arXiv subjects

Hayata Yamasaki

Publications and source records attributed to Hayata Yamasaki.

At least 19 recordsLinked to original sources

arXiv2026

Hyperbolic color codes with constant rate and polynomial distance

Recent advances in quantum hardware relax the strict geometric-locality constraints traditionally imposed on quantum error-correcting codes, motivating interest in high-rate quantum low-density parity-check (qLDPC) codes. At the same time, color codes provide a particularly rich setting for fault-tolerant quantum computation, underlying protocols such as single-shot error correction and self-correcting quantum computation. Hyperbolic color codes provide a class of high-rate qLDPC codes that also retain the structural features of color codes relevant to fault-tolerant quantum computation. However, previous constructions of hyperbolic color codes have achieved at most logarithmic code distance. In this work, we construct hyperbolic color codes with both constant rate and polynomial distance by building on arithmetic hyperbolic manifolds that support polynomial-distance hyperbolic toric codes. Our construction applies in arbitrary dimension $D\geq 4$. In even dimensions, the resulting type-$D/2$ color codes have constant encoding rate and polynomial distance, while in other cases the number of logical qubits and the code distance both exhibit polynomial scaling. We further derive explicit exponents for polynomial lower bounds as functions of the dimension and code type. These results establish a family of hyperbolic color codes simultaneously achieving constant rate and polynomial distance and providing a testbed to explore fault-tolerant quantum computation protocols that combine high-rate quantum codes with the structural advantages of color codes.

quant-ph↗

arXiv2026

NAQsim: Full-Stack Architecture Simulation Framework for Fast and Space-Efficient Neutral Atom Quantum Computing

Technological advances in neutral-atom platforms have opened a new path toward designing efficient protocols for fault-tolerant quantum computing (FTQC). However, each physical operation is still orders of magnitude slower than on other platforms, such as superconducting qubits. Therefore, architects must identify fast and efficient FTQC architectures, which require reliable modeling tools to explore various design choices across the software, classical hardware, and quantum device stacks of neutral-atom platforms. In this paper, we propose NAQsim, an open-source simulation framework for neutral-atom FTQC architectures based on transversal gates. As its key feature, NAQsim enables detailed full-stack architecture evaluation that opens opportunities to explore previously overlooked performance bottlenecks. As a first use case for NAQsim, we identify one such bottleneck, patch rotations, perform full-stack co-optimization, and finally derive a near-rotation-free architecture (D3-ROT). For practical FTQC benchmark workloads, D3-ROT achieves a 2.27x speedup from this single bottleneck alone, with minimal footprint overhead. These results point to a much broader space of full-stack optimizations that NAQsim makes accessible for transversal surface-code architectures and beyond.

quant-ph↗

arXiv2026

Sparse-Blossom Decoding in $o(1)$ Time

Matching-based decoding is widely used in quantum error correction, and accelerating it is key to enabling fast and scalable fault-tolerant quantum computation. Minimum-weight perfect matching (MWPM) decoding provides rigorous guarantees for error suppression, while sparse blossom enables its practical implementation at modest problem sizes. However, the runtime of existing sparse-blossom implementations unavoidably increases with problem size, motivating a rigorous parallelization framework that guarantees correctness and a runtime shorter than the syndrome-extraction timescale. Here, we present such a framework and prove that the resulting parallel sparse-blossom algorithm produces the same correction as the original, non-parallel sparse blossom. For the rotated surface code with code distance $d$ and physical error rates below a finite threshold, we prove that the average parallel runtime of decoding for $O(d)$ rounds of syndrome extraction is upper bounded by a quasi-polylogarithmic function of $d$. For a $d$-round decoding window, this implies that the average parallel runtime per round is $o(1)$. We also perform numerical simulation to identify conditions under which the parallel runtime per round decreases with increasing code distance. These results suggest that increasing code distance need not lead to longer parallel decoding times, providing a foundation for scalable parallel matching-based decoding.

quant-ph↗

arXiv2026

Loss-correcting fault-tolerant quantum computing architecture for neutral atoms

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.

quant-ph↗

arXiv2026

A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features

Quantum-inspired classical algorithms have dequantized several quantum machine learning routines by replacing quantum linear-algebra subroutines with classical counterparts. However, the sampler based on quantum singular value transformation (QSVT) for learning with optimized random features is not covered by existing dequantization frameworks, because the matrix to be inverted is not itself available through sampling access. In this work, we develop a classical algorithm to address this type of quantum-advantage candidate. Our method samples heavy indices, reduces the transformation to a small principal block, and outputs a sparse classical representation with operator-norm guarantees. Applying this method dequantizes the sampler for optimized random features, giving a classical sampler with prescribed accuracy and polynomially related runtime. These results show that the factorization underlying a quantum block encoding can itself provide sufficient classical structure even when sampling-and-query access to the composite matrix is unavailable.

quant-ph↗

arXiv2026

Quantum Information Decoupling Beyond Finite Dimensions

Quantum information decoupling is a pillar of quantum information theory, underlying quantum communication, error correction, and information recovery. However, its existing formulations rely on random unitary operations tied to finite-dimensional assumptions on quantum systems. Here we establish a decoupling framework for arbitrary separable, possibly infinite-dimensional systems. For finite-dimensional inputs and arbitrary separable reference/output systems, we derive error bounds on one-shot decoupling for completely positive maps in terms of sandwiched Rényi conditional entropies. For partial-trace decoupling with finite-dimensional references, the error exponent is optimal up to the known critical rate. To handle infinite-dimensional inputs, we assume finite entropy of the manipulated system. We construct finite-rank projections on independent and identically distributed (IID) states to restrict randomization to a projected finite-dimensional subspace, while ensuring high success probability by including auxiliary components in the discarded subsystem at asymptotically negligible cost. This leads to an infinite-dimensional IID partial-trace decoupling protocol achieving optimal asymptotic dimension rates. As an application, we construct an infinite-dimensional quantum-state-merging protocol, a mother protocol of quantum information theory. Under finite entropy of Alice's marginal, it achieves the same quantum-communication and total-cost rates as in finite dimensions, governed by mutual information and conditional entropy. These results show that the operational interpretation of entropic quantities through these achievable rates constitutes a universal principle beyond finite dimensions. More broadly, our framework provides foundational tools for exploring quantum information regardless of whether we model the physical world using finite- or infinite-dimensional spaces.

quant-ph↗

arXiv2026

Degeneracy Cutting: A Local and Efficient Post-Processing for Belief Propagation Decoding of Quantum Low-Density Parity-Check Codes

Quantum low-density parity-check (qLDPC) codes are promising for realizing scalable fault-tolerant quantum computation due to their potential for low-overhead protocols. A common approach to decoding qLDPC codes is to use the belief propagation (BP) decoder, followed by a post-processing step to enhance decoding accuracy. For fast decoding, the post-processing algorithm is desirable to have a small computational cost and rely only on local operations on the Tanner graph to facilitate parallel implementation. To address this requirement, we propose degeneracy cutting (DC), an efficient post-processing technique for the BP decoder that operates on information restricted to the support of each stabilizer generator. DC selectively removes one variable node with the lowest error probability for each stabilizer generator, significantly improving decoding performance while retaining the favorable computational scaling and structure amenable to parallelization inherent to BP. We further extend our method to realistic noise models, including phenomenological and circuit-level noise models, by introducing the detector degeneracy matrix, which generalizes the notion of stabilizer-induced degeneracy to these settings. Numerical simulations demonstrate that BP+DC achieves decoding performance approaching that of BP followed by ordered statistics decoding (BP+OSD) in several settings, while requiring significantly less computational cost. Our results present BP+DC as a promising decoder for fault-tolerant quantum computing, offering a valuable balance of accuracy, efficiency, and suitability for parallel implementation.

quant-ph↗

arXiv2026

Lean-Quantum: Toward AI-Assisted Formalization of Quantum Information

Quantum information theory is built on entropic quantities; among them, the sandwiched Rényi relative entropy is a fundamental divergence with various applications, and its data processing inequality (DPI) under quantum channels is a cornerstone result. In this work, we present a Lean 4 library for quantum information, designed as a reusable formal infrastructure for theoretical analysis. As a central demonstration of the library, we formalize the DPI for the sandwiched Rényi relative entropy for positive semidefinite operators on finite-dimensional quantum systems. The library provides a basis-independent operator-theoretic framework for finite-dimensional quantum mechanics compatible with the standard mathematical library Mathlib, including reusable interfaces for finite-dimensional systems, states, channels, tensor products, partial traces, Choi operators, Kraus representations, and Stinespring representations. It also builds infrastructure for noncommutative trace inequalities, including operator monotonicity and convexity via the real continuous functional calculus, block-operator positivity, Hilbert-Schmidt operator spaces, Jensen's operator inequality, generalized perspectives, operator power means, and Lieb-Ando trace inequalities. On top of this framework, we formalize entropy-specific ingredients for the DPI: variational formulas for the sandwiched quasi-entropy via Young and reverse-Young inequalities, tensor-product compatibility of real powers, and Haar measures on unitary groups. Together, these components yield a Lean formalization of the DPI, give strong subadditivity as a corollary, and provide the last missing component needed to complete the Lean formalization of the generalized quantum Stein's lemma. More broadly, the development provides machine-checkable foundations for future formalized and AI-assisted research in quantum information theory.

quant-ph↗

arXiv2026

Quantum State Preparation via Free Binary Decision Diagram

Quantum state preparation (QSP) is a fundamental task in quantum computation to prepare a quantum state for a given classical description of the quantum state. The classical description of an $n$-qubit quantum state may have $\exp(O(n))$ parameters in general, which are inherently inefficient to prepare the corresponding state in the worst case. However, in many practical cases, we may be able to employ suitable data structures for QSP. An ordered binary decision diagram (OBDD) and a free BDD (FBDD) are such data structures to represent the large-scale data in a compressed way. An efficient QSP for a subclass of OBDDs is known, but requires an $O(2^n)$-sized quantum circuit in general, while QSP based on FBDDs, which includes OBDDs as a special case, remains unexplored. We here construct a quantum algorithm for QSP when the classical description of a quantum state is given by an FBDD with weighted edges, and analyze the space, and time complexity of QSP in this setting. We provide a nontrivial example of an $n$-qubit state that can be represented by a weighted FBDD with $N=O(\mathrm{poly}(n))$ nodes rather than $\mathrm{exp}(O(n))$. We show that any quantum state represented by the weighted FBDD with $N$ nodes can be prepared by an $O(N)$-sized quantum circuit using $N$ ancillary qubits, exponentially improving the required circuit size for QSP compared to other BDD-based QSPs. We also provide another example of an $n$-qubit state that can be represented by a weighted FBDD with $N=O(n^2)$ nodes, and $O(n^2)$ ancillary qubits, but cannot be prepared efficiently by a QSP based on the amplitude amplification. These results provide techniques to employ FBDDs as a tool for broadening the possibility of efficient QSP.

quant-ph↗

arXiv2026

Rethinking quantum information in gravity and fields

This paper presents a curated selection of research questions at the intersection of quantum gravity and quantum information, chosen to highlight issues that we regard as particularly important for researchers in both fields. We organize the discussion into four main themes: the operational characterization of observables, the role of observers, quantum error correction, and the infinite-dimensionality of Hilbert spaces. We hope that addressing these questions will engage researchers across both communities and further strengthen the profound interplay between the two disciplines.

hep-th↗

arXiv2026

Entanglement cost for infinite-dimensional physical systems

We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state $ρ_{AB}$ with finite quantum entropy on at least one of the subsystems $A$ or $B$. This generalizes a foundational result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems. The extension to infinite-dimensional systems is nontrivial because the conventional tools for establishing both the direct and converse bounds, i.e., strong typicality, monotonicity, and asymptotic continuity, are no longer directly applicable. To address this problem, we construct a new entanglement dilution protocol for infinite-dimensional states implementable by local operations and a finite amount of one-way classical communication (one-way LOCC), using weak and strong typicality multiple times. We also prove the optimality of this protocol among all protocols, even under infinite-dimensional separable operations, by developing an argument based on alternative forms of monotonicity and asymptotic continuity of the entanglement of formation for infinite-dimensional states. Along the way, we derive a new integral representation for the quantum entropy of infinite-dimensional states, which we believe to be of independent interest. Our results allow us to fully characterize an important operational entanglement measure -- the entanglement cost -- for all infinite-dimensional physical systems.

quant-ph↗

arXiv2026

Generalized quantum Stein's lemma for mixed sources

The generalized quantum Stein's lemma characterizes the optimal asymptotic exponent of the type-II error in quantum hypothesis testing for an independent and identically distributed (IID) null hypothesis against a composite alternative hypothesis. Classically, a probabilistic mixture of IID sources arises as a natural generalization of IID sources, and, in the non-composite setting, the optimal type-II error exponent in hypothesis testing for such classical mixed sources is known to be characterized concisely by the worst-case component of the mixture. In this work, we extend these foundational results to composite quantum hypothesis testing where the null hypothesis is a mixed source, i.e., a probabilistic mixture of IID quantum states, and the alternative hypothesis is composite as in the generalized quantum Stein's lemma. When the type-I error vanishes asymptotically, we characterize the optimal type-II error exponent of this composite quantum hypothesis testing problem in terms of the worst-case component of the mixture, by developing techniques for the non-commutative quantum setting inspired by the classical information-spectrum analysis. We also show that the analogous characterization does not hold in general for a fixed nonzero type-I error threshold, by providing a counterexample beyond the vanishing type-I error regime. These results clarify the applicability of the generalized quantum Stein's lemma to highly non-IID null hypotheses arising from arbitrary finite probabilistic mixtures of IID quantum states.

quant-ph↗

arXiv2026

Winning Lottery Tickets in Neural Networks via a Quantum-Inspired Classical Algorithm

Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly solving an optimization problem over a large-scale network, this algorithm constructs a sparse subnetwork by sampling hidden nodes from an optimized probability distribution defined using the ridgelet transform. The quantum algorithm performs this sampling in time $O(D)$ in the data dimension $D$, whereas a naive classical implementation relies on handling exponentially many candidate nodes and hence takes $\exp[O(D)]$ time. In this work, we construct and analyze a quantum-inspired fully classical algorithm for the same sampling task. We show that our algorithm runs in time $O(\operatorname{poly}(D))$, thereby removing the exponential dependence on $D$ from the previous classical approach. Numerical simulations show that the proposed sampler achieves empirical risk comparable to exact sampling from the optimized distribution and substantially lower than sampling from the non-optimized uniform distribution, while also exhibiting exponentially improved runtime scaling compared with the conventional classical implementation. These successful dequantization results show that sparse subnetwork selection via optimized sampling can be achieved classically with polynomial data-dimension scaling on conventional computers without quantum hardware, providing an alternative to the existing quantum algorithm.

quant-ph↗

arXiv2026

Proof of a finite threshold for the union-find decoder

Fast decoders that achieve strong error suppression are essential for fault-tolerant quantum computation (FTQC) from both practical and theoretical perspectives. The union-find (UF) decoder for the surface code is widely regarded as a promising candidate, offering almost-linear time complexity and favorable empirical error suppression supported by numerical evidence. However, the lack of a rigorous threshold theorem has left open whether the UF decoder can achieve fault tolerance beyond the error models and parameter regimes tested in numerical simulations. Here, we provide a rigorous proof of a finite threshold for the UF decoder on the surface code under the circuit-level local stochastic error model. To this end, we develop a refined error-clustering framework that extends techniques previously used to analyze cellular-automaton and renormalization-group decoders, by showing that error clusters can be separated by substantially larger buffers, thereby enabling analytical control over the behavior of the UF decoder. Using this guarantee, we further prove a quasi-polylogarithmic upper bound on the average runtime of a parallel UF decoder in terms of the code size. We also show that this framework yields a finite threshold for the greedy decoder, a simpler decoder with lower complexity but weaker empirical error suppression. These results provide a solid theoretical foundation for the practical use of UF-based decoders in the development of fault-tolerant quantum computers, while offering a unified framework for studying fault tolerance across these practical decoders.

quant-ph↗

arXiv2026

Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation

Distributed architecture is a promising route to scaling fault-tolerant quantum computing (FTQC) beyond the inherent limitations of single processors. For practical implementation of distributed FTQC, logical Bell pair preparation must be designed not only for efficient Bell pair consumption but also for the spacetime volume of the protocol; however, entanglement distillation protocols have primarily focused on minimizing the consumption of Bell pairs, often resulting in protocols that require a substantial number of local operations. To resolve this issue, we introduce a metric for characterizing the practical cost of preparing high-fidelity logical Bell pairs, link-limited volume (LLV), which is a circuit-volume metric incorporating both the cost of physical Bell pairs and the spacetime volume of local operations. Guided by this metric, we propose entanglement boosting protocol, which achieves efficient preparation of logical Bell pairs encoded in rotated surface code with LLV reduced by orders of magnitude compared to prior state-of-the-art methods. In this protocol, paralleling recent advances in magic state cultivation, we employ soft-information decoders and postselection to suppress the logical error rates of Bell pairs to practical levels in the order of $10^{-10}$ from 86 noisy physical Bell pairs at 1% error, while all local operations are implementable within a spatial region of a single surface code patch with 2D local connectivity. We also present a pipelined implementation of entanglement distillation using high-rate quantum error-correcting codes, enabling arbitrarily low logical error rates while also maintaining physically efficient implementations. These results pave the way for the practical implementation of distributed FTQC, reinforcing the benefits of fast interconnect technologies and serving as a guiding principle for the efficient design of protocols and devices.

quant-ph↗

arXiv2026

Operational criteria for quantum advantage in latency-constrained nonlocal games

Remote entanglement enables coordinated decision making without communication and produces correlations beyond those achievable by any classical strategy, representing a practical quantum advantage in time-critical distributed decision-making problems. However, existing analyses of quantum-classical gaps in such latency-constrained tacit coordination (LCTC) have focused on idealized models that neglect the finite stationary window of the LCTC, finite operation times, and limited entanglement generation rates, leaving fundamental constraints unaccounted for. In this work, we develop a comprehensive framework to quantitatively analyze quantum advantage in LCTC that explicitly incorporates finite-duration and finite-rate operations, as well as generalized utility structures with a limited stationary window. These advances are made possible by adapting statistical certification methods for nonlocal games to the decision-making scenarios of LCTC, identifying operational criteria that must be satisfied by the hardware implementations to realize quantum advantage with sufficient statistical significance. To meet the stringent criteria, we propose time-multiplexed, event-ready operations of cavity-assisted trapped-atom quantum network nodes that provide a continuous stream of entangled qubit pairs, with decision latencies of a microsecond and decision rates of $8\times 10^3~\text{s}^{-1}$ per channel for a representative metropolitan-scale $50$-km fiber network to keep up with the fast-changing environment, such as financial markets and electric grid networks. These results bridge the gap between the theoretical notions of the quantum-classical gap in nonlocal games and concrete implementations that meet the stringent operational criteria for achieving robust quantum advantage in realistic coordination tasks.

quant-ph↗

arXiv2026

Overflow-Safe Polylog-Time Parallel Minimum-Weight Perfect Matching Decoder: Toward Experimental Demonstration

Fault-tolerant quantum computation (FTQC) requires fast and accurate decoding of quantum errors, which is often formulated as a minimum-weight perfect matching (MWPM) problem. A determinant-based approach has been proposed as a novel method to surpass the conventional polynomial runtime of MWPM decoding via the blossom algorithm, asymptotically achieving polylogarithmic parallel runtime. However, the existing approach requires an impractically large bit length to represent intermediate values during the computation of the matrix determinant; moreover, when implemented on a finite-bit machine, the algorithm cannot detect overflow, and therefore, the mathematical correctness of such algorithms cannot be guaranteed. In this work, we address these issues by presenting a polylog-time MWPM decoder that detects overflow in finite-bit representations by employing an algebraic framework over a truncated polynomial ring. Within this framework, all arithmetic operations are implemented using bitwise XOR and shift operations, enabling efficient and hardware-friendly implementation. Furthermore, with algorithmic optimizations tailored to the structure of the determinant-based approach, we reduce the arithmetic bit length required to represent intermediate values in the determinant computation by more than $99.9\%$, making it possible to implement it on machines supporting $512$-bit computing while preserving the decoder's polylog runtime scaling. These results open the possibility of a proof-of-principle demonstration of the polylog-time MWPM decoding in the early FTQC regime.

quant-ph↗

arXiv2026

Classical simulation and quantum resource theory of non-Gaussian optics

We propose efficient algorithms for classically simulating Gaussian unitaries and measurements applied to non-Gaussian initial states. The constructions are based on decomposing the non-Gaussian states into linear combinations of Gaussian states. We use an extension of the covariance matrix formalism to efficiently track relative phases in the superpositions of Gaussian states. We get an exact simulation algorithm, which costs quadratically with the number of Gaussian states required to represent the initial state, and an approximate simulation algorithm, which costs linearly with the $l_1$ norm of the coefficients associated with the superposition. We define measures of non-Gaussianity quantifying this simulation cost, which we call the Gaussian rank and the Gaussian extent. From the perspective of quantum resource theories, we investigate the properties of this type of non-Gaussianity measure and compute optimal decompositions for states relevant to continuous-variable quantum computing.

quant-ph↗