Papers

We theoretically investigate the control of the Goos-Hänchen shift (GHS) of a reflected weak probe field in both parity-time ($\mathcal{PT}$)-symmetric and conventional optomechanical systems. The proposed scheme consists of a single optomechanical platform where a passive optical cavity is coupled to an active mechanical resonator, in contrast to standard passive-passive configurations. Analysis of the eigenfrequency spectrum reveals the emergence of an exceptional point under balanced gain-loss conditions at a tunable effective optomechanical coupling strength. Using the transfer-matrix method combined with stationary-phase analysis, we examine the GHS across broken and unbroken $\mathcal{PT}$ phases and compare it with that in the conventional system. The lateral shift exhibits strong phase dependence: it is markedly enhanced in the unbroken regime relative to both the broken phase and the passive configuration. We further show that the GHS can be actively tuned through the cavity detuning and the intracavity medium length. These results provide a controlled means for manipulating beam shifts in optomechanical systems and suggest pathways toward tunable photonic components and precision optical sensing.

Magnetic Resonance Spectroscopy (MRS) offers a unique non-invasive window into metabolic processes, yet its potential remains strictly constrained by severe spectral congestion and intrinsic insensitivity. Traditional pulse sequence design, tethered to human intuition, predominantly targets simple quantum states, thereby overlooking the vast majority of the exponentially scaling operator space which consists of complex spin superpositions. Here, we introduce a spectrum-driven, end-to-end differentiable physical framework that transcends these heuristic limitations. By integrating physical laws with automatic differentiation algorithm, our approach directly navigates the high-dimensional spin dynamics space, bypassing the intractable inverse problem of state preparation. This enables the discovery of non-intuitive, complex mixed states that simultaneously satisfy the dual objectives of selective excitation and interferometric signal enhancement. We validate this paradigm by achieving the robust separation of Glutamate and Glutamine, which is a longstanding neuroimaging challenge, in the human brain at 3T, demonstrating spectral fidelity superior to conventional methods. By unlocking the "dark" informational content of nuclear spin ensembles, our work establishes a generalizable paradigm for goal-driven quantum state engineering in magnetic resonance and beyond.

Non-Hermitian skin effect is one of the most captivating phenomena in non-Hermitian systems, characterized by the extensive localization of eigenstates near open boundaries. In its conventional form, the localization length of a skin mode is independent of the system size. Remarkably, however, when the open boundaries are coupled to realize a generalized boundary condition, the localization length can undergo a drastic transformation, becoming proportional to the system length. This intriguing regime is known as the scale-free skin effect (SFSE). Although SFSE has been observed in numerous one-dimensional non-Hermitian models through case-by-case studies, a unified theoret ical framework capable of predicting its emergence and characteristic properties remains absent. In this work, we take a firm step forward by establishing a model-independent framework for the ana lytic determination of scale-free localization lengths in certain regimes. Our key insight is to treat generalized boundary conditions as a perturbation of the periodic boundary conditions, thereby circumventing the singular response-to-perturbation that would otherwise arise if they were pertur batively treated relative to open boundary conditions. Our work sheds new light on understanding SFSE in non-Hermitian systems.

We propose a privacy-aware hybrid framework for federated medical image classification that combines tensor-network representation learning, MPC-secured aggregation, and post-aggregation quantum refinement. The framework is motivated by two practical constraints in privacy-aware federated learning: MPC can introduce substantial communication overhead, and direct quantum processing of high-dimensional medical images is unrealistic with a small number of qubits. To address both constraints within a single architecture, client-side tensor-network frontends, Matrix Product State (MPS), Tree Tensor Network (TTN), and Multi-scale Entanglement Renormalization Ansatz (MERA), compress local inputs into compact latent representations, after which a Quantum-Enhanced Processor (QEP) refines the aggregated latent feature through quantum-state embedding and observable-based readout. Experiments on PneumoniaMNIST show that the effect of the QEP is frontend-dependent rather than uniform across architectures. In the present setting, the TTN+QEP combination exhibits the most balanced overall profile. The results also suggest that the QEP behaves more stably when the qubit count is sufficiently matched to the latent dimension, while noisy conditions degrade performance relative to the noiseless setting. The MPC benchmark further shows that communication cost is governed primarily by the dimension of the protected latent representation. This indicates that tensor-network compression plays a dual role: it enables small-qubit quantum processing on compressed latent features and reduces the communication overhead associated with secure aggregation. Taken together, these results support a co-design perspective in which representation compression, post-aggregation quantum refinement, and privacy-aware deployment should be optimized jointly.

A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard variational approaches posit a wave-function ansatz and minimize over the possible states expressible by that ansatz, the problem can alternatively be formulated as a noncommutative polynomial optimization problem and treated through a hierarchy of semidefinite programming relaxations. In contrast to variational calculations, these relaxations provide lower bounds on ground-state energies and both lower and upper bounds on observable expectation values. However, this approach typically suffers from severe scalability issues, limiting its applicability to small-to-medium-scale systems. In this article, we demonstrate that systematically leveraging the inherent structures of the system can substantially mitigate these scalability challenges and thus permits computing meaningful bounds for quantum spin systems on square lattices of size up to $16\times16$.

Single-shot measurement learning (SSML) learns a compensation unitary from a one-bit success/failure record and halts after a prescribed run of consecutive successes. We recast SSML as an adaptive estimator on a parameterized sensing manifold and ask what role it can play in quantum-enhanced sensing. First, we show that the terminal run itself furnishes an intrinsic certificate of local alignment: longer terminal runs certify smaller infidelity, and near the optimum this becomes a Fisher-calibrated certificate of parameter error. Second, for compensation-type sensing families, the Bernoulli success/failure record is locally matched to the probe quantum Fisher information (QFI), so SSML preserves the probe's metrological content despite using only one classical bit per copy. In this sense, SSML makes the quantum enhancement carried by the probe operationally available in an online self-terminating protocol. Applied to GHZ/NOON probes of depth $m$, SSML retains the familiar square-root entanglement gain over product probes at fixed total resource, while an ideal multiscale architecture remains compatible with Heisenberg scaling. Monte Carlo simulations of photonic NOON-state phase sensing show the expected near-inverse decay of terminal infidelity with entangled shots, SQL-like total-resource scaling at fixed entanglement depth, the corresponding fixed-resource entanglement gain, the global limitation of a single fringe scale, and the recovery of Heisenberg-compatible behavior under ideal multiscale hand-off. These results identify SSML as a Fisher-preserving, self-certifying estimator layer for quantum-enhanced sensing.

We study the computational complexity of estimating the normalized trace $2^{-n}\mathrm{Tr}[f(A)]$ for a log-local Hamiltonian $A$ acting on $n$ qubits. This problem arises naturally in the DQC1 model, yet its complexity is only understood for a limited class of functions $f(x)$. We show that if $f(x)$ is a continuous function with approximate degree $\Omega(\mathrm{poly}(n))$, then estimating $2^{-n}\mathrm{Tr}[f(A)]$ up to constant additive error is DQC1-complete, under a technical condition on the polynomial approximation error of $f(x)$. This condition holds for a broad class of functions, including exponentials, trigonometric functions, logarithms, and inverse-type functions. We further prove that when $A$ is sparse, the classical query complexity of this problem is exponential in the approximate degree. Together, these results identify the approximate degree as the key parameter governing the complexity of normalized trace estimation: it characterizes both the quantum complexity (via efficient DQC1 algorithms) and the classical hardness, yielding an exponential quantum-classical separation. Our proof develops a unified framework that cleanly combines circuit-to-Hamiltonian constructions, periodic Jacobi operators, and tools from polynomial approximation theory, including the Chebyshev equioscillation theorem.

Topological phase transitions in generic multiband systems are mediated by band-touching defects whose codimension – the number of momentum directions along which the gap closes linearly – varies across universality classes. Although singular behavior of fidelity susceptibilities and quantum Fisher information (QFI) has been computed for specific models, no unifying principle connecting these results has been identified: it has remained unclear whether the controlling variable is spatial dimensionality, band structure, or an intrinsic geometric property of the defect. We resolve this question by showing that the singular contribution to the QFI with respect to the tuning parameter $m$ obeys a universal power-law scaling $\sim |m|^{p-2}$ for $p \neq 2$, with a logarithmic divergence $\sim \ln(1/|m|)$ at the marginal codimension $p = 2$, where $p$ denotes the codimension of the band-touching defect. This exponent is independent of spatial dimensionality, anisotropies, ultraviolet regularization, and additional gapped bands, and is protected by renormalization-group arguments at the linearized fixed point. The result unifies previously isolated observations for SSH chains ($p=1$), Chern insulators ($p=2$), and Weyl semimetals ($p=3$) as instances of a single codimension-dependent universality class, and reveals that only defects with $p \leq 2$ generate divergent information-geometric responses. This establishes a direct and previously missing link between topological classification in momentum space and quantum distinguishability in parameter space, with implications for metrological sensitivity near topological transitions and for the experimental detection of topological criticality via quantum geometric observables.

Let $G$ be a strongly regular graph of prime order $p$ with connection degree $k \geq 6$. We prove that the quantum walk characteristic polynomial $\chi_q(G,\lambda) \coloneqq \det(\lambda I - U_G)$, where $U_G$ is the coined quantum walk operator on $G$, completely determines $G$ up to isomorphism within the class of strongly regular graphs of the same order. The proof proceeds in three steps. First, we show that $U_G$ block-diagonalizes under the discrete Fourier transform over $\Z_p$, yielding $p$ blocks $U_G^{(j)}$ of size $k \times k$. Second, we prove an explicit formula \[ \chi_q\!\bigl(U_G^{(j)}, \lambda\bigr) = (\lambda-1)^{(k-2)/2}(\lambda+1)^{(k-2)/2} \!\left(\lambda^2 - \tfrac{2\widehat{A}_G(j)}{k}\,\lambda + 1\right), \] from which the Fourier coefficient $\widehat{A}_G(j)$ is recovered as the unique real part of an eigenvalue of $U_G^{(j)}$ distinct from $\pm 1$. Third, the inverse discrete Fourier transform recovers the connection set $S$ of $G$, and Turner's theorem (1967) identifies $G$ up to isomorphism. As a consequence, graph isomorphism is decidable in polynomial time within this class using the quantum walk spectrum, without resorting to the general quasi-polynomial algorithm of Babai (2016).

Characterising multi-time quantum processes is essential for analysing temporally correlated noise and for designing effective control and mitigation strategies. A complete operational description through multi-time process tomography requires an informationally complete set of probes, which necessarily includes non-deterministic intermediate operations. On present-day quantum devices, such operations are commonly implemented using mid-circuit measurements and reset, which are technologically limited and can introduce noise and overhead in terms of ancilla requirement. In this work, we study the minimal ancillary dimension required for complete characterisation of multi-time processes. We show that sequential interactions with a single qubit ancilla can generate an informationally complete family of correlated probes for processes of arbitrary length, without requiring mid-circuit measurements or reset. Our result provides a resource-efficient route for complete multi-time process tomography and establishes that one qubit of coherent ancillary memory suffices for full reconstruction of arbitrary multi-time dynamics.

We introduce a twisted fiber bundle construction of quantum CSS codes over group algebras \(R=\mathbb F_2[G]\), where each base generator carries a generator-dependent \(R\)-linear fiber twist satisfying a flatness condition. This construction extends the untwisted lifted product code, recovered when all twists are identities. We show that invertible twists (satisfying a flatness condition) give a complex chain-isomorphic to the untwisted one, so the resulting binary CSS codes have the same blocklength \(n\) and encoded dimension \(k\). In contrast, singular chain-compatible twists can lower boundary ranks and increase the number of logical qubits. Examples over \(R=\mathbb F_2[D_3]\) show that singular chain-compatible twists can increase the encoded dimension \(k\) at fixed blocklength \(n\), and in these finite examples the minimum distance \(d\) remains unchanged. This provides evidence that singular twisting enlarges the design space beyond the ordinary lifted product construction.

Large language models (LLMs) are increasingly explored for NP-hard combinatorial optimization problems, but most existing methods emphasize feasible-instance solution generation and do not explicitly address infeasibility detection. We propose an infeasibility-aware framework that combines certifiable dataset construction, supervised fine-tuning, and LLM-assisted downstream search. For the minor-embedding problem, we introduce a new mathematical programming formulation together with provable zero-phase infeasibility screening, which enables scalable construction of training instances labeled either as feasible with structured certificates or as certifiably infeasible. Using training data generated through this exact optimization pipeline, we show that an 8B-parameter LLM can be fine-tuned to jointly perform solution generation and infeasibility detection. We further utilize LLM outputs as warm starts for downstream local search, providing a practical way to accelerate optimization even when the LLM outputs are imperfect. Experiments show that our fine-tuned model improves overall accuracy by up to 30% over GPT-5.2; meanwhile LLM-guided warm starts provide up to $2\times$ speedup compared with starting from scratch in downstream local search.

Classical shadows (CS) has recently emerged as an important framework to efficiently predict properties of an unknown quantum state. A common strategy in CS protocols is to parametrize the basis in which one measures the state by a random group action; many examples of this have been proposed and studied on a case-by-case basis. In this work, we present a unified theory that allows us to simultaneously understand CS protocols based on sampling from general group representations, extending previous approaches that worked in simplified (multiplicity-free) settings. We identify a class of measurement bases which we call "centralizing bases" that allows us to analytically characterize and invert the measurement channel, minimizing classical post-processing costs. We complement this analysis by deriving general bounds on the sample-complexity necessary to obtain estimates of a given precision. Beyond its unification of previous CS protocols, our method allows us to readily generate new protocols based on other groups, or different representations of previously considered ones. For example, we characterize novel shadow protocols based on sampling from the spin and tensor representations of $\textsf{SU}(2)$, symmetric and orthogonal groups, and the exceptional Lie group $G_2$.

This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of which is known only to a single noisy intermediate-scale quantum (NISQ) computer. Each NISQ computer communicates with certain other quantum computers in the same row and column of the block partition, where the communication patterns are described by the row- and column-neighbor graphs, both of which are connected. The proposed algorithm integrates a variant of the variational quantum linear solver at each computer with distributed classical optimization techniques. The derivation of the quantum cost function provides insight into the design of the distributed algorithm. Numerical quantum simulations demonstrate that the proposed distributed quantum algorithm can solve linear systems whose size scales with the number of computers and is therefore not limited by the capacity of a single quantum computer.

Commutativity gadgets provide a technique for lifting classical reductions between constraint satisfaction problems to quantum-sound reductions between the corresponding nonlocal games. We develop a general framework for commutativity gadgets in the setting of quantum homomorphisms between finite relational structures. Building on the notion of quantum homomorphism spaces, we introduce a uniform notion of commutativity gadget capturing the finite-dimensional quantum, quantum approximate, and commuting-operator models. In the robust setting, we use the weighted-algebra formalism for approximate quantum homomorphisms to capture corresponding notions of robust commutativity gadgets. Our main results characterize both non-robust and robust commutativity gadgets purely in terms of quantum polymorphism spaces: in any model, existence of a commutativity gadget is equivalent to the collapse of the corresponding quantum polymorphisms to classical ones at arity $|A|^2$, and robust gadgets are characterized by stable commutativity of the appropriate weighted polymorphism algebra. We use this characterisation to show relations between the classes of commutativity gadget, notably that existence of a robust commutativity gadget is equivalent to the existence of a corresponding non-robust one. Finally, we prove that quantum polymorphisms of complete graphs $K_n$ have a very special structure, wherein the noncommutative behaviour only comes from the quantum permutation group $S_n^+$. Combining this with techniques from combinatorial group theory, we construct separations between commutativity-gadget classes: we exhibit a relational structure admitting a finite-dimensional commutativity gadget but no quantum approximate gadget, and, conditional on the existence of a non-hyperlinear group, a structure admitting a quantum approximate commutativity gadget but no commuting-operator gadget.

Resource estimation is a significant challenge in evaluating fault tolerant quantum computers. Existing approaches often rely on either fixed architectural assumptions or coarse analytical models that fail to capture the interaction between hardware constraints and circuit compilation. This challenge is particularly acute for neutral atom quantum computers, where architectural features such as atom movement, measurement zones, and multi-species arrays introduce a broad design space for implementing fault tolerant computation. Addressing the need for a tighter feedback loop between hardware design and practical application development, we present a compilation-driven framework for quantum resource estimation that translates arbitrary quantum circuits into logical primitive operations with known physical resource costs. This framework allows for easily configurable hardware assumptions that enable rapid comparison of different architectural design choices. We apply our approach to two early fault tolerant quantum simulation and optimization workloads, assuming the use of the surface code, revealing several architectural trends. While the production of magic states continues to be the dominant source of overhead for these benchmarks, access to movement can save time on cultivation and important transversal gates. As problem size grows, routing and qubit movement become dominant bottlenecks, highlighting the need for movement-aware compiler optimizations and frugal routing strategies. Finally, our results suggest that neutral atom architectures combining dual-species arrays with controlled qubit movement offer a promising path toward near-term advantage on fault tolerant devices.

General-purpose programmable photonic processors offer a flexible foundation for integrating various functionalities within a single chip. A two-dimensional hexagonal waveguide mesh of Mach Zehnder interferometers has been shown to have great potential in the field of microwave photonics. Additionally, they are a promising platform for the creation of unitary linear transformations, which are key elements in photonic neural networks, In this article, we expand the portfolio of available applications for recirculating bricks mesh architecture to quantum technologies. We will show that a single programmable optical system is capable of performing various functions depending on the requirements. In particular, we will focus in this work on boson sampling, a task that best demonstrates quantum advantage, as well as on tasks that enable the determination of photon indistinguishability, which plays a key role in photonic quantum technologies. We will also show that, in addition to spatial modes, the same optical system can be equally well-suited for work on temporal modes through the implementation of an appropriate number of loops.

We study algorithms for approximating the permanent of a random matrix when the entries are slightly biased away from zero. This question is motivated by the goal of understanding the classical complexity of linear optics and boson sampling (Aaronson and Arkhipov '11; Eldar and Mehraban '17). Barvinok's interpolation method enables efficient approximation of the permanent, provided one can establish a sufficiently large zero-free region for the polynomial $\mathrm{per}(zJ + W)$, where $J$ is the all-ones matrix and $W$ is a random matrix with independent mean-zero entries. We show that when the entries of $W$ are standard complex Gaussians, all zeros of the random polynomial $\mathrm{per}(zJ + W)$ lie within a disk of radius $\tilde{O}(n^{-1/3})$, which yields an approximation algorithm when the bias of the entries is $\tilde{\Omega}(n^{-1/3})$. Previously, there were no efficient algorithms at biases smaller than $1/\mathrm{polylog}(n)$, and it was unknown whether there typically exist zeros $z$ with $|z| \ge 1$. As a complementary result, we show that the bulk of the zeros, namely $(1 - \epsilon)n$ of them, have magnitude $\Theta(n^{-1/2})$. This prevents our interpolation method from contradicting the conjectured average-case hardness of approximating the permanent. We also establish analogous zero-free regions for the hardcore model on general graphs with complex vertex fugacities. In addition, we prove universality results establishing zero-free regions for random matrices $W$ with i.i.d. subexponential entries.

We construct a broad class of completely positive maps and Gorini-Kossakowski-Sudarshan-Lindblad generators for fermionic systems induced by linear transformations of system and environment modes. For these maps, we derive explicit Heisenberg-picture formulas for arbitrary normally ordered monomials in terms of minors of the underlying mode-transformation matrices and environment correlation tensors. We show that for even environment states the linear span of monomials up to any fixed order is invariant, which yields closed equations for low-order moments and makes their computation efficient. We also discuss the relation of this construction to second quantization of non-Hermitian one-particle contractions and extend the formalism to completely positive maps arising from post-selection.

We present an exact solution in the large-$N$ limit of the Lévy Sachdev-Ye-Kitaev (LSYK) model introduced in Ref. [1], wherein the couplings are drawn from a Lévy Stable distribution parameterized by a tail exponent $\mu \in [0, 2]$. Starting from the Hamiltonian and its associated partition function, we highlight the key differences from the standard Gaussian SYK model and derive the large-$N$ Schwinger-Dyson equations via a bosonic oscillator representation of the action. These equations are solved both numerically and analytically in the large-$q$ and infrared limits. We subsequently analyze the chaotic properties of the model by computing the Krylov exponent from the large-$q$ Green's function and extracting the Lyapunov exponent from the $4$-point function. The parameter $\mu$ continuously interpolates between a free theory at $\mu = 0$ and the conventional, maximally chaotic Gaussian SYK model at $\mu = 2$, with non-maximal chaos persisting throughout the intermediate regime $0 < \mu < 2$. Thermodynamic quantities, including the entropy, free energy, average energy, and specific heat capacity, are computed and compared with their Gaussian SYK counterparts. The interpretations of the thermodynamics are discussed with respect to the holographic dual and non-Fermi liquid theory. Finally, we discuss an alternative representation of the LSYK model based on a distinct decomposition of the Lévy Stable distribution, which establishes a non-trivial connection to Gaussian SYK, and provide supporting analytical and numerical results in the appendices.

Achieving fast, excitation-free quantum control is a vital challenge in modern quantum technologies. In many cases, shortcuts to adiabaticity enable fast adiabatic-like protocols, yet determining control parameters that satisfy practical constraints is often challenging in complex systems. Here, we combine an analytical shortcut to adiabaticity approach with several numerical optimization methods to boost the performance of the protocol. As a proof-of-principle for this hybrid approach, we study a particularly intricate control problem, the separation of two trapped ions. We show that this analytical-numerical approach, along with the physical insight gained through the variety of suboptimal solutions, leads to the exploration of new solutions in a complex landscape that yield improvements of up to 3 orders of magnitude. Moreover, this improvement comes with no additional cost from an experimental point of view.

Symmetries play a central role in quantum many-body physics, yet uncovering them systematically remains challenging. We introduce a bootstrap framework to reconstruct the representation theory of hidden finite group symmetries of quantum many-body lattice Hamiltonians, using only a known symmetry subgroup $N$ and spectral correlations between its sectors. We introduce the cross spectral form factor (xSFF) as a subgroup-resolved diagnostic of hidden symmetry, computed via exact diagonalization to seed the bootstrap. Applying constraints from these data alongside the algebraic conditions of the fusion rules, our bootstrap sharply restricts candidate groups $G$. Without prior assumptions about $G$, our method can systematically recover its representation-theoretic data, including the number and dimensions of irreducible representations, their branching rules with respect to $N$, the fusion algebra, and the full character table. This framework applies to chaotic and integrable systems and accommodates unitary and anti-unitary symmetries. Through examples, we demonstrate that $G$ can be uniquely identified. Our bootstrap recovers the $\mathbb{Z}_4$ symmetry at the self-dual point of the three-state quantum torus chain, detects signatures of projective representations in the effective Hamiltonian of the driven Bose-Hubbard model, and rediscovers the $\eta$-pairing $\mathrm{SO}(4)$ symmetry of the one-dimensional Fermi-Hubbard model. Leveraging the universal random-matrix ramp in chaotic systems, we demonstrate the possibility of ramp-only bootstrap alongside an example with hidden commuting symmetries. We establish the xSFF as a diagnostic for conserved order parameters in a symmetry-breaking spin-$1$ chain and introduce an ancilla-assisted measurement circuit for experimental realization. Our framework establishes a practical route to identify symmetries from dynamical spectral observables.

Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of a system so that it is described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond which Floquet heating sets in, as it results from unwanted driving induced resonant excitation. Moreover, the preparation of the ground state of such Floquet engineered effective Hamiltonians usually has to be accomplished adiabatically, which is another source of heating, especially when a phase transition has to be passed in a large system. Here, we propose a general dissipative strategy for the preparation and stabilization of effective ground states that are protected by an energy gap, such as topologically ordered states. It is scalable and relies on coupling the driven system to a thermal bath, the properties of which are chosen so that it both suppresses Floquet heating and guides the system into a non-equilibrium steady state with a large occupation of the effective ground-state. The small residual occupations of effective excited states are non-thermal, reflecting the non-equilibrium nature of the scheme. We use the Floquet-Born-Markov master equation to verify the proposed strategy. In particular, we discuss the preparation of both a one-dimensional Mott insulator and a two-dimensional fractional Chern insulator in strongly driven Bose-Hubbard systems.

We reveal a correspondence between temperature and integrability-breaking in classical and quantum many-body systems through the lens of geometry and adiabatic transformations. Decreasing the temperature, obtained in a standard way through the derivative of entropy with respect to energy, steers the system towards an integrable point despite strong integrability-breaking interactions. Auto-correlation functions of local observables exhibit slow relaxation dynamics, which violates ergodicity on the approach to this integrable point. Subsequently, the average fidelity susceptibility of stationary states satisfies scaling relations near the integrable point, in close analogy with continuous phase transitions. We further find that the dynamical exponent encompassing relaxation can be different in the quantum and classical models, depending on dimension of the systems. Collectively, our results establish temperature as a tunable control parameter for chaos and puts it on equal footing with integrability-breaking perturbations.

An important measure of utility for a quantum code is the identification of which logical operations can be implemented fault-tolerantly on its codespace. We introduce a framework which leverages the automorphism groups of associated classical codes, the choice of logical basis and exploitation of code equivalence to construct all distinct implementable realisations of each valid logical operation for a given $[[n,k,d]]$ code. We establish conjugacy classes and group transversals (unrelated to transversality) as key explanatory concepts. We subsequently motivate and calculate two figures-of-merit that can be optimised with this framework. Our results yield a table of optimal logical operations and their corresponding physical circuits for all small stabiliser codes with $n \leq 7$ and $k \leq 2$, drawn from quantum databases. This exhaustive table of results provides the optimal physical implementations of logical operations which may be advantageous for both magic state cultivation and experimental purposes.

Routing in wireless communication networks is shaped by mobility, interference, congestion, and competing service requirements, making route selection a high-dimensional constrained optimization problem rather than a simple shortest-path task. This paper investigates the use of hybrid classical–quantum methods for wireless routing, focusing on the Quantum Approximate Optimization Algorithm (QAOA) and quantum walks as candidate mechanisms for exploring complex routing spaces. The paper examines how wireless routing can be expressed as a constrained graph optimization problem in which routing objectives, flow constraints, connectivity requirements, and interference effects are mapped into quantum-compatible Hamiltonian representations. It then discusses how these approaches can be integrated into a hybrid architecture in which classical systems perform network monitoring, graph construction, pre-processing, and deployment, while quantum subroutines are used for selected optimization components. The analysis shows that the potential value of quantum routing lies primarily in the treatment of difficult combinatorial subproblems rather than end-to-end replacement of classical routing frameworks. The paper also highlights practical limitations arising from state preparation, constraint encoding, oracle construction, hardware noise, limited qubit resources, and hybrid execution overhead. It is argued that any meaningful near-term advantage will depend on careful problem decomposition, compact encoding, and tight classical–quantum integration.

The thermodynamic resourcefulness of quantum channels primarily depends on their underlying causal structure and their ability to generate quantum correlations. We quantify this interplay within the resource theory of athermality for bipartite quantum channels in the presence of a side channel acting as memory, referred to as the resource theory of conditional athermality. For channels with trivial output Hamiltonians, we characterize the optimal one-shot rates for distilling the identity gate from a given channel, as well as the cost of simulating the channel using the identity gate, under conditional Gibbs-preserving superchannels. We show that these rates have a direct trade-off relation with the conditional channel entropies, attributing operational significance to signaling in quantum processes. Furthermore, we establish an asymptotic equipartition property for the conditional channel min-entropy for classes of channels that are either tele-covariant or no-signaling from the non-conditioning input to the conditioning output. As a consequence, we demonstrate asymptotic reversibility of the resource theory for these channels. The asymptotic conditional athermality capacity of a tele-covariant channel is half the superdense coding capacity of its Choi state. Our work establishes the conditional channel entropy as a primitive information-theoretic concept for quantum processes, elucidating its potential for wider applications in quantum information science.

Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly sophisticated inference and adaptive design strategies, the signal family used for phase learning is often largely pre-specified. Here we propose a programmable signal design framework for quantum phase estimation based on quantum signal processing, which enables the measurement signal to be tailored to the current uncertainty region. We cast phase estimation as a max-min optimization problem over admissible signals and introduce a sensitivity efficiency parameter that quantifies information gain per query depth. The resulting iterative algorithm combines optimized quantum signal transformations with structured classical inference, retaining Heisenberg-limited scaling while improving sensitivity efficiency and practical resource prefactors. Numerical results show reduced estimation variance compared with standard protocols such as robust phase estimation. Our framework also extends to Hamiltonian eigenvalue estimation in higher dimensions and establishes a quantum-classical co-design paradigm through programmable signal shaping.

Learning quantum states from measurement data is a central problem in quantum information and computational complexity. In this work, we study the problem of learning to generate mixed states on a finite-dimensional lattice. Motivated by recent developments in mixed state phases of matter, we focus on arbitrary states in the trivial phase. A state belongs to the trivial phase if there exists a shallow preparation channel circuit under which local reversibility is preserved throughout the preparation. We prove that any mixed state in this class can be efficiently learned from measurement access alone. Specifically, given copies of an unknown trivial phase mixed state, our algorithm outputs a shallow local channel circuit that approximately generates this state in trace distance. The sample complexity and runtime are polynomial (or quasi-polynomial) in the number of qubits, assuming constant (or polylogarithmic) circuit depth and gate locality. Importantly, the learner is not given the original preparation circuit and relies only on its existence. Our results provide a structural foundation for quantum generative models based on shallow channel circuits. In the classical limit, our framework also inspires an efficient algorithm for classical diffusion models using only a polynomial overhead of training and generation.

We develop a rigorous and implementable framework for Gibbs sampling of infinite-dimensional quantum systems governed by unbounded Hamiltonians. Extending dissipative Gibbs samplers beyond finite dimensions raises fundamental obstacles, including ill-defined generators, the absence of spectral gaps on natural Banach spaces, and tensions between implementability and convergence guarantees. We overcome these issues by constructing KMS-symmetric quantum Markov semigroups on separable Hilbert spaces that are both well-posed and efficiently implementable on qubit hardware. Our generation theory is based on the abstract framework of Dirichlet forms, adapted here to the case of algebras of bounded operators over separable Hilbert spaces. Leveraging the spectral properties of our self-adjoint generators, we establish quantitative convergence results in trace distance, including regimes of fast thermalization. In contrast, we also identify Hamiltonians for which a naive choice of generators guaranteeing implementability generally comes at the cost of losing uniform exponential convergence guarantees for the associated evolutions, thereby establishing a strong trade-off between implementability and convergence. Our framework applies to a wide class of models - including Schrödinger operators, Gaussian systems, and Bose-Hubbard Hamiltonians - and provides a unified approach linking rigorous infinite-dimensional analysis with algorithmic Gibbs state preparation.