methods, and optimization are naturally intertwined. We state a version of Zermelo's problem and then solve it as formulate it as an adiabatic quantum-computing problem using quantum trits, or qutrits for short. The construction includes a penalty term that enforces the prescribed boundary conditions and an exploration term that allows the system to move through intermediate configurations toward the optimal feasible path. In the adiabatic description, the evolution proceeds through a sequence of avoided crossings, so that the resulting fidelity can be estimated using the Landau-Zener formula. Remarkably, the regime in which this approximation is valid also provides a deterministic way to identify the correct solution with computational effort that scales only quadratically with the problem size. Thus, a quantum formulation initially motivated by the apparent exponential complexity of the problem reveals an underlying classical structure that can be exploited efficiently. Our approach also provides a pedagogical illustration of how a real-world optimization problem can be cast into a quantum-annealing framework and then analyzed using the Schrödinger equation, avoided crossings, and Landau-Zener theory.

The controlled generation of quantum entanglement from separable states remains a central challenge in quantum information science. Here, we investigate entanglement generation using two related control paradigms: coherent path superposition of local unitary operations and stochastic implementations of Pauli channels under coherent control. We show that entangled states belonging to the Bell, GHZ and W classes, can be deterministically generated from fully separable inputs by coherently superposing alternative sets of local unitary transformations. Conditions on the local operators for entanglement generation are derived, and the resulting states are shown to be locally unitary equivalent to standard multipartite entangled states. We further extend the analysis to noisy scenarios, where separable mixed states evolve through pairs of Pauli channels arranged in path-superposition and indefinite causal order configurations. Closed-form expressions for the output states are obtained, and entanglement is quantified using concurrence. By exploring representative channel families across their parameter space, we identify regimes where stochastic entanglement emerges, determine the associated success probabilities, and characterize trade-offs between entanglement and purity.

We revisit quantum field theory in curved spacetime (QFTCS) as a semi-classical framework for quantum matter on classical geometries, emphasizing its limitations, including vacuum ambiguity and background dependence. We briefly review major approaches to quantum gravity (QG), including Loop Quantum Gravity (LQG), string theory, and asymptotic safety, highlighting their conceptual challenges. Motivated by these issues, we outline a teleparallel framework based on coframe and spin-connection variables, where gravity is encoded in torsion rather than curvature. This framework naturally incorporates local Lorentz symmetry and fermionic couplings while displaying a gauge-like structure. We argue that the coframe/spin-connection pair provides an alternative and geometrically refined description of gravitational variables, which may serve as a useful starting point for future investigations of QG. The purpose of this work is not to provide a complete quantization of teleparallel gravity but to identify the geometric and conceptual ingredients that such a formulation would require.

The model of interactive oracle proofs (IOP) generalizes the notion of probabilistically checkable proof (PCP), in which a static proof is verified probabilistically by querying a small number of bits, to the interactive setting: a polynomial-time verifier interacts with an unbounded prover, but is restricted to only reading a small number of bits, in total, from the messages sent by the prover. IOPs provide a relaxed setting in which to study local probabilistic verification. They have proved instrumental in devising efficient methods for verification through subsequent compilation into non-interactive or succinct protocols. We study a quantum analogue of interactive oracle proofs (qIOP) in which the verifier and communication are both allowed to be quantum; yet the verifier is restricted to perform measurements only on a small number of qubits received from the prover. Our main result is a qIOP for any language in QMA, in which the total communication is polynomial but the verifier only reads a polylogarithmic number of qubits in total. The protocol has completeness parameter exponentially close to $1$ and soundness bounded away from $1$ by a constant. In the absence of a quantum PCP theorem, this provides the first information-theoretically sound local and robust characterization of QMA, albeit interactive. Our protocol combines the use of a quantum locally testable code (LTC) with classical techniques, notably probabilistically checkable proofs of proximity (PCPP). We avoid the necessity for complex multi-qubit tests employed in other settings by leveraging the local indistinguishability property of the quantum LTC.

We establish an operational framework connecting the classical Kolmogorov--Arnold (KA) representation theorem to quantum information theory. By introducing and proving an algebraic, bounded-degree polynomial version of the theorem, we demonstrate that any target physical property of an unentangled multi-qubit product state can be exactly decomposed using a finite, fixed set of local <<inner>> observables and a shallow architecture of univariate polynomials. We further analyze the stability of this Quantum Kolmogorov--Arnold (QKA) representation under adversarial perturbations. In stark contrast to the pathological instabilities and severe reparameterization sensitivities inherent to the classical Kolmogorov--Arnold representation theorem, our algebraic quantum framework exhibits remarkable resilience. We prove that the representation remains stable against bounded physical perturbations acting on the inner measurement operators, and show via the Heisenberg picture that it is inherently immune to adversarial quantum channel attacks acting on the input states.

We introduce a unified theoretical framework for single-plasmon transport in one-dimensional nanowires, bridging the quantized electromagnetic Green's tensor formalism with effective non-Hermitian Hamiltonian models. This approach naturally incorporates propagating surface plasmon polaritons, high-order modes dissipative channels, and intrinsic losses. We investigate both the stationary regime and the spatio-temporal dynamics of a single-plasmon pulse travelling through an atomic chain coupled to a dispersive nanowire. We analyze modal contributions to reflection and transmission spectra for quantum emitter coupled to a silver nanowire, a configuration proposed as a single-plasmon transistor, and we demonstrate that optimized multi-emitter systems offer significant advantages. In case of one quantum emitter coupled to a silver nanowire at telecom wavelengths, we predict a single-plasmon transmittivity down to 7\% under realistic conditions, and an atomic qubit population of 12\%. Extension to multi-emitter systems using a Löwdin orthogonalization procedure enables a consistent treatment of collective interactions. We show that optimized positioning with just five emitters enhances plasmon modulation, achieving a transmittivity of 2\% but also reduces coupling losses to one-third compared to the single-emitter case. Our results establish a robust foundation for analyzing and designing plasmonic waveguide quantum electrodynamics systems.

Denial-of-service (DoS) and distributed denial-of-service (DDoS) mitigation requires separating malicious traffic from benign traffic while minimizing disruption to legitimate users. Prior work proposed mapping honeypot traffic partitioning to a weighted MaxCut problem and solving the resulting graphs with variational quantum algorithms. We extend this proof of principle direction with a reproducible event-level honeypot-to-QUBO pipeline, labeled temporal bipartite benchmark graphs with 16, 32, 66, and 110 event nodes, QAOA executions on IBM quantum hardware, classical heuristic baselines, a noiseless matrix product state reference, and a routing overhead analysis across quantum processor architectures. The largest benchmark is a 110-node, 181-edge instance executed on three IBM backends. Our results show that a shallow QAOA can execute real traffic partitioning workloads at the utility scale, while backend architecture and routing overhead affect objective quality, security metrics, and observed runtime. Because simple classical heuristics can solve the current labeled benchmark graphs, these experiments are not a quantum advantage claim. Instead, we deliberately use a fixed, shallow QAOA implementation to enable controlled comparisons across problem sizes and hardware architectures. This work establishes a hardware feasibility and architecture benchmark framework, and demonstrates that MaxCut cost, security quality, routing overhead, and runtime must be reported as separate metrics for cybersecurity relevant quantum optimization.

Resonant $Z$-boson production is a cornerstone of precision electroweak physics, with its vacuum line shape set by the $Z$ mass, width, and collision kinematics. We show that a strong laser field can significantly alter this picture. By treating the field nonperturbatively, we find that laser dressing of the incoming fermions alters the effective collision kinematics and opens laser-photon exchange channels, including multiphoton processes, in $e^{+}e^{-}$ collisions. As a result, the $Z$-resonance profile develops distinct intensity-dependent regimes, evolving from the vacuum limit to saturation at intermediate field strengths and to an approximately quadratic enhancement at higher intensities. Additionally, the polarization composition of the produced $Z$ bosons is redistributed. In particular, at high intensities the laser-induced contribution can compensate the intrinsic chiral asymmetry of the electroweak interaction, leading to nearly parity-balanced $Z$-boson production. Our results identify that strong classical fields can dynamically control electroweak resonance phenomena, opening a bridge between strong-field QED and high-energy collider physics.

We suggest that quantum algorithms can be used to model classical stochastic simulations as the measurement process is inherently random. To illustrate, we solve the classical Lorenz system with stochastic behavior using a Python random number generator. We compare the classical stochasticity of the Lorenz system with the measured output of the system obtained using quantum algorithms.

We study energy transport between two quantum systems coupled through a random interaction. The central feature of our approach is to model the coupling as a Gaussian random matrix, which enables a simple and systematic perturbative expansion. In the large-$N$ limit, we derive explicit expressions for the energy transfer rate and heat conductance up to second order in the coupling strength. Using spectral methods and diagrammatic expansions, we obtain the leading- and next-to-leading-order contributions to the energy transfer rate. We illustrate our results through explicit calculations for Gaussian, constant, semicircular, and Gamma densities of states.

Reservoir engineering can stabilize states inaccessible to unitary dynamics. Directed particle-conserving dissipation creates Lindbladian skin states, where Pauli exclusion turns edge accumulation into a many-body density imbalance. In a monitored fermion chain with tunable hopping range, we identify, within a Gaussian trajectory approximation, two finite-size scaling regimes: short-range hopping is consistent with complete skin accumulation and area-law entanglement, whereas sufficiently long-range hopping produces a finite bulk tail and effective algebraic sub-volume-law entanglement. Dissipation and coherent hopping thus jointly control skin localization and quantum entanglement, highlighting their close interconnection.

Topological insulators have attracted numerous attentions recent years, where the Su-Schrieffer-Heeger (SSH) model is one of the most studied models. While the interacting version of it has been explored recently, the interplay between interactions and long-range hoppings merit further investigations. In this work, we uncover a rich phase diagram of the interacting SSH model with extended-range hoppings, in which it consists of several topological phases, two novel superconducting-like (SC-like) phases and five distinct charge-density-wave (CDW) phases. We substantiate that the SC-like and two CDW phases are direct consequences of imbalanced interactions and extended-range hoppings. We derive the order parameters (OPs) for each of the phases and verify them in large-system simulations, finding consistency with the entanglement entropy and the fidelity in capturing the phase transitions. In contrast to the non-interacting case where the favored hoppings are unidirectional in the topological phases, the derived OPs suggest non-unidirectional hoppings are possible under the influence of interactions.

We study Family-Vicsek scaling of charge, spin, and energy fluctuations in the one-dimensional Hubbard model at infinite temperature. Using a quantum generating function approach, we compute time-dependent cumulants of transferred conserved quantities and analyze how the corresponding roughness depends on subsystem size and time. We start by focusing on a single interface at half the chain and determine the transport exponents. Then we turn to fluctuations of a small finite interval and study the Family-Vicsek universality of fluctuations over an extended timescale. We find that the long-time scaling behavior is controlled by integrability. In the free limit, charge, spin, and energy all display ballistic transport. In the interacting integrable Hubbard chain, charge and spin cross over to a KPZ scaling regime, while the energy sector remains ballistic. Once integrability is broken by a next-nearest-neighbor density interaction, the long-time dynamics becomes diffusive in all sectors. In every case we also observe a short-time microscopic regime with apparently universal ballistic growth before the hydrodynamic scaling window sets in. The Family-Vicsek setup allows us to determine the growth, the saturation as well as the dynamical exponents.

We present the transformation-response framework, an operational reformulation of quantum mechanics. A quantum state is not a Hilbert space object but the catalog of a system's responses to all physical transformations: for each operation $g$ from the system's local group $G$, an interference experiment gives a complex value $χ(g)$. The collection $\{χ(g): g\in G \}$ is the characteristic function and defines the state. The only postulate is that $χ$ is positive-definite, encoding the requirement that no superposition of transformations yields negative probability. From this single assumption, the entire standard formalism is derived: Hilbert space via GNS construction, Born rule via Bochner theorem, Schrödinger equation from group automorphisms, and especially Feynman path integral as a Trotter limit. The framework is background-independent and time-neutral: time is a coordinate along a one-parameter subgroup of $G$. It also reveals a new physical constraint, product order positivity, which may lead to testable predictions. The framework provides a unified, economical, and falsifiable foundation for quantum theory rooted in operational primitives.

We study the relativistic nature of the interactions that, at tree level, generate spin correlations between two electrons in Møller scattering, as well as in an extended process involving a witness particle $C$. The corresponding processes, $e^{-}e^{-}\rightarrow e^{-}e^{-}$ and $e^{-}e^{-}C\rightarrow e^{-}e^{-}C$, are analyzed both in the center-of-mass frame and, for the former process, in a Lorentz-boosted frame where Wigner rotations arise. It is found that, through a nonrelativistic approximation of the scattering amplitudes, dipole-dipole and current-dipole interactions are responsible for the emergence of these correlations. This is evidenced by the variation of the von Neumann entropy of one electron for initially separable states, and of $C$ for an initially prepared three-particle entangled W-state. In Wigner rotations, the invariance of entropy under local unitary transformations is maintained at the expense of the emergence of quantum coherence in the density matrix at large rapidities. As a consequence, the final states of both particles are evaluated and shown to encode information about the scattering process through their spin expectation values. This framework is then used to comment on the correlations in the inelastic process $e^{-}e^{+}\rightarrowμ^{-}μ^{+}$, for which some research has reported differing results.

Multiparameter quantum estimation has emerged as a central task in quantum metrology. In this work, we investigate multiparameter quantum estimation in a hybrid exciton--optomechanical (EOM) system. The system consists of a semiconductor quantum well embedded inside a driven optomechanical microcavity, where the excitonic, optical, and mechanical modes interact coherently through exciton--photon and radiation-pressure couplings. Using the Gaussian-state formalism, we derive the covariance matrix of the steady-state quantum fluctuations and employ both the symmetric logarithmic derivative (SLD) and right logarithmic derivative (RLD) approaches to evaluate the quantum Fisher information matrix associated with the simultaneous estimation of the exciton--photon coupling strength $g$ and the excitonic decay rate $k_x$. We analyze the corresponding quantum Cramér--Rao bounds and determine the most informative precision limit governing the attainable estimation accuracy. The influence of several experimentally relevant parameters, including temperature, driving power, optomechanical coupling strength, and dissipation rates, is investigated in detail. Our results show that strong hybrid interactions and low-temperature regimes significantly enhance the estimation precision, whereas thermal fluctuations and dissipation processes deteriorate the metrological performance. Furthermore, we compare the ultimate quantum limits with experimentally feasible Gaussian measurement strategies based on homodyne and heterodyne detection. We show that heterodyne detection provides better estimation performance than homodyne schemes and can approach the optimal quantum precision limit in suitable parameter regimes.

Theoretical quantum dynamics calculations scale deeply with system size, rendering classical calculations intractable for complex systems. While quantum computing offers a natural solution, its application to nuclear quantum dynamics remains scarce. Here, we present a quantum algorithm to study photodissociation dynamics on quantum computers, benchmarked on the NOCl molecule. The wavefunction is propagated via a split-operator method, utilizing the Quantum Fourier Transform and unitary transformation matrix to switch representations. To impose outgoing boundary conditions on a truncated grid, we use a non-unitary absorbing potential propagator, implemented through a dilation scheme. The photodissociation cross section is calculated from the auto-correlation function, which is extracted using the Hadamard test. Our quantum computing results agree well with benchmarks under ideal conditions, and we further demonstrate that the algorithm is robust to noise and statistical sampling errors, indicating the promising application of noisy devices to quantum dynamics studies.

Chemical substitution offers an effective route to tune magnetic ordering and magnetocaloric performance in rare-earth oxides for cryogenic refrigeration. Here we investigate the structural evo lution, magnetic properties, and magnetocaloric effect of polycrystalline zircon-type Gd1-xErxVO4 (x=0, 0.1, 0.25, 0.5, and 0.75). Powder X-ray diffraction confirms that all samples crystallize in the tetragonal zircon structure without detectable impurity phases. Substitution of Gd3+ by the smaller Er3+ ion produces a systematic lattice contraction and modifies the magnetic behavior of the rare-earth sublattice. In particular, the magnetic ordering temperature is suppressed from 3.65(2) K in GdVO4 to 2.76(2) K in Gd0.9Er0.1VO4 , accompanied by a weakening of the spin-flop-like field-induced anomaly observed in the parent compound. A low Er concentration correspondingly improves the low-temperature magnetocaloric performance, with Gd0.9Er0.1VO4 exhibiting a max imum magnetic entropy change of 45.1 J kg-1 K-1 for mu_0 Delta H=7T. These results demonstrate that weak Er substitution effectively tunes the competition among exchange interactions, dipolar coupling, and magnetic anisotropy, optimizing the balance between magnetic ordering and available spin entropy in zircon-type rare-earth vanadates, which is crucial for developing efficient cryogenic refrigeration materials.

Gaussian quantum channels constitute a pivotal physical framework for characterizing the dynamics of Gaussian quantum states. Extensive scholarly attention has been devoted to the estimation of parameters associated with Gaussian channels. However, while previous research has predominantly focused on parameter estimation within inertial frames, the noninertial scenario, particularly in the context of the Unruh effect, remains largely unexplored. In this paper, we analyze the impact of the Unruh effect on the estimation precision of Gaussian channel parameters, with a specific focus on thermal attenuator and thermal amplifier channels. Our findings reveal that the Unruh effect significantly degrades the precision of single-parameter estimation for Gaussian channel parameters when employing both the input coherent state and squeezed vacuum state. For the two-parameter estimation, we further demonstrate that the quantum Cramér-Rao bound serves as an asymptotically achievable precision limit. Consistent with the single-parameter case, the Unruh effect exerts a detrimental impact on the precision of two-parameter estimation. Notably, heterodyne measurement is near-optimal for both single- and two-parameter estimation in the limit of high acceleration or large thermal mean numbers. These results provide crucial theoretical insights and practical guidance for advancing quantum parameter estimation in a relativistic context.

Quantum computers offer a route to outperform classical methods in tasks such as molecular simulation, motivating hybrid algorithms like the Variational Quantum Eigensolver (VQE) for near-term devices. Silicon spin qubits are a promising platform for scalable quantum computation, but their performance is limited by hardware imperfections -- most notably charge-noise-induced potential fluctuations and static miscalibration of gate-electrode voltages -- which degrade quantum gate fidelities and, ultimately, algorithmic accuracy. Here we develop a hardware-algorithm co-simulation framework for silicon quantum-dot processors that links 3D electrostatics to effective $g$-factors and exchange couplings, and propagates voltage-level noise through realistic control pulses. Using VQE for $\mathrm{H}_2$ ground-state energy estimation as a circuit-level testbed, we study both static scaling/offset errors on the gate-electrode voltages and stochastic fluctuations modeled as random-telegraph noise with tunable amplitudes and switching times. At the gate level, we show that exchange-based two-qubit gates are roughly an order of magnitude more sensitive to these types of noise than ESR-driven single-qubit rotations. Quantum process tomography and Kraus-operator analysis further distinguish coherent and incoherent contributions and quantify the fraction of error that is, in principle, correctable by a compensating unitary. Embedding these noise models into the VQE circuit, we identify regimes of miscalibration strength and noise switching time compatible with chemically accurate energy estimates, and discuss how statistical post-processing based on the full distribution of noisy energy estimates could further improve accuracy.

Atomic clocks have made time and frequency the most precisely measured quantities in physics, progressing from microwave standards that realize the SI second to optical clocks that now reach unprecedented levels of precision. A nuclear clock would shift the frequency reference from an electronic transition to the uniquely low-lying, laser-accessible isomeric transition in the $^{229}$Th nucleus, offering a route to compact, robust timekeeping and sensitive tests of fundamental physics. However, turning recent advances in spectroscopy of the $^{229}$Th nuclear resonance into clock operation requires the nuclear transition to serve as a stable discriminator for steering a traceable oscillator. Here we demonstrate the operation of a $^{229}$Th nuclear clock by stabilizing a continuous-wave narrow-linewidth 148.4 nm vacuum-ultraviolet (VUV) laser to a resolved nuclear transition in a solid-state host. This clock operation is enabled by fast frequency discrimination based on phototube photocurrent readout of the transmitted VUV power. The 10 $μ$W VUV laser, generated by four-wave mixing in cadmium vapour, provides a high-signal-to-noise absorption signal from a home-grown $^{229}$Th:CaF$_2$ crystal, allowing the laser to be locked to a weakly temperature-sensitive nuclear transition. The clock reaches a fractional frequency instability of $2\times10^{-12}/\sqrt{τ/s} $, where $τ$ is the averaging time. Remarkably, nuclear-clock frequencies measured with two distinct crystals agree at the $10^{-13}$ level, demonstrating the reproducibility of solid-state nuclear frequency references. By making a laser-addressed atomic nucleus an operational clock reference, this work extends quantum metrology from electronic to nuclear transitions, and opens a new platform for compact clocks, solid-state nuclear quantum sensors and precision tests of fundamental physics.

The information-theoretic concept of identification describes a sender-receiver architecture in which the receiver only checks whether a particular message was sent or not, thereby promising a low-energy receiver design. In low received-energy regimes, quantum receivers are a promising tool for studying the system limits. However, the known information-theoretically optimal identification codes typically assume perfect synchronization. In this work, we study deterministic identification in a satellite setting under explicit synchronization constraints, where a satellite broadcasts the signature of a specific User Equipment (UE) which it assumes to be attached to one out of several possible Ground Station (GS), with the goal of establishing communication with the target UE. Within the proposed design, and assuming a specific phase-encoded coherent-state clock scheme in which the discrete time index is represented by equidistant phase rotations on the unit circle, our results reveal a fundamental asymmetry: At any transmission power, identification performance improves with blocklength, whereas synchronization accuracy degrades. In particular, the energy needed for transmitting the satellite clock to the GS can be several orders of magnitude higher than the one needed for the identification signal. This indicates that synchronization strongly impacts identification performance and motivates the investigation of the error-correcting capabilities of bosonic codes under jitter.

We investigate the properties of heat conduction in a network of harmonic oscillators interacting with heat baths, described by a generalized model of Brownian motion. This model includes noise and dissipation terms in both the momentum and position equations. This generalization is motivated by the requirement of consistency with the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. Because standard definitions of heat current based on velocity become mathematically inconsistent in this framework, we derive an analytical expression for the steady-state heat flow based on an extended framework of stochastic energetics. We confirm that Fourier's law (linear thermal response) is satisfied and that the model naturally captures microscopic thermal boundary resistance, analogous to Kapitza resistance. This demonstrates that our generalized model functions as a valid phenomenological framework for simulating non-equilibrium processes, marking a crucial step toward a unified formulation of stochastic and quantum thermodynamics. Furthermore, we analyze the time evolution of heat conduction by numerically solving the corresponding differential equations for the correlation functions. Unlike standard Brownian motion, the generalized model generates continuous and nowhere differentiable trajectories for both momentum and position (as is characteristic of overdamped dynamics). Finally, we show that the heat current exhibits characteristic transient behavior when the inter-particle interaction is switched on. Specifically, an instantaneous heat flow emerges, whose direction is strictly governed by whether the interaction is attractive or repulsive, significantly differing from the predictions of the standard model.

Adaptive variational quantum algorithms like ADAPT-VQE construct tailored ansätze by iteratively selecting operators from a pool using gradient-based criteria. While this avoids oversized parameter spaces, repeatedly scanning the full pool incurs a classical cost that scales linearly with pool size-a major bottleneck for systems with long-range interactions or large operator sets. Here, we reformulate adaptive operator selection as a graph-based decision problem and introduce a graph neural network (GNN) policy that predicts the next entangling operator directly from the interaction graph and state-dependent observables. Training data are generated from exact simulations of disordered long-range spin chains, using gradient magnitudes as supervision signals. The learned policy accurately reproduces the dominant structure of the greedy gradient-based selection rule, significantly outperforming heuristics based solely on interaction strength. Integrated into a variational quantum eigensolver (VQE) workflow, this GNN-VQE approach achieves energy errors close to standard ADAPT-VQE while drastically reducing full-pool gradient evaluations. To test transferability beyond spin models, we evaluate the policy on small active-space molecular benchmarks (LiH and BeH_$2$). We find the GNN is highly effective as a shortlist generator: exact rescoring over just a few GNN-proposed candidates recovers near-oracle rollout behavior while searching only a small fraction of the pool. These results demonstrate that adaptive circuit construction contains learnable structure that can be exploited to accelerate variational quantum algorithms.

We study the problem of implementing a quantum channel using a small ancilla with classical randomization and postselection on an output failure flag. The simulation is probabilistic, but exact conditioned on success. We prove that any unital channel on a $d$-dimensional system can be simulated with ancilla dimension $k$ and success probability $Ω(\frac{k}{\log d})$. Equivalently, every unital channel on $n$ qubits can be simulated with constant success probability using only $O(\log n)$ ancillary qubits. We show that this tradeoff is best possible by constructing a family of channels which cannot be simulated with success probability better than $O(\frac{k}{\log d})$. We also show that the class of \textit{highly noncommutative} channels, which includes random channels, admits constant-success simulation with just a single ancillary qubit. We further show that this model of simulation necessarily fails for strongly non-unital channels and discuss possible extensions involving adaptivity. On the technical side we rely on a partition-based protocol and matrix concentration inequalities, including the recent refinement of noncommutative Khintchine inequalities due to Bandeira, Boedihardjo and van Handel.

Tensor networks and quantum circuits are structural objects whose meaning depends on connectivity, indices, contraction order, gate placement, measurements, and related design choices. They are often easier to reason about visually than as code, yet in Python they are frequently constructed, transformed, and checked through backend-specific objects or compact symbolic expressions. This can make structural mistakes hard to notice during development, debugging, and communication. This paper presents three complementary packages: Tensor-Network-Visualization for visual debugging and structural inspection of supported tensor-network and traced einsum workflows; Tensor-Network-Editor for visual-to-code authoring, backend code generation, JSON preservation, export, and design-level analysis; and Quantum Circuit Drawer for clear circuit rendering, inspection, and complementary comparison of circuits or documented result distributions. The packages form a visual authoring and inspection layer around existing tensor-network libraries, array-based scientific Python workflows, and quantum SDKs. They are not simulators: they do not implement new contraction algorithms, execute quantum circuits, or guarantee full semantic equivalence across arbitrary backends. Their contribution is to make structural artifacts visible, editable, inspectable, comparable, exportable, and reproducible within those ecosystems.