Papers

We introduce $Krylov$ $edge$ $spectroscopy$, a many-body operator-space protocol for detecting and classifying one-dimensional symmetry-protected topological phases from local boundary dynamics. A Hermitian boundary operator generates a semi-infinite Krylov hopping chain whose boundary weight obeys an exact zero-frequency normalizability criterion. Open-periodic, boundary-bulk, and symmetry-preserving boundary-perturbation tests identify protected boundary memory, while a finite-depth leakage residual certifies when an explicitly reconstructed operator is already near zero frequency. Classification minimizes the normalized commutator over symmetry-resolved boundary operators in fixed charge sectors. For bosonic $\mathbb{Z}_N \times \mathbb{Z}_N$ phases, the recovered endpoint charge gives the cohomology label. The method requires no explicit ground-state wavefunction, entanglement spectrum, or guessed dressed edge or string operator. For finite-range Hamiltonians, locality eliminates full-system exact diagonalization and guarantees thermodynamic-limit convergence at fixed Krylov depth. We demonstrate the protocol in cluster, clock, Haldane, and trivial spin-1 chains. In the exactly solvable cluster chain, the transition between the gapped topological and trivial phases manifests as a localization-delocalization transition of the Krylov edge mode on the Krylov chain. This transition occurs precisely at the bulk gap closing, and its localization-length exponent coincides with the Ising correlation-length exponent. Through operator Krylov dynamics, our work turns local boundary evolution into a direct spectroscopy of many-body topology.

Leakage, occurring when a qubit undetectably exits the computational subspace, poses a significant challenge for quantum error correction by inducing correlated errors in space and time. These correlations reduce both the code threshold and the effective code distance. To address this challenge, we introduce two zero-overhead walking circuits for the honeycomb Floquet code (hFC), termed the swirling and sliding circuits, which periodically remove leakage while dynamically protecting logical qubits via a schedule of anticommuting two-body measurements. Unlike previous dynamic circuits for the hFC, ours preserves the distance to Pauli errors. We further study their performance under leakage and find that, for two leakage noise models, they may correct as many leakage errors as Pauli errors, improving on the more widely known walking surface code. Through numerical simulation, we observe that finite-error-rate performance under leakage is strongly influenced by entropic effects, producing a pronounced waterfall regime in which the logical error rate decreases much more rapidly with physical error rate than the expected distance-limited scaling. In this regime, even when asymptotic predictions suggest otherwise, the hFC can outperform the same-distance walking surface code in error rates and sub-threshold logical error scaling.

We present an implementation of a conditional-squeezing gate that squeezes a SQUID-terminated resonator mode along a direction determined by the state of a dispersively coupled qubit. This gate generalizes the controlled-squeezing gate [Phys. Rev. A 111, 042606 (2025)], and relies on a refocusing technique to suppress unwanted effects arising from slowly varying time-dependent terms in the Hamiltonian during the state-dependent parametric resonance required for the operation. As an application, we use the gate to encode an arbitrary qubit state into superpositions of single- and two-mode squeezed states of the resonator. These non-Gaussian states enable error-detectable encoding through parity measurements. We show that refocusing substantially improves the encoding fidelity, which is ultimately limited by Kerr nonlinearities and dissipation in realistic implementations. For experimentally optimistic values of the nonlinearities and decay rates, we obtain encoding fidelities above 0.99 for arbitrary input qubit states. Our results provide a route toward extending this scheme to the generation of higher-order superpositions of squeezed states (a class of rotation-symmetric bosonic codes) using a control qudit.

We present a nonrecursive method to compute the small-time heat kernel asymptotic expansion. The Klein-Gordon operator in flat space-time coupled to electromagnetic fields is considered. We obtain closed-form expressions for the expansion coefficients up to the second order in time. Our approach can be regarded as an extension of the method described in [R.I. Nepomechie, Phys. Rev. D 31, 3291 (1985)], but unlike that work, our approach is valid for arbitrary space-time dependence of the heat kernel, i.e. for off-diagonal values. We verify that our results correctly reproduce small-time asymptotics of the heat kernel for a plane wave field and for constant electromagnetic fields.

Recent advances in topological phases have highlighted the role of symplectic (Krein-space) topology in the classification of bosonic Bogoliubov-de Gennes (BBdG) systems. In this work, we construct a BBdG realization of Hopf topology, which we dub the symplectic Hopf insulator, starting from a microscopic Bose-Hubbard generalization of the Moore-Ran-Wen model with weak on-site interactions treated within a Bogoliubov approximation. The resulting BBdG system admits a symplectic Hopf invariant, which we show to be integer-quantized for isolated bands. We establish that this topology is intrinsically delicate, requiring exactly two bosonic modes per unit cell, while remaining robust against weak interactions over a range of mass parameters. Upon terminating the three-dimensional insulator at a boundary, we find topologically protected in-gap surface states at finite excitation energy, whose protection is itself delicate. Our results establish the symplectic Hopf insulator as a robust yet delicate topological phase in weakly interacting bosonic systems lying beyond the tenfold-way classification.

Violations of Bell's inequalities offer a definitive signal of non-classical (quantum) behavior in local deterministic systems. Yet, in many physical settings where quantum mechanics is expected to play an important role, one cannot construct a Bell-type test using the available observables. Cosmology offers one concrete example, where cosmic structure may have originated from quantum vacuum fluctuations yet all observations are effectively classical. Nevertheless, recent work suggests that quantum and classical time evolution may still be differentiated by the pattern of statistical correlations of these observables. In this paper, we explore and generalize the use of correlations as Bell-type test of the nature of time evolution. We show that quantum vacuum fluctuations of closed systems undergoing Hamiltonian evolution produce unique correlations that are not mimicked by classical Hamiltonian systems. Correlations in the quantum vacuum are generally time-independent and are controlled by the energy gap between the ground and exited states. Classical systems exhibit apparent poles at physical frequencies that do not arise in the quantum vacuum. As one approaches the poles, the evolution becomes dominated by a resonant Hamiltonian giving rise to time dependent correlations that eventually decay through dephasing. Finally, we show that this behavior is distinct from other signals of quantum evolution, including applications to quantum optics, quantum walks, and quantum search.

We consider the general principles for when deterministic energy harvesting (DEH) is possible. DEH means absorbing energy from a fluctuating source without entropy being absorbed. We show that the symmetry structure of the source–harvester dynamics gives a general route beyond existing examples to identify DEH capable source states. Any continuous symmetry with a conserved Noether charge induces a source-side orbit of states that all implement the same deterministic harvester transition, provided the harvester boundary states are symmetry invariant. Consequently, one DEH capable source state with nonzero asymmetry between charge sectors can generate infinitely many simultaneously DEH capable source states. A Jaynes-Cummings model, a three-spin XX chain, and an SU(2) model illustrate the construction. We further extend Noether's theorem to generalised probabilistic theories and thereby generalise our main result. We further establish an asymmetry bound for harvesting, showing that source asymmetry cannot increase on average, while DEH saturates the bound exactly preserving asymmetry.

Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.

We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples. For sufficiently small $\varepsilon$, estimating an unknown state on $\mathbb{C}^d$ of rank at most $r$ to trace norm error $\varepsilon$ with constant success probability requires, and is achievable with, $$\Theta\left(\frac{dr}{\varepsilon^2}\mathop{\mathrm{max}}\left\{1,\frac{r}{\sqrt{t}}\right\}\right)$$ samples. The lower bound allows the protocol to choose each joint measurement adaptively using all previous classical outcomes; the matching upper bound is nonadaptive. Thus joint measurements on at most $t$ samples improve the complexity of algorithms making single-sample measurements by at most a factor $\sqrt{t}$. Further, measuring order $r^2$ samples jointly is necessary and sufficient to attain the unrestricted collective rate. For the lower bound, we vary the support of a state with fixed uniform spectrum and bound the Fisher information trace of every joint measurement on $t$ samples. The adaptive Fisher chain rule and the van Trees inequality then give the trace norm lower bound. For the upper bound, we construct and analyze a nonadaptive tomography protocol based on a Gaussian joint measurement. An explicit second moment identity and a conditional Gaussian law outside the state's support give a rank-dependent error analysis, yielding the matching rate.

In a quantum walk, the first-detection return probability (FDRP) characterizes salient features, determining whether the quantum walk is transient or recurrent. We study the FDRP of quantum walks on a chain where the initial site is stroboscopically monitored by a detector and the walker performs long-range hopping between sites. We assume that the hopping strength decays with the distance $d$ as $d^{-\alpha}$ and $\alpha\geq 0$ and show that the power-law exponent $\alpha$ critically determines the behavior of the FDRP. The value $\alpha=1$ separates recurrent ($\alpha<1$) from transient ($\alpha>1$) quantum walks through a continuous phase transition in the total detection probability. For $\alpha<1$, strong long-range hopping induces localization, resulting in unit total detection probability. Instead, for $\alpha>1$ the long-range walk is transient and the return probability decays algebraically as a function of time as $t^{-\beta}$. The associated decay exponent $\beta$ features nonanalytic points as a function of $\alpha$. Such singularities are not exclusively determined by the low-energy spectrum, but are caused by the interference between infrared and ultraviolet energy modes induced by projective measurements, signalling the emergence of critical behavior intrinsic to the non-unitary dynamics. These dynamics are solely controlled by tuning the long-range exponent $\alpha$ and can thus be experimentally probed in atomic and molecular systems.

Information causality (IC) was introduced as a physical principle constraining correlations in non-signaling theories. Whether it can recover the exact quantum correlation boundary, beyond Uffink's inequality, has remained an open question. Here, we combine its generalized formulation for correlated inputs with a new communication protocol to derive quantum Bell inequalities that exactly characterize the quantum correlations in the simplest bipartite Bell scenario, with two binary measurements. In particular, we derive the Tsirelson-Landau-Masanes criterion directly from IC. Thus, the generalized IC implies macroscopic locality, while we also present macroscopically local correlations that violate the generalized IC. This establishes that generalized IC is a strictly stronger principle in this scenario. Together with our earlier result that generalized IC implies a nontrivial communication complexity principle, these findings strengthen the role of information causality in explaining the limits of quantum nonlocality and provide a systematic route to deriving tighter bounds on the set of quantum correlations in more general Bell scenarios.

Credit default prediction is a tabular classification problem in which modest gains in F1 translate directly into reduced financial exposure. We ask whether Instantaneous Quantum Polynomial-time (IQP) circuits can produce features that improve a classifier over both its raw classical baseline and Kernel PCA - the strongest unsupervised classical non-linear alternative - at an equal feature budget. The dataset provides 23 financial attributes per client; for an n-qubit circuit we select n of them, encode each as a rotation angle, and read 2n expectation values back out as new features. The motivation for using a quantum circuit is computational: an n-qubit IQP circuit runs in constant depth and encodes feature correlations in a 2^n-dimensional Hilbert space, whereas classical simulation of its exact output statistics scales exponentially in n. Using the UCI Default of Credit Card Clients dataset and five-fold cross-validation, we find that appending 16 IQP features (n = 8 qubits) to a Logistic Regression model raises F1 from 0.462 to 0.517 (+0.055, p < 0.0001). Kernel PCA, the next-best method, reaches only 0.493 at the same feature count; the gap survives Benjamini-Hochberg correction across 12 tests (p = 0.00007). No other classifier - Random Forest, SVM, XGBoost, or k-NN - benefits, which points to a linear-expressivity mechanism rather than a generic improvement. We also show that how the 8 input features are chosen matters: Random Forest importance-guided selection reaches F1 = 0.523, while encoding maximally uncorrelated features drops it to 0.496, demonstrating that the circuit amplifies informative structure rather than creating it from scratch.

Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.

Understanding symmetry restoration in isolated quantum many-body systems is an important problem in nonequilibrium many-body quantum physics. Recent studies have shown that the quantum Mpemba effect can be characterized through entanglement asymmetry, where states with stronger initial symmetry breaking restore symmetry faster. However, it remains unclear whether conventional energy-based measures, such as the trace distance, capture the same phenomenon. We investigate this question in closed spin-$1/2$ quantum systems with different symmetries by analyzing the dynamics of symmetry-breaking initial states. Combining numerical simulations with an analytical decomposition of the trace distance into symmetry-coherence and residual contributions, we identify the conditions under which trace distance tracks entanglement asymmetry and reproduces the Mpemba–like behavior observed in it. For charge symmetry, the residual contribution is negligible, making the trace distance effectively governed by symmetry-sector coherences. In contrast, for permutation symmetry, a significant residual contribution leads to qualitatively different relaxation dynamics. Our results establish when conventional energy-based diagnostics reliably capture symmetry-restoration dynamics and clarify the distinct physical information encoded by entanglement asymmetry and trace distance.

The rising energy consumption of AI has generated interest in physical systems as alternative substrates for trainable computation. Recent experimental advances have enabled precise control over the couplings between molecular chromophores, which give rise to coherent excitation dynamics. Here, we study driven-dissipative excitonic networks as a computational platform, where the intersite couplings define the input and the steady state defines the output. We show that coherence enables computational expressivity to scale with network size, analogous to artificial neural networks. Both this scaling and the overall expressivity are suppressed by strong dephasing. Our work establishes coherence as a resource for expressive computation in nonequilibrium quantum systems.

Quantum walks are the quantum analogues of classical random walks or Markov chains. They are universal models of quantum computing, and they underpin a variety of quantum algorithms. We prove that a continuous-time quantum walk effected by a generalized Laplacian, which can arise in spin chains, can solve a computational problem more quickly than typical quantum walks governed by the standard Laplacian or adjacency matrix. This generalized Laplacian consists of the standard Laplacian plus a real-valued multiple of the degree matrix, and we prove that as the magnitude of the multiple of the degree matrix is increased, its corresponding quantum walk can search the complete bipartite graph with multiple marked vertices in time that approaches the optimal. This raises the potential for the generalized Laplacian quantum walk to be a useful method for developing additional faster quantum algorithms.

We prove the sharp Hausdorff–Young inequality on the quantum Euclidean space. Our result implies the sharp Hausdorff–Young constants for the Weyl transform, as well as that for Heisenberg groups. The key ingredient is a novel flow related to the mixed-norm of noncommutative Gabor transform. This, meanwhile, implies a new proof of the classical sharp Hausdorff–Young inequality. We then apply the sharp Hausdorff–Young inequality to establish the sharp Young inequality for noncommutative convolution in the range $1\le p,q\le2\le r\le\infty$, with $1/p+1/q=1+1/r$. After appropriate rescaling and trace normalization, this convolution coincides with beam-splitter convolution for bosonic systems, yielding the corresponding Young inequalities with optimal constants in the same range.

Reliable and scalable readout strategies are essential for quantum technologies. As quantum processors grow, extracting useful information must remain feasible without measurement circuits becoming a dominant bottleneck. Randomized measurements and classical shadows provide a powerful route, but global estimation is conventionally associated with highly random ensembles that require increasing circuit depth and hence substantial experimental overhead. In this work, we show that substantially less randomness suffices when the readout is meaningfully adapted to the quantities being estimated. We introduce shallow phase shadows, based on a sparse Clifford-IQP ensemble, and prove efficient global estimation of stabilizer-state fidelities despite the ensemble not forming an approximate relative-error design. On all-to-all architectures, the protocol admits a constant-depth implementation using mid-circuit measurements and classical feedforward, or logarithmic depth without auxiliary systems. The protocol requires only controlled-phase entangling gates and offers a tunable trade-off between circuit resources and estimation accuracy, making it particularly amenable to experimentally relevant architectures with long-range connectivity. Our results show that scalable quantum readout need not reproduce generic randomness: task-adapted randomization can enable substantially shallower global characterization protocols.

We provide a unified analysis of scalar-field quantization and detector response in relativistic rotating frames, comparing rigid and Trocheris-Takeno (TT) descriptions in unbounded Minkowski spacetime. We distinguish three questions that are often conflated: (i) how a fixed quantum state is represented in rotating coordinates, (ii) whether rotating time evolution selects a global ground state, and (iii) how a rotating detector responds to the vacuum. Coordinate-transformed rigid and TT modes span the same positive-frequency subspace as inertial modes: their Bogoliubov beta coefficients vanish and their mode sums reproduce the Minkowski Wightman function. Neither rotating time flow selects a global scalar ground state, although for different reasons: the rigid generator is not globally timelike and is unbounded below, whereas TT time translation is not a Killing symmetry. Nevertheless, a circular Unruh-DeWitt detector in the Minkowski vacuum has a stationary, nonzero response. We relate this response to negative corotating frequencies, evaluate it after an explicit Hadamard subtraction, and show that it is nonthermal. Thus vanishing Bogoliubov mixing, the absence of a symmetry-selected rotating vacuum, and detector excitation are mutually consistent.

Since neutrinos are quantum systems inherently, the precision with which oscillation parameters can be estimated ultimately depends on how much information about these parameters is encoded in the neutrino state and how efficiently that information can be extracted through measurement. In this work, we quantify how information encoded in reactor antineutrino states flows through the measurement process to the events observed at the detector, using quantum and classical Fisher information. We establish the information ladder for JUNO, revealing that the loss of precision across different information levels is strongly parameter dependent. We demonstrate that the JUNO configuration approaches the optimal statistical limit for the oscillation parameters of the solar sector, while information on $\theta_{13}$ and $\Delta m_{31}^{2}$ is significantly degraded by the measurement strategy and detector effects. Despite this information loss, the remaining information is sufficient for JUNO to achieve sub-percent precision on $\Delta m_{31}^{2}$ within six years.

The critical phase of a non-Hermitian quasicrystal can support stronger transport than its surrounding delocalized phase. We demonstrate this anomalous behavior in the one-dimensional nonreciprocal Aubry-André-Harper model through a combined study of dynamical quantum phase transitions (DQPTs) and wavepacket diffusion. Using a parity-sorted energy-spectrum classification that directly encodes the generalized $\mathcal{PT}$ symmetry, we find that DQPTs in this system are energy-resolved, in contrast to the energy-independent DQPTs of Hermitian quasicrystals. The energy-resolved features are most pronounced when the initial and final Hamiltonians belong to different phases (localized or extended), and they are tied to the even-odd index structure of the spectrum, which we exploit to organize the quench-dynamical landscape. For wavepacket dynamics after a single-site quench, the diffusion exponent $\beta$, extracted from the long-time power-law scaling of the root-mean-square displacement $\sigma(\tau)$, partitions the phase diagram into four distinct regimes. In the Hermitian limit the extended phase is ballistic ($\beta=1$), the critical phase is normally diffusive ($\beta=0.5$), and the localized phase yields $\beta\to 0$. Nonreciprocity reverses this hierarchy: the extended phase becomes normally diffusive, while the critical phase turns ballistic. We trace the anomalous $\beta=1$ at criticality to the self-similar multifractal structure of the critical eigenstates, whose nodal positions are organized by the golden ratio. A finite-size scaling ansatz built on the wave-front propagation yields $\sigma(\tau)\propto\tau$. The parity-resolved DQPTs and the $\beta$-phase diagram establish two complementary dynamical diagnostics of nonreciprocal quasicrystals, in which nonreciprocity promotes transport at the critical point and suppresses it in the delocalized phase.

Probabilistic photonic sources generate elementary states in different trials, whereas multiphoton protocols require them to interfere in common temporal modes. We propose a fusion protocol that overcomes this mismatch by successively loading independently heralded photonic states into active storage loops. Conditioning on vacuum in monitored dump modes selects events in which each newly generated state is transferred into the same circulating modes as the photons already stored, thereby removing its generation time label. Provided the two alternatives of each elementary state undergo the same loading transformation, the accumulated state is described by a product of programmable linear factors, allowing a target superposition to be constructed by polynomial factorization. Adjusting the storage loop coupling as the state grows substantially improves the loading efficiency, changing the faster-than-exponential penalty of fixed balanced couplers to exponential scaling. We apply the protocol to two-photon path–frequency states for photonic clock interferometry and estimate the detected rate including source waiting time and round-trip loss.

We study the relative power of public randomness and quantum communication in the multiparty Simultaneous Message Passing (SMP) model. By analyzing a total Boolean function and a relational problem, we establish polynomial and exponential separations between classical public-coin protocols and quantum protocols without shared randomness or prior entanglement. We first introduce XOR Equality, a total Boolean function in which each of $k$ players receives an unrestricted string $x_j\in\{0,1\}^n$, and the referee must decide whether $x_1\oplus\cdots\oplus x_k=0^n$. For $k\ge8$ and worst-case error at most $1/3$, we prove quantum lower bounds of $\Omega(\min\{n,k^2\})$ on total communication and $\Omega(\min\{n/k,k\})$ on maximum message length. A classical public-coin protocol uses two bits per player with error at most $1/4$. For $n=k^2$ and worst-case error at most $1/3$, we prove that quantum protocols require maximum message length $\Omega(\sqrt n)$ qubits, whereas two public-coin bits per player suffice. We then turn to relations, for which we obtain exponential separations. Specifically, we study Multiparty Index Coordination, a $k$-player generalization of the two-player relation studied by Gavinsky, Kempe, Regev, and de Wolf (STOC 2006). We prove an unambiguous quantum lower bound of $\Omega(n^{1-1/k})$ on maximum message length, matched by a classical private-coin protocol. For any fixed error $\varepsilon\in(0,1/8)$, we also prove a bounded-error quantum lower bound of $\Omega(n^{(k-1)/(k+1)})$ while we show that public-coin protocols solve the relation unambiguously with maximum message length $O(\log n)$, giving exponential separations in both regimes. The implicit constants are independent of $k$, and both quantum lower bounds become linear when $k\ge c\log n$ for any fixed $c>0$.

We present a quantum algorithm for solving partial differential equations through a linear-system formulation, focusing on wave propagation problems described by the discretized Helmholtz equation in frequency domain. Although quantum linear-system solvers offer exponential compression of the system degrees of freedom, their runtime complexity is generally governed by the condition number of the discretized operator. Exploiting the analytic structure of the differential operator can provide an alternative to explicit matrix inversion, as illustrated for the screened Poisson equation through an explicit quantum circuit. For the Helmholtz equation, however, the inverse operator becomes singular on the dispersion surface $k^2=\omega^2/c^2$, rendering direct Fourier-space state-preparation methods exponentially inefficient. We address this challenge by directly preparing quantum states supported on the resonant manifold and encoding source locations through Fourier phases. The resulting algorithm eliminates the exponentially large overhead associated with post-selection on the resonant manifold, yielding a success probability that depends linearly on the number of sources and is independent of the computational domain size. More generally, our approach applies to hyperbolic differential equations whose Fourier-space solutions possess singular support on dispersion manifolds, recasting their solution as a problem of geometric quantum state preparation.

We present and analyze an iterative refinement (IR) framework for improving the precision dependence of algorithms that combine a quantum linear system algorithm (QLSA) with quantum state tomography. Existing QLSAs achieve polylogarithmic dependence on the inverse error tolerance to prepare a quantum state encoding the solution, but extracting a classical description of such a state via tomography typically introduces a polynomial dependence on the target precision. To retain polylogarithmic dependence in the inverse error tolerance throughout the entire process, we develop an IR scheme that solves a sequence of related linear systems to progressively refine the solution while requiring only fixed-precision quantum subroutines, finally obtaining a classical description of a high-precision solution. We analyze the proposed framework under three input models: quantum-read/classical-write RAM (QRAM), linear combinations of unitaries (LCU), and sparse-access oracles. We evaluate the proposed scheme through numerical experiments on both quantum simulators and real quantum hardware. The results demonstrate that iterative refinement efficiently improves the precision of the solution and exhibits robustness to hardware noise.

Our central premise is that quantum mechanics may be the statistical limit of a more fundamental discrete theory: any such theory equips a physical system with a finite information capacity, and its departure from quantum statistics is controlled by how much of that capacity the system uses. We show that commercial cloud photonic quantum processors have reached the precision required to bound this capacity from below, using the binary-sequence model of Powers et al. as the concrete test theory: outcome probabilities arise from counting discrete sequences of length $n$, quantum mechanics is recovered as $n \to \infty$, and $n$ measures the information capacity of the register behind a prepared state. Photon Fock states $|1\rangle$, $|1,1\rangle$, heralded $|2\rangle$, and cascaded beam-splitter pairs are measured on programmable interferometers with dominant systematics determined in situ. The model's composition-consistent parametrization, singled out by requiring that rotations compose, recovers quantum mechanics with deviations $1.24/n$; a random-effects likelihood analysis calibrated by parametric bootstrap excludes all $n \le 100$: the information capacity of the register carrying the two-photon state, if finite, exceeds $10^2$. Cascaded beam splitters test the composition law directly: the data are split-invariant, excluding naive count composition at $8\sigma$ and confirming the interference-sign rule. Model-independently, curve-averaged deviations from the quantum partition law larger than $2.3\times10^{-2}$ are excluded at 95% CL, and the originally published linear parametrization is excluded outright. Because the compilation offset is frozen per circuit it is calibratable, opening the $10^{-3}$ floor ($n \sim 10^3$) to current hardware: cloud photonic processors are quantitative instruments for quantum foundations, and information capacity an experimentally boundable quantity.

Thermodynamics is useful because it lets us predict and control complex systems from a few accessible quantities when microscopic reconstruction is impractical. We ask whether this operational reduction can be less costly in a finite quantum system than in a matched classical one. We compare a few-boson Bose–Hubbard chain with its number-conserving classical-field counterpart under the same driving and the same coarse spatial record. The quantum system relaxes more in the observed particle distribution, yet the retained mean energy resolves more of the microscopic structure hidden by that record, leaving less information unusable and smaller entropy generation. We then close the process into a heat-engine cycle whose controls use only the measured mean energy and spatial record, not full state tomography; at matched thermal resources, the smaller entropy generation gives more work and higher efficiency. The advantage fades as the particle number grows toward the classical-field regime.

We present a pedagogical showcase of BRST quantization for restoring symmetries in nuclear many-body systems as a reformulation and potential alternative to conventional projection methods. The formalism is illustrated using translational invariance for a simple system of two interacting masses in one dimension, but with an eye toward generalizing to more particles, higher dimensions, and other symmetries. We explain the considerations underlying particular choices within the BRST construction, and develop both Hamiltonian and path integral formulations to provide guidance for the variety of many-body and effective field theory contexts where gauge fixing for symmetry restoration might be useful. For the demonstration system we show how to diagonalize within the extended BRST phase space, how variation after projection is recovered for product reference states, how the corresponding gauge-fixed functional integral is constructed, and how collective zero modes are isolated and controlled. Throughout, we keep in mind extensions of BRST symmetry to various approximation schemes as a guide for consistent symmetry restoration.

Certifying a quantum bound can require more information than realizing the correlations that attain it. We show that this distinction becomes unbounded when a proof must condition on one party's measurement question. A fixed Bell scenario attained by one entangled qubit pair has a standard degree-two sum-of-squares certificate, yet the minimum degree in either conditioning direction grows as the inverse square root of the distance to a local endpoint. Choosing the better party does not remove this cost. The obstruction also survives approximate certification: bounding the quantum maximum to any fixed fractional accuracy relative to its Bell advantage requires the same diverging level. Thus a short standard proof cannot be transferred to a uniformly bounded conditioned level, even after relaxing exactness and optimising the direction. Mixing directions within a proof removes this family's obstruction, while a separate finite separation establishes its limits. Contact geometry explains the cost and connects it to a sharp precision law for randomness certification.

We propose a quantum version of the Barankin bound as an alternative to the quantum Cramér-Rao bound for quantum parameter estimation. The quantum Barankin bound provides a lower bound on the mean squared error of estimators satisfying arbitrarily chosen bias constraints at arbitrarily chosen parameter points. In particular, unbiasedness over the entire parameter space can be imposed, yielding precision limits for globally unbiased quantum parameter estimation. In contrast to the recently derived quantum Barankin bound, which is based on a symmetric division superoperator, our bound is based on a nonsymmetric right-division superoperator. This formulation enables us to find analytic expressions for the Barankin matrix for Gaussian states, which allows for an efficient calculation of the bound. We demonstrate the usefulness of our results by applying them to various examples that exhibit the threshold effect in the few-shot regime, which is invisible to the standard quantum Cramér-Rao bound approach.