Neutral-atom arrays are a leading qubit technology for large-scale, fault-tolerant quantum computing (FTQC). A dominant error source on this platform is qubit loss, which accrues with every operation and movement. The presence of loss undermines the promises of existing architectural work. Standard error correction targets stochastic Pauli errors and cannot correct loss, so most FTQC performance analyses are not directly compatible with it. Moreover, compilation and routing decisions, which strongly affect overall loss, are typically optimized against Pauli-error cost models and often remain loss-agnostic, potentially increasing exposure to the loss channel. In this work, we comprehensively model the effect of qubit loss on neutral-atom FTQC and develop a loss-tolerant transversal-gate architecture. We treat loss not as a predetermined error parameter but as a dynamic budget spent across a whole program, allowing us to control it by co-designing layout, compilation, and decoding. We target a physical implementation with no separate storage and entangling zones, eliminating the repeated SLM-AOD handoffs and long-distance shuttling that dominate loss in other layouts. We develop compiler optimizations that maximize gate parallelism while respecting the RF tone budget and AOD bandwidth constraints. Our work couples these with a loss-aware, delayed-erasure decoder and an end-to-end loss-aware magic state cultivation protocol. Overall, we improve accumulated loss per syndrome-extraction round by up to 2.15X against a zoned baseline and reduce logical error rates by over two orders of magnitude versus current architectures. Our framework also informs concrete device targets such as continuous reloading rates, AOD counts, and shuttling trajectory choices. We expect these insights to matter for system architects as neutral-atom hardware scales.
Quantum channel discrimination is a primitive task for identifying, verifying, and benchmarking quantum dynamics. Previous studies have primarily considered either the best-case tester-input setting or the worst-case jammer-input setting. Here, we introduce a game-theoretic framework in which both the tester and jammer control separate inputs. Combining three input structures, characterized by whether the tester and jammer use entangled inputs or IID inputs across channel uses, with four information patterns, determined by the visibility of the jammer's strategy and its knowledge of the true hypothesis, yields twelve game models. We provide exact finite blocklength hypothesis testing characterizations of all twelve models in terms of nine minimax hypothesis testing divergences and derive their asymptotic Stein exponents. Notably, for entangled jammers, neither the visibility of the jammer's strategy nor its knowledge of the true hypothesis affects the asymptotic Stein exponent, whereas the information pattern remains consequential for IID jammers. As an example, we study the discrimination of a general channel from a replacer channel and show that all asymptotic Stein exponents coincide with the same additive, single letter quantity. We further develop a general argument that upgrades achievability results to strong converse results, thereby establishing strong converse properties for several game models, resolving an open problem in composite hypothesis testing posed by Berta et al. [Commun. Math. Phys. 385, 55 (2021)], and strengthening several recent results of Lami [arXiv:2510.06340]. The framework and techniques developed here may support future studies of quantum information tasks involving competing roles.
The Holevo barycenter of a quantum channel is the unique output state obtained as the average output of any ensemble achieving the Holevo capacity. Given two quantum channels, the multiplicativity problem asks whether this barycenter tensorizes under parallel composition, namely whether the barycenter of the product channel coincides with the tensor product of the individual barycenters. This question is closely related to the additivity problem for the Holevo capacity: additivity implies tensorization of the Holevo barycenter, while tensorization alone is not sufficient for additivity. Although a construction is known that demonstrates the existence of channels with non-additive Holevo capacity, their corresponding Holevo barycenters still tensorize, leaving open whether multiplicativity might ultimately hold universally. Here, we answer this question in the negative by exhibiting channels for which the Holevo barycenter is not multiplicative under the tensor product of the channel with itself. Moreover, we show that the entropy of the Holevo barycenter is neither universally subadditive nor universally superadditive under tensor product.
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.
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.
Quantum low-density parity-check (QLDPC) codes represent a promising approach for error correction in quantum computing. The recently proposed Tesseract decoder uses the A* search algorithm that guarantees finding the most likely error pattern. However, practical implementations of Tesseract often involve an extremely large graph, and the inherently sequential nature of the search results in high computational overhead and long runtime. To improve decoding efficiency, we propose a two-stage decoding framework. First, a belief propagation (BP) decoder efficiently processes the syndrome. This step generates hard decisions (a binary error vector) and soft information (per-qubit confidence levels). In non-convergent BP cases, a gating mechanism examines the BP decoder's output to identify and filter out qubits with oscillating confidence values. In these cases, the refined output serves as input to Tesseract, which then attempts to identify and correct any residual errors. This hybrid approach leverages the high speed of BP decoding and delegates the more challenging decoding instances to Tesseract. Numerical results demonstrate a substantial reduction in overall decoding complexity while maintaining the logical error rate (LER) of the stand-alone Tesseract. Across all tested physical error rates, the proposed method achieves at least 5x reduction in the number of expanded nodes in the Tesseract, with a peak reduction of nearly 15x at a physical error rate of p = 0.05 for the [[126, 12, d < 11]] T1 code, and approximately 8.8x at p = 0.05 for the [[72, 12, 6]] bicycle bivariate (BB) code.
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, $$ \Theta\left( \fracdr\varepsilon^2 \max\left{1,\frac r\sqrt t\right} \right)$$ 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.
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 how thermal fluctuations modify or suppress quantum-enhanced sensing is a central problem in quantum metrology. Closely related questions arise in quantum thermodynamics, particularly regarding the relation between the work induced by a signal and the information acquired by a sensor. Here, we establish general relations among the sensitivity of thermal quantum states, as quantified by different quantum Fisher information metrics, their temperature dependence, and the work induced by a unitary signal. We further show that, at high temperature, all monotone QFI metrics coincide to leading order with a universal quantity that can be expressed as the variance of a simple observable and itself defines a lesser-known QFI metric. This emergent uniqueness is reminiscent of the uniqueness of classical Fisher information in information geometry. In continuous-variable systems, the infinite-temperature limit is finite and generically non-zero for quadratic Gaussian signals, while it diverges for higher-degree signals. Remarkably, for any purely quadratic signal generator, the infinite-temperature QFI is at least twice the zero-temperature SLD QFI or, equivalently, at least eight times the ground-state variance of the generator. Consequently, the Cramér--Rao lower bound on the estimator variance is reduced by at least a factor of two. We illustrate these results using harmonic chains of bosonic modes relevant to trapped-ion platforms and quantum field-theoretic models.
Fermionic quantum cellular automata (QCA) are automorphisms of local fermionic operator algebras ($\mathbb Z_2$-graded superalgebras) that have bounded spread: they map local operators to nearby operators. We prove that every 2-dimensional fermionic QCA on a locally finite-dimensional algebra is a composition of local automorphisms and a fermionic shift. This is implied by our result that every locally finite-dimensional fermionic invertible subalgebra in a one-dimensional lattice is Brauer trivial, \textiti.e., it is stably bounded-spread isomorphic to a tensor product fermionic algebra.
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 study thermodynamic state transformations in the resource theory of work and heat when the initial quantum state is unknown. Moving beyond state-dependent protocols, we develop a universal framework in which a single transformation applies to all admissible input states. For mutually commuting conserved charges, we construct charge-conserving protocols whose transformation error, quantified by trace distance, decays super-polynomially with the number of system copies. As an application, we demonstrate universal work extraction: asymptotically optimal work can be extracted without microscopic knowledge of the initial state, with a super-polynomially small error. Our results show that thermodynamic state transformations remain achievable under limited prior information and establish a universal framework for resource-theoretic thermodynamics beyond the state-aware setting.
Quantics tensor trains are attracting intense interest for quantum-inspired computing and quantum state preparation. These methods, which approximate continuum functions by representing their amplitude encoding as a matrix product state (MPS), are exceedingly powerful for univariate functions but rapidly become challenging when handling multivariate functions, since the linear chain topology leads to a large distance between highly-entangled qubits. We overcome this limitation by introducing SCENT (Spectral Clustering for Entanglement miNimizing Trees). SCENT is a protocol that utilizes efficiently-computable pairwise entanglement metrics to determine a suitable tree tensor network (TTN) structure, which can then be efficiently approximated using tensor cross-interpolation (TCI); we find that it substantially outperforms MPS methods and improves upon previous TTN methods. We then apply these optimized TTNs to state preparation, introducing an approximate circuit compilation method based on environment-tensor methods without significantly conceding overall accuracy. Importantly, the inherent gauge freedom of TTNs can be directly exploited in this method, resulting in higher fidelity at a given circuit depth. We demonstrate this quantum state-preparation pipeline on archetypal state-preparation problems in quantum chemistry and financial portfolio optimization. In our flagship demonstration, we encode a 20-variable probability distribution with long-ranged, non-nearest neighbor inter-variable correlations in a 200-qubit state-preparation circuit with infidelity $7.44\times 10^{-9}$ using only 43284 CNOTs; depth and fidelity can be traded, allowing the same distribution to be prepared to infidelity $10^{-3}$ with as few as 5584 CNOTs.
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.
Magic-state cultivation has so far focused mainly on single-qubit non-Clifford resources. We develop a direct cultivation architecture for the entangled state $|CS\rangle=CS|++\rangle$. Two commuting Clifford involutions project onto four usable branches related by Pauli-frame updates. A minimal six-bit $[6,2,4]$ record protects the branch label against readout errors that map one valid record to another. Verified CAT$_7$ gadgets, Steane error detection, CZZ-based controlled checks, and immediate Steane-to-surface expansion form the complete factory. The decoder uses 263 operational detector bits, while 168 additional bits are withheld for later validation. Decoding proceeds through exact low-order resolution, a precomputed higher-order catalogue, and four-coset BP+OSD. Under the stated active-location stochastic-Pauli model, exact enumeration finds no accepted closed-boundary logical-failure mechanism through fault order two, while explicit order-three failure mechanisms exist. Finite-$p$ simulations quantify acceptance, residual syndromes, and decoder workload, and targeted sampling of order-three faults estimates the leading logical-error channels. Optimizing the direct $d=5\rightarrow13$ expansion reduces accepted-output operation count by approximately 35--37\%. We compare the two routes at the same binary logical-error rate. Direct CS remains cheaper in operation count at the two lower-noise benchmark points even when the three-$T$ route is given pre-existing output patches. The ordering reverses between $8\times10^{-4}$ and $9\times10^{-4}$. These results show that an entangled non-Clifford state can be cultivated directly with a protected branch record and an explicitly certified fault-order-three output channel.
Quantum states generated by generic time evolution are locally featureless: local measurements return random outcomes that are identical for all states. However, global snapshots in the computational basis are surprisingly effective at distinguishing between quantum states. We explore the ability of Bayesian classifiers to discriminate between many random quantum states using a small number of measurement outcomes. We identify a phase transition in the ability of the classifier to distinguish between $k$ candidate states with $m$ shots controlled by the variable $x = m / \ln k$, and derive the threshold value $x_c$. We extend our results to low-depth circuits near the onset of anti-concentration, as well as to noisy circuits and phase-random states.
Quantum reservoir computing (QRC) is a machine learning approach which employs the internal dynamics of a physical system (the reservoir) to encode and process information. In this work, we explore the use of dual-unitary circuits in a brickwork architecture as a platform for QRC, well suited to current noisy intermediate-scale quantum devices. Dual-unitary circuits present both practical and conceptual advantages. Our results indicate that, under appropriate conditions, dual-unitarity can lead to an enhanced regime of operation: we numerically verify that it improves memory effects and nonlinear processing, and shields against finite-shot noise, mitigating exponential concentration. Moreover, dual unitarity offers an intuitive picture of how operator dynamics gives rise to memory and nonlinear processing in circuit-based reservoirs.
Quantum approaches for combinatorial optimization problems have attracted considerable attention in recent years. Among these approaches, Pauli Correlation Encoding (PCE) has emerged as a promising framework for quantum devices with limited qubit resources because it embeds optimization variables in expectation values of Pauli strings. However, the mechanisms underlying its performance and the reasons for its saturation remain unclear. In this work, we investigate these questions through a systematic analysis of expressivity and trainability. First, we compare PCE with classical surrogate models based on tensor networks whose structures progressively approach the topology of the PCE circuit. The results show that PCE attains comparable solution quality with substantially fewer trainable parameters, indicating strong parameter efficiency. Second, to determine whether the performance saturation of conventional PCE is caused by insufficient expressivity or by optimization difficulty, we perform a diagnostic expressivity test in which the circuit is trained toward reference configurations for Max-Cut. The results show that even shallow PCE circuits can represent strong solutions, indicating that the main bottleneck is not the representational power of the ansatz, but the trainability under the relaxed objective function. Motivated by this finding, we propose a multistage continuation framework that gradually transforms a smooth relaxed objective into a sharper objective that more closely approximates the target discrete problem. Numerical experiments on G-set instances with 800 vertices show that the proposed method consistently outperforms conventional PCE and is competitive with representative graph neural network (GNN) methods. These results clarify the main factors behind PCE performance and provide a practical strategy for improving PCE on quantum devices with limited qubit resources.
We study the structure of Gibbs states in weakly perturbed interacting fermionic systems. First, for a sparse Hamiltonian $H=H_0+V$ with a quadratic term $H_0$ and a non-quadratic perturbation $V$ of scale $\epsilon$, we show that the Gibbs state $\rho_{\beta}$ decomposes into a convex combination of Gaussian states whenever the inverse temperature satisfies $\beta \le O(\log(1/\epsilon))$. Moreover, we prove that this bound is asymptotically tight by establishing that $\beta \le \Theta(\log(1/\epsilon))$ is necessary for certain sparse Hamiltonians. This general framework applies directly to the weak-coupling (small-$\vert{}U\vert{}$) regime of the Fermi--Hubbard model with hopping $t$ and on-site interaction $U$ on any graph of maximum degree $D$. Complementarily, in the strong-coupling (small-$\vert{}t\vert{}$) regime, we show that the Gibbs state remains convex-Gaussian up to $\beta \le O\big(\vert{}U\vert{}^{-1}\log(\vert{}U\vert{}/(D\vert{}t\vert{}))\big)$, revealing a mechanism for convex-Gaussianity distinct from the weak-coupling setting.
The Simultaneous Message Passing (SMP) model provides a fundamental framework for comparing classical and quantum communication. For two players, Gavinsky et al. (STOC 2006) established a separation underlying the incomparability of shared randomness and quantum communication: \textscIndex Coordination needs $O(\log n)$ public-coin bits but $\Omega(n^{1/3})$ bounded-error qubits. In this work, we establish a multiparty exponential separation through $\operatorname{IC}_{k,n}$, a natural $k$-party generalization of \textscIndex Coordination. Public-coin protocols solve it unambiguously with maximum message length $O(\log n)$ bits. In contrast, quantum SMP protocols without shared entanglement or public coins require maximum message length $\Omega(n^{1-1/k})$ qubits in the unambiguous regime and $\Omega(n^{(k-1)/(k+1)})$ qubits in the bounded-error regime. A classical private-coin protocol matches the unambiguous bound, so quantum communication provides no asymptotic advantage over private randomness in this regime. For fixed error parameters, all constants are independent of $k$, establishing the exponential separation for every integer-valued function $k=k(n)\ge2$, without restricting its growth. Both quantum lower bounds become $\Omega(n)$ when $k\ge c\log n$ for any fixed $c>0$, matching the full-input protocol and yielding tight linear complexity in both regimes. Our results demonstrate that quantum superposition cannot efficiently simulate the coordination afforded by public randomness, extending this separation to arbitrary $k$. To bound success probabilities for multiparty product states, we prove an exact factorization theorem for unambiguous quantum state identification, which may be of independent mathematical interest.
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.
Non-Gaussian interactions are a key ingredient for achieving universality in continuous-variable quantum computation, yet their experimental characterization and the validation of their correct implementation remain challenging tasks. In this work, we focus on a three-mode non-Gaussian trilinear Hamiltonian that has recently been realized in superconducting microwave platforms, and present a comprehensive theoretical analysis of the computational resources it generates, together with experimentally accessible protocols to validate their presence. We systematically investigate its ability to generate two key resources for quantum computation: multipartite entanglement and Wigner negativity. In particular, using displaced-parity Bell tests, we demonstrate the generation of nonlocal states and thereby provide an operational certification of multipartite entanglement in the non-Gaussian states produced by the dynamics. We further quantify the Wigner logarithmic negativity and benchmark it against that of established non-Gaussian resource states. Building on this resource-based characterization, we introduce a measurement-efficient protocol for the experimental validation of the Hamiltonian implementation without requiring full reconstruction of the Wigner function. The protocol combines the measurement of zero-variance observables (nullifiers and stabilizers) with a limited number of targeted phase-space measurements, leading to a drastic reduction of the experimental overhead.
Magic-state cultivation suppresses errors by measuring logical Clifford symmetries and discarding inconsistent outcomes. For an entangled resource several branches are accepted, so the retained branch carries a multibit classical record whose corruption produces a logical-frame error. We show that this record layer is exactly a binary linear code. For any third-level Clifford-hierarchy unitary $U \in \mathcal{C}_3$, the branches $UZ(a)|+\rangle^{\otimes k}$ are resolved by commuting Hermitian Clifford observables $C(v) = UX(v)U^{\dagger}$, so a measurement schedule is a generator matrix and postselection on valid records gives $P_{\mathrm{wv}} = O(q^{d})$ at record distance $d$. A Plotkin bound then limits every binary record, linear or not. The physically realizable Clifford family already saturates it: at distance four, six logical measurements suffice for $|CS\rangle$ and seven for $|CCZ\rangle$, against eight and twelve for independent repetition. Restricting to fault-tolerantly measurable parities therefore costs nothing in record length. The saving survives compilation: in a native-CZZ-assisted Steane realization the $[6,2,4]$ CS schedule is the unique minimum-cost distance-four solution, reducing the cultivation core by 26.6\% in active locations, and exact state-vector simulation without a final ideal code-space projection confirms higher acceptance and roughly half the residual Steane-boundary weight. Coding thus reduces logical redundancy and compiled overhead together.
Recent work in quantum key distribution (QKD) has yielded finite-size keyrates based on convex optimisation problems, using the framework of entropy accumulation. Multiple solvers have been developed to address these optimisations in recent years, but have been based on a somewhat elaborate framework using sophisticated algorithms, in order to accommodate a broad range of QKD protocols. In this work, we note that for basic QKD protocols such as qubit BB84, the keyrates can be easily computed using off-the-shelf solvers instead, by obtaining suitable tangent lines to lower bound terms in the objective function. We compute the resulting finite-size keyrates and compare them to previous work. Moreover, we extend this approach to the six-state protocol, by deriving closed-form expressions for the single-round Rényi entropies in the protocol. This should facilitate subsequent study of the six-state protocol via entropy accumulation.
We present the case of a Gottesman-Kitaev-Preskill (GKP) state-enhanced optical interferometry with detailed analysis of the phase sensitivity for both the SU(2) and SU(1,1) interferometers. The conventional quantum-enhanced SU(2) interferometer, employing coherent light at one input port and squeezed light at the other, is compared with a modified configuration using coherent light and a GKP state. While it is known that the squeezed vacuum state is the optimal Gaussian resource input mode when paired with the coherent state, we show that the finite-energy GKP state with sufficiently broad envelope outperforms the squeezed vacuum injection, irrespective of the presence of optical losses. This can be attributed to the enhanced robustness coming from the availability of multiple squeezed peaks in the GKP case. However, because lowering the mean photon number reduces the GKP envelope width, the squeezed vacuum input performs better when compared with a GKP state of equal or lower mean photon number. We also observe that optical losses tend to diminish the relative advantage of either input state, since both states approach the (unsqueezed) vacuum state asymptotically. Our work demonstrates the direct application of finite-energy GKP states in optical interferometry along with a methodology for estimating the quantum Fisher information (QFI) and presents a phase estimation procedure using non-Gaussian resources in comparison with conventional Gaussian states.
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.
The Jarzynski relation enables the estimation of equilibrium free energy differences from non-equilibrium, finite-time switching simulations. These estimates usually converge poorly because rare trajectories dominate the exponential work average. Here, we numerically determined and explored the sequence of intermediate Hamiltonians connecting initial and final states that minimize the mean squared error (MSE) of the Jarzynski estimator and thereby enhance convergence. For discrete-time Markov models, an exact tilted-master-equation representation of the MSE in the large-sample limit, combined with automatic differentiation, enables efficient gradient-based minimization over all intermediate energies. We applied our approach to three model systems of increasing complexity: a two-state model, a double-well potential, and a shifted potential well. In all three systems, the optimal intermediate Hamiltonians jump at the initial and final times. Extensive Monte Carlo simulations show that optimal intermediates can reduce the MSE by more than an order of magnitude compared with linear and logarithmic interpolation, most strongly for large changes in the energy landscape. Remarkably, they need not dissipate less work than intermediates yielding larger errors. Our results suggest heuristics for more efficient non-equilibrium free energy calculations of realistic molecular systems: optimal intermediate Hamiltonians jump at the initial and final times; for barrier-crossing problems, the barrier should be lowered rapidly and raised again later; and minimizing dissipation does not guarantee faster convergence.
We give the first deterministic polynomial time algorithm that approximates the permanent of arbitrary nonnegative rational matrices within a subexponential factor. For a matrix of order $n$, the approximation factor is \[ \exp\!\left(O\!\left(\fracn(\log\log n)^2\log n\right)\right)=\exp(o(n)). \]All previously known deterministic polynomial time guarantees for unrestricted inputs had approximation factors $\exp(\Omega(n))$. Our proof uses convex optimization to tighten an upper bound on the permanent. The bound is based on weighted sums over all matchings in a bipartite graph representing the matrix, and correlations between unmatched vertices control its error. We approximate these sums deterministically using correlation decay and a bound on the effect of vertex deletion.
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.
Entanglement-assisted optical interferometry promises diffraction-limited imaging over baselines where light cannot be physically combined, but existing theory treats only a single visibility on one two-station baseline. This work formulates the multiparameter estimation problem for an M-station array imaging an extended scene. A reduction lemma shows that the multimode quantum Fisher information (QFI) equals the mean photon number times the QFI of a single delocalized photon, collapsing the problem to a finite-dimensional one. The local photon-number superselection rule (SSR) erases all phase information from the bare state, while shared entanglement restores a fraction f(r)=r/(1+r) of the QFI on a baseline supplied with r pairs -- a factor shown to be achievable, since the reduced two-mode state of any pair is exactly the two-station weak-thermal state. The QFI matrix and its mean Uhlmann curvature reveal numerically that a point source is measurement-compatible, whereas for every extended-source model examined it is incompatible, the Holevo bound exceeding the symmetric-logarithmic-derivative (SLD) bound by up to ~74%. An explicit collective receiver -- a global mode-sorting (quantum Fourier transform) measurement -- then attains a weighted variance within ~7% of the SLD bound and roughly an order of magnitude below an explicit pairwise receiver, and a noisy-resource advantage threshold gives the break-even baseline (~20 km for near-term parameters) beyond which repeater-distributed entanglement beats direct transmission. Finally, the optimal allocation of a finite entanglement budget is a convex program with a closed-form proportional (square-root-law) solution favoring low-visibility baselines. These results recast quantum aperture synthesis as collective multiparameter estimation and give concrete design targets, illustrated on the CHARA array.
Photon subtraction is one of the most important techniques for generating non-Gaussian optical states and constitutes a key resource for quantum information processing and quantum metrology. The practical performance of a photon-subtraction device is primarily determined by the transmissivity of the beam splitter and the quantum efficiency of the heralding detector. Accurate knowledge of these parameters is therefore essential for assessing the quality of the generated non-classical states. In this work, we propose an experimentally feasible in situ scheme for the simultaneous estimation of these two parameters using only the measurement data produced during the operation of the device. Our protocol combines the click statistics of an on/off heralding detector with homodyne measurements performed on the transmitted mode of the beam splitter when fed by a displaced squeezed state. Within the framework of classical multi-parameter estimation theory, we derive the corresponding Fisher information matrix and investigate both joint and sequential estimation strategies. For simultaneous measurement of parameters, we evaluate the sloppiness of the underlying statistical model and analyze its dependence on the measured quadrature, probe photon number, squeezing fraction, beam splitter transmissivity, and detector efficiency. Our analysis proves that an appropriate choice of the homodyne quadrature substantially reduces parameter degeneracy and enables efficient simultaneous estimation. Furthermore, we show that the joint estimation strategy consistently provides a lower estimation bound than the sequential estimation approach over a broad range of experimentally relevant parameters.
We study Haar-Bayesian prediction of one unmeasured copy of an unknown finite-dimensional pure quantum state after an arbitrary collective measurement on $n$ observed copies. Performance is evaluated by quantum relative entropy. For a fixed measurement, the Bayes predictive state is the posterior mean and the optimized conditional loss is its entropy. We then optimize the measurement over all POVMs on the symmetric subspace. For every nonzero positive effect $E$, the corresponding posterior predictive state is $\mu_E=(I+n\rho_E)/(n+d)$, where $\rho_E$ is the normalized one-particle marginal of $E$. Since a pure spectrum majorizes every density-operator spectrum, this identity gives an outcome-wise entropy lower bound. Coherent rank-one effects attain the bound, and their Haar orbit yields the highest-weight covariant POVM. Hence this POVM is globally Bayes optimal over all collective measurements and, by covariance, globally minimax. Its exact risk is $h_d((n+1)/(n+d))$, where $h_d(r)=-r\log r-(1-r)\log((1-r)/(d-1))$. The same arbitrary-effect reduction shows that the highest-weight POVM also maximizes the joint overlap between the latent pure state and its posterior predictive state, equivalently the mean posterior purity, with optimum $((n+1)^2+d-1)/(n+d)^2$.
Complex solid-state systems are promising platforms for scalable, high-bandwidth quantum random-number generation, yet certifying the quantum origin of their fluctuations remains difficult because the underlying microscopic dynamics are hard to model and validate. Here we demonstrate semi-device-independent quantum randomness certification from semiconductor spin noise, to our knowledge the first such certificate on any spin-noise source, without relying on a microscopic model of the spin system. The untrusted optical source is constrained by an experimentally tested mean-photon-number bound together with a declared analogue-range and per-sample clipping ceiling, while the trusted receiver is described as a calibrated, noisy, coarse-grained homodyne measurement. Using a semidefinite programme with rigorously controlled Fock-space truncation, we certify randomness that remains private against an adversary holding arbitrary quantum side information. Offline analysis yields certified entropy rates of $3.2$--$3.4$\u2009Gbit/s from a singly charged (In,Ga)As quantum-dot ensemble and $33$\u2009Mbit/s from $n$-GaAs in a spin-noise-matched detection mode. This exceeds the certified entropy rate of earlier spin-noise generators by more than two orders of magnitude, and the certificate tolerates a resolved per-symbol energy contribution from the solid-state emitter itself rather than requiring a near-vacuum input.
Consistent submodular maximization studies the tradeoff between solution quality and stability when elements arrive over time. For a monotone submodular objective, which models diminishing returns, an algorithm maintains a set of at most $k$ available elements and changes only $O(1)$ elements after each insertion. Dütting et al. [2025] established a tight $2/3$ approximation with unrestricted computation and a polynomial-time $0.51$ approximation. They left open at STOC 2025 whether efficient algorithms can match the offline $1-1/e$ guarantee. We resolve this problem by proving that the supremum approximation achievable with polynomially many value queries and worst-case constant recourse is \[ \beta=2-\sqrt2\approx0.5858<1-1/e. \]For every $\varepsilon>0$, our randomized algorithm attains $\beta-\varepsilon$ with $O(\varepsilon^{-2})$ changes per insertion. Any fixed improvement requires exponentially many queries before one critical insertion or linear recourse of $\Omega(k)$ changes at that insertion, even with unlimited queries afterwards. This gap quantifies the cost of consistency: the current oracle hides which elements will be needed after an arrival. We also determine the exact curvature-dependent threshold $1-(\sqrt2-1)\vartheta$, attain $1-1/e-\varepsilon$ for weighted coverage with $O(\varepsilon^{-1})$ recourse, and separate the existence of universal future-price certificates from their efficient computation. Our algorithm has a bounded-bit polynomial-time implementation for polynomial-bit rational oracle answers; the lower bound uses only logarithmic-bit rational answers.
High Performance Computing-Quantum Computing (HPCQC) platforms expose multiple Quantum Processing Units (QPUs) that may differ in size, topology, native gates, and noise characteristics. For current noisy devices, errors compound along the compiled circuits quickly, and minimizing them, that is, maximizing the circuits' execution fidelity, is essential for reliable results. Fidelity depends on the compilation to a specific target device: the same high-level circuit may produce different executables and, therefore, different expected fidelities across QPUs. We present a low-overhead fidelity-aware scheduling framework for multi-QPU systems based on a Graph Neural Network (GNN) that estimates, before compilation, the expected fidelity of each circuit on each available QPU. Then, a tunable scheduler uses these estimates to control the trade-off between execution fidelity and parallelism. Results show that this framework allows for approximating an exhaustive fidelity-based assignment, saving computational resources compared to a brute-force approach that compiles each circuit on every device.
Julian Pick, Eric Henker, Florian Löwinger, Rick Vogt, Sebastian Hüttl, Andreas Trützschler, Julia Voß, Simon Hirt, Malte Schulz-Ruhtenberg, Aleksandra Buchta, Alexander Kassner, Folke Dencker, Marc Wurz, Stephan Hannig, Simone Callegari, Saskia Bondza, Jens Kruse, Tobias Leopold, Roman Schwarz, Carsten Klempt Quantum sensors, like optical lattice clocks, undergo a continuous development from lab-based towards mobile systems. A key aspect in the miniaturization of the experimental setups is the development of compact atom sources. Conventional atom sources for alkaline-earth-like elements consist of a high-power oven and a six-beam magneto-optical trap (MOT) inside of vacuum chamber with extensive flanges, viewports and electrical feedthroughs. Here we present a highly compact vacuum package utilizing key technologies for future quantum sensor systems: A chip-based low-power atomic oven, a planar grating MOT chip, and a miniaturized vacuum pump all held inside an additively manufactured titanium vacuum chamber, featuring custom-sized vacuum flanges. In this miniaturized setup, spanning a volume of only 750 ml, we trap up to $10^5$ Sr atoms in a MOT, requiring an oven heating power below 1 W.
Device-independent certification of a quantum gate requires the input and output tests to identify the same reference qubits. Self-testing the output Choi state alone does not guarantee this consistency. We develop a robust certification scheme for Boolean-phase gates, a broad family of computational-basis diagonal gates specified by Boolean functions. Boolean derivatives convert the target-dependent phase information into classical signs that can be evaluated from local measurement outcomes. This leads to Bell tests built from CHSH blocks using two binary measurements per party and no entangling measurements. At maximal violation, the tests self-test the normalized Choi state and the measured observables. Away from the maximum, they give an explicit affine lower bound on the extracted-state squared fidelity that is uniform over all Boolean functions and valid in arbitrary local dimensions. We then combine an identity test and a gate-output test in an independent-source network in which the reference devices use the same physical observables, obtaining a closed-form Choi-fidelity bound for an effective \(n\)-qubit channel. For CCZ, a joint six-party analysis gives a stronger robustness bound without changing the Bell expression or measurement settings. The construction shows how the algebraic structure of a gate can shift target-dependent information from quantum measurement design to classical processing of local outcomes.
In online inverse linear optimization, the learner predicts a weight at each round, observes the optimal action of the agent, and updates its prediction. In the general setting, the gap of $\log T$ between the regret upper bound $O(d \log T)$ and the lower bound $\Omega(d)$ is unresolved (here $T$ is the total number of rounds and $d$ is the dimension). When the action set is M-convex, the regret is known to be bounded by $O(d \log d)$, but the method attaining it computes a center of gravity at every round. This paper therefore proposes Small-Gradient Skipping (SGS), a mechanism that skips the update at rounds without a mistake in the case where the correct action is uniformly separated from the other candidates, and applies it to online gradient descent, the online Newton step, and MetaGrad. The number of mistakes is then bounded, for all three, by a quantity independent of $T$; and for the online Newton step and for MetaGrad with SGS, the dimension dependence of the regret becomes $O(d^2)$ when the forward problem is an integer linear program, that is, the factor $\log T$ is removed. Moreover, when the action set is M-convex, the regret is bounded efficiently without computing a center of gravity.
By decomposing quantum dynamics across the Lie orbits of a list of observables, we find polynomial bounded classical simulations for the dynamics of the quantum system given a polynomial sized dynamic Lie algebra (DLA) for the generators of the quantum system. To do so, we describe how to construct the Dynamic Observable Subspace (DOS) that captures all the relevant dynamics for calculating expectation values for a specific observable for Pauli strings, diffusor mixers, and general local generators. Efficient sparse matrix representation, decoupling nonlinearity from such representation and basis construction with permissible pruning allows us to simulate the closed dynamics of such systems with hundreds of qubits. Moreover, we find that while restricted DOS circuits may not express the space of an associated Hamiltonian, they can dramatically outperform a fully expressive circuit due to the absence of the Barren Plateau. While classically simulatable, such circuits can still exhibit a form of quantum advantage through inference, act as warm starting for more expressive circuits, and find high quality trial states for Quantum Amplitude Amplification or Quantum Phase Estimation. In the simulation of quantum dynamics, we find that our restricted circuit can be simulated in polynomial time while producing high quality guiding state for downstream tasks like Quantum Phase Estimation with significantly lower energy than circuits with full expressivity.
Generalized Arimoto--Blahut (AB) algorithms are widely used in information theory and quantum optimization, but monotonic objective decrease and numerical stabilization do not guarantee global optimality. We establish necessary and sufficient conditions for the global optimality of full-rank AB fixed points for convex differentiable objectives under linear constraints. An AB fixed point is globally optimal if and only if the AB update direction and the objective gradient differ by an element of the constraint normal space at that point. The same compatibility condition characterizes agreement between individual AB and mirror-descent (MD) updates, whereas pathwise equivalence requires it along the entire common trajectory. Thus, an AB algorithm may follow a trajectory different from MD and still reach the global optimum. We also develop a posteriori optimality certificates based on feasible directional derivatives, including finite-difference upper bounds on the objective gap that require only objective evaluations. For channel relative entropy between dephasing and depolarizing channels, we analytically identify the global minimizer as the unique full-rank AB fixed point, although pathwise equivalence fails. Numerical experiments illustrate convergence of AB and MD along different trajectories and validate the certificates. By contrast, an amplitude-damping example shows that a monotone AB iteration can stabilize at a suboptimal fixed point, whose nonoptimality is detected by the finite-difference certificate. These results provide structural and computable criteria for assessing global optimality in quantum AB algorithms.
Sep 10 2026
cs.DS arXiv:2609.09701v1
We study fast algorithms for sparse-PCA certification. Given a positive semidefinite matrix $M$, the problem asks either to rule out a large $k$-sparse quadratic form or to return a high-value (relaxed) witness. The standard semidefinite relaxation provides such certificates, but existing general-purpose solvers require $\Omega(d^4)$ time. We give a bicriteria algorithm running in $O(d^2+d k^{O(\log k)})$ time: if some $k$-sparse unit vector has quadratic form greater than $2$, it returns either an $O(k^2)$-sparse unit vector or an SDP-feasible matrix of value at least $1$. For $k\leq\exp(O(\sqrt{\log d}))$, this running time is $O(d^2)$. We also go below the quadratic barrier in the sample-access model: Given $n=d^{o(1)}$ samples, our algorithm obtains a related one-sided certificate in $d^{2 - \Omega(1)}$ time for $k=\mathrm{polylog}(d)$, without forming the empirical covariance matrix. As an application, these certificate routines yield the first quadratic and subquadratic-time algorithms for robust sparse estimation for broad families of distributions. Our sparse-PCA algorithm reduces a high-value sparse direction to a bounded-radius set in the graph of large correlations and searches the resulting candidate supports. The subquadratic implementation constructs this graph using fast correlation detection.
Exact finite-dimensional descriptions exist for a few important classes of continuously monitored quantum systems, but there is no general criterion separating systems that admit such filters from those that do not. We formulate this question as a realization problem and introduce the linearized observable Hankel operator $K_O$, which maps changes in the past measurement record to changes in a future conditional observable. For polynomial bosonic systems under continuous quadrature monitoring, this gives a sharp boundary between finite and infinite realizability. Gaussian dynamics and the Conditional Momentum Moment class admit exact finite-dimensional filters, while nonlinear dynamics outside these classes generically produce infinitely many independent response directions and admit no robust finite-dimensional $C^1$ observable- or state-level filter. The singular values of $K_O$ then extend the same realization framework to approximation, giving the optimal rank-$d$ local-response error beyond the finite classes. Numerical experiments with the Kerr and Duffing oscillators, together with a dynamics-adapted Poisson--Charlier construction for Kerr dynamics, show how this observable-level benchmark interacts with concrete reduced representations. Together, these results identify the boundary of exact quantum filtering and quantify finite-dimensional approximation beyond it.
Jieyi Long, Theodore Pender, Zhao Huang, Manuel B. Santos, Samrendra Kumar Singh, Bartosz Naskręcki, Bit Wonka, Joe Doyle, Pierre-Luc Dallaire-Demers, Francesco Giannicola, Ruben M. L. Paschoarelli, Oli Freuler, Jackie Chia-Hsun Lee, Vasily Gnuchev, Gopi Kannappan, John Boyer, Xavier Butler, Akash Balasubramani, Jordan Newman, Bereket Dereje, et al (16) We propose Open Autoresearch, a paradigm in which humans and AI agents publish evaluator-verified improvements to a public leaderboard. We instantiate it in ECDSA.Fail, optimizing reversible secp256k1 point-addition circuits, a bottleneck in Shor's algorithm for elliptic-curve cryptography. The benchmark minimizes the spacetime-inspired score $S=Q\times T$, where $Q$ is peak logical qubit width and $T$ is average executed Toffoli count. Participants reduced $S$ by 86.1%. At the data cutoff (26 July 2026), the best-scoring circuit uses 1,151 qubits and 1,299,453 average executed Toffoli gates, giving $Q\times T\approx1.496$ billion. This is more than 50% below Google's published point-addition score thresholds (arXiv:2603.28846), under different accounting conventions. Because the benchmark supplies one addend classically, we construct a coherent windowed-addition-compatible variant implementing the single-call interface required by windowed Shor. It uses 1,162 qubits and 1,684,161 average executed Toffoli gates. On 100,000 random inputs, its empirical success probability is $\hat{p}=0.99809$, giving $Q\times T/\hat{p}\approx1.961$ billion under an independently rerunnable per-call sensitivity model, not a full-Shor success estimate. Its qubit and Toffoli counts lie below Google's published thresholds and Schrottenloher's reported operating points (arXiv:2606.02235), although differing interfaces, accounting conventions, and validation scope preclude formal dominance. After the cutoff, the score was further reduced to 1.259 billion, while a separate low-width circuit reached 813 qubits. The public record shows AI agents complementing human judgment, providing evidence for open autoresearch on efficiently evaluable, machine-checkable objectives.
We all know that a density matrix $\rho$ is pure if and only if $\mathrm{Tr} \,\rho^2 = 1$. But is this the only way to prove the purity of $\rho$ using the trace of its powers? Here I systematically study the necessary and sufficient conditions of the more general question of guaranteeing that all eigenvalues of a Hermitian matrix belong to a specified set through its trace of powers. More importantly, these characterization results are automatically witnesses certifying a quantum state as entangled, a Hermitian operator has least one negative eigenvalue and a linear operator as non-Hermitian. I demonstrate the effectiveness of these witnesses, analyze their performance, and study their strength, weakness together with resource requirement through numerical simulation as well as analytical work. I also discuss briefly the effects of numerical stability, uncertainty in measurement and rounding errors on these problems.
We find through direct, time-domain measurement of trapped $\mathrm{Yb}^+$ ions that the excited ${}^3[11/2]_{9/2}^o$ state has a collision-free lifetime of 17.8(6) min, long enough for use in atomic clockwork or quantum information processing. We locate and benchmark a broad ``repump'' transition at $701\, \mathrm{nm}$ that readily transfers population back into the Doppler cooling cycle with the ground state, which may allow for quantum nondemolition measurement of sub-structure in the metastable manifold. Using a bi-stable Coulomb-crystal manometer, we find that the collisional quenching of this metastable ${}^3[11/2]_{9/2}^o$ manifold by background gas is more efficient than for ${}^2\mathrm{F}_{7/2}^o$, but nonetheless we observe an average lifetime exceeding 10 minutes at the base pressure of our apparatus.
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.
Zheng-Hui Huang, Guixu Lin, Jiacheng Lin, Yi-Chuan Huang, Ruihan Yu, Muyao Niu, Siqi Yang, Yu-Lun Liu, Yung-Yu Chuang, Kaipeng Zhang, Zhixiang Wang Sep 10 2026
cs.CV arXiv:2609.10540v1
Recent video world models generate increasingly realistic and interactive visual experiences, yet lack reliable mechanisms for maintaining persistent world state and enforcing programmable rules over extended interactions. We introduce Programmable World Model, a framework that decouples world-state evolution from visual observation generation. An agent translates natural-language instructions into executable programs that specify entity states and state-transition rules, enabling direct control over individual entities and their interactions. A lightweight engine executes these programs to update and maintain an explicit, persistent global world state, including off-screen entities and non-visual attributes. To connect world state with visual generation, we introduce state-augmented 3D oriented bounding boxes (OBBs) as an intermediate representation. This representation, together with the target camera trajectory, is deterministically compiled into pixel-aligned spatiotemporal conditioning signals for a pretrained video model serving as the generative renderer. This design allows users to create playable games with predefined mechanics, direct control over individual entities, and persistent world state throughout gameplay. We further introduce CombatStateBench, a benchmark for evaluating programmable world models. On CombatStateBench, our method achieves 94% Count Accuracy and 98% State Accuracy, substantially outperforming existing interactive video world models while supporting coherent long-horizon generation. These results demonstrate the effectiveness of separating explicit state evolution from generative rendering for building persistent, programmable worlds.
Sep 10 2026
cs.CL arXiv:2609.10539v1
A research idea may be novel, coherent, and scientifically plausible, yet its proposed method may remain insufficiently specified for faithful implementation. We study the codification readiness of implementation-facing research-method specifications, defined by whether they provide sufficient methodological information for a competent implementer or coding agent to construct the intended method without unsupported assumptions. We construct evidence-grounded specifications and their supported resolutions from papers, codebases, issue threads, and reproduction artifacts. We introduce IdeaAMBIG, a benchmark of 660 evidence-grounded instances: 163 real-world gaps from reproducibility reports and GitHub issues, and 497 controlled synthetic gaps injected into codification-ready references. IdeaAMBIG evaluates three capabilities: codification-readiness assessment, defect localization, and clarification action generation. Defect localization receives only the specification, whereas clarification additionally receives the annotated defect. Across 13 LLMs, the best model achieves 9.6% Macro Defect Recovery Rate on real-world instances but 80.6% Macro Clarification Action Success Rate when given the defect. In an oracle study, supplying the gold resolution raises the downstream codification-ready rate from 14% to 98%. Across all evaluated models, defect localization is the main bottleneck, with stronger clarification given the defect.
Sep 10 2026
math.DS arXiv:2609.10538v1
We prove exact dimensionality of ergodic stationary measures for random $C^1$ diffeomorphisms in the single negative Lyapunov scale setting. Let $\nu$ be a Borel probability measure on $\mathrm{Diff}^1(M)$ satisfying a logarithmic $C^1$ moment condition, and let $\mu$ be a $\nu$-stationary ergodic probability measure. If $\lambda_{\mathrm{top}} = \lambda_{\mathrm{bot}} = \lambda<0,$ then $\mu$ is exact dimensional and $ \mathrm{dim}(\mu)={h_\mu^{\mathrm{F}}(\nu)}/{(-\lambda)}.$ No discreteness assumption is imposed on the driving measure.
Sep 10 2026
cs.CR arXiv:2609.10537v1
Logic flaws pose significant challenges in the design and implementation of modern, semantically rich systems and applications, impacting security, privacy, and trust. These flaws are inherently tied to business-specific semantics and threat models, making their discovery and reasoning difficult and hard to scale. Real-world systems often exhibit diverse application features, complex protocol logic, and domain-specific threat models, necessitating substantial human effort and domain expertise for effective security analysis. In this paper, we introduce LL-Verifier, a novel, automated framework for identifying logic vulnerabilities built on (1) large language models for autonomous modeling, and (2) logic model checkers for rigorous reasoning. LL-Verifier processes natural language inputs, in particular protocol descriptions and security goals, to automatically generate formal logic models and properties expressed in a new logic language built on a generic logic language Maude, optimized for modeling arbitrary application-level semantics. These formal models are then converted into logical state machines, enabling exhaustive, rigorous verification through logic level model checking. This approach streamlines the analysis of diverse, application-level protocols deployed in real-world scenarios, offering automated, exhaustive, and precise reasoning within their logical constraints. We evaluated the high effectiveness, efficiency, and practicality of LL-Verifier by applying it to 27 access control protocols of widely used IoT devices, which come with vendor-specific logic flows and semantics. While LL-verifier tackles a hard problem in application security, i.e., automatic logic flaws discovery, our analysis uncovers a range of sophisticated logic vulnerabilities in IoT protocols and devices with serious security and privacy implications.
Braneshop, and
the US National Science Foundation.
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