中文速览 本文提出了一种名为“子电路体积基准测试”（Subcircuit Volumetric Benchmarking, SVB）的创新方法，旨在解决评估当前量子计算机执行未来大规模、实用级量子算法能力的难题。由于现有硬件的规模和噪声水平有限，无法直接运行这些庞大的“目标”算法，因此难以衡量技术进展。SVB方法的核心思想是，从一个编译好的、任意大的目标算法电路中“剪切”出许多不同宽度（量子比特数）和深度（门层数）的小型子电路片段。随后，在实际的量子硬件上运行这些可管理的片段，并高效地测量它们的执行质量（具体为过程保真度）。通过分析这些片段的性能如何随其尺寸变化，该方法不仅能直观地展示设备的性能瓶颈，还能外推出整个目标电路的预期保真度，并最终计算出一个简洁的“能力系数”，用以量化当前系统距离成功执行目标算法还有多远。该方法具有可扩展性，能够为追踪量子实用性的进展提供一个稳定且有针对性的衡量标准。 English Research Briefing Research Briefing: Benchmarking quantum computers with any quantum algorithm 1. The Core Contribution This paper introduces Subcircuit Volumetric Benchmarking (SVB), a novel and scalable method for assessing a quantum computer’s performance on any target quantum algorithm, even those far too large to run on current hardware. The central thesis is that by systematically “snipping” small, executable subcircuits from a utility-scale target circuit and measuring their process fidelity, one can realistically predict the performance on the full circuit and track progress toward quantum utility. The primary conclusion, demonstrated on IBM Q systems, is that this method is not only practical but also reveals crucial performance limitations missed by simpler benchmarks. Specifically, it shows that optimistic fidelity predictions based on small-scale (e.g., 2-qubit) tests are misleading, with realistic performance on wider circuits being orders of magnitude worse due to the severe impact of crosstalk and other correlated errors. SVB distills this complex performance into a single, intuitive capability coefficient that quantifies how close a system is to successfully executing a given large-scale application. ...

中文速览 本文提出了一种高效且可高度并行化的经典算法，用于模拟受任意单量子比特噪声影响的n比特量子线路。该算法基于张量网络，其核心思想是将含噪量子系统的状态表示为一组矩阵乘积态（MPS）的系综。关键创新在于，对于作用在任意纯态上的每个单比特噪声过程，算法会选择一种特定的“展开”（即Kraus分解），这种展开能最小化该噪声比特与系统其余部分之间的平均纠缠（即纠缠形成熵）。通过将这个n比特问题映射到一个等效的两比特问题，作者为这种最优展开提供了封闭形式的解析解，从而避免了启发式优化并适用于任何单比特噪声模型。这种方法使得在给定的精度和噪声水平下，能够用更紧凑的MPS来表示量子态。此外，该工作还为这类基于展开的模拟器提供了严格的误差上限，并证明了先前工作中使用的固定展开策略，在其适用的特定噪声模型下，等价于本文方法在随机态上的特例。 English Research Briefing Research Briefing: Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings 1. The Core Contribution This paper introduces a highly general and efficient tensor-network-based algorithm for the classical simulation of one-dimensional noisy quantum circuits. The central thesis is that the simulation’s efficiency can be dramatically improved by strategically choosing how to represent the effect of noise. The primary contribution is a method to select a state-dependent, locally entanglement-optimal unraveling for any single-qubit noise channel. This is achieved by finding the specific Kraus decomposition that minimizes the average von Neumann entanglement (achieving the entanglement of formation) between the noisy qubit and the rest of the system. This approach provides a provably optimal local strategy for reducing the entanglement in the underlying Matrix Product State (MPS) representation, thereby lowering computational cost and improving accuracy for a given bond dimension, and importantly, comes with rigorous, a posteriori error guarantees. ...

中文速览 本文深入研究了在表面码架构下实现连续旋转门的实际时空成本。传统观点认为，减少T门数量是优化容错量子算法的关键。然而，本文指出，随着魔术态蒸馏技术的进步，总运行时间或物理量子比特数（即时空体积）是更根本的成本指标。文章的核心贡献在于，它首次为一种名为“催化剂塔”的高级旋转合成技术构建了明确的表面码物理布局，并与传统的Clifford+T门合成方法进行了全面的资源成本比较。研究以期权定价算法中的两个实用子程序为例，进行了详细分析。主要结论是：在低到中等码距（这正是早期容错量子计算机的典型工作范围）下，催化剂塔不仅能显著缩短运行时间，还能降低总体的时空体积，表现出比传统方法更高的效率。然而，在高码距下，催化剂塔引入的额外辅助量子比特开销会超过其节省的T门成本，此时传统门合成方法反而更优。 因此，该研究为早期容错应用中的算法选择和硬件资源评估提供了重要的量化依据。 English Research Briefing Research Briefing: Space and Time Cost of Continuous Rotations in Surface Codes 1. The Core Contribution This paper provides a holistic, architecture-aware resource analysis of implementing continuous-angle rotation gates on a surface code quantum computer. The central thesis is that the optimal implementation strategy is not universal but depends critically on the operating regime, specifically the code distance \(d\). The authors conclude that “catalyst tower” circuits—an advanced technique for parallelizing rotations—are superior to conventional Clifford+T gate synthesis at the low-to-medium code distances expected for early fault-tolerant devices, offering reductions in both runtime and overall spacetime volume. However, at high code distances, the substantial ancilla qubit overhead required by catalyst towers makes conventional synthesis the more resource-efficient approach. This work reframes the optimization problem from minimizing abstract T-counts to minimizing concrete spacetime cost on a realistic hardware platform. ...

中文速览 这篇论文展示了在一个由256个中性镱原子构成的量子处理器上实现的容错量子计算。其核心创新在于一种“擦除转换”技术，该技术将关键的门操作错误转化为可被探测到的原子丢失。这种方法使得量子纠错变得更加高效。研究团队通过该平台成功演示了两项关键实验：一是制备并纠缠了24个逻辑量子比特（由48个物理原子编码），并有效纠正了原子丢失错误；二是在多达28个逻辑量子比特（由112个物理原子编码）上运行了Bernstein-Vazirani算法。实验结果明确表明，经过编码和容错处理的逻辑电路，其性能超越了直接使用物理比特的未编码电路，这为利用中性原子平台实现可扩展、可靠的量子计算开辟了道路。 English Research Briefing Research Briefing: Fault-tolerant quantum computation with a neutral atom processor 1. The Core Contribution This paper presents the design and experimental demonstration of fault-tolerant quantum computation on a scalable neutral atom processor. The central thesis is that by architecting the system to convert dominant gate errors into detectable atom loss (erasure errors), it is possible to achieve superior performance with logical qubits compared to their physical counterparts, even with low-distance quantum error-correcting codes. The authors substantiate this by implementing two key demonstrations at an unprecedented scale: the creation of an entangled 24-logical-qubit cat state and the execution of the Bernstein-Vazirani algorithm on up to 28 logical qubits. The primary conclusion and most important takeaway is that the combination of large qubit numbers, all-to-all connectivity via atom transport, and hardware-level erasure conversion establishes neutral atoms as a highly promising platform for building scalable, reliable quantum computers. ...

中文速览 这篇论文提出了一个通用框架，用于在同调积（homological product）量子码中构建逻辑门。其核心思想是，利用构成同调积码的输入码（可以是经典码或量子码）自身的对称性（即自同构），来系统地生成最终量子码的逻辑操作。这些逻辑操作被称为“自同构小工具”（automorphism gadgets），在物理层面通过物理量子比特的置换（permutation）和子系统上的量子线路组合实现。论文证明，当输入码具有一种更强的对称性——“Tanner图自同构”时，对应的逻辑门可以仅通过物理比特置换来完成。此外，研究还表明，这些小工具具有内在的容错特性，例如在假设物理置환无错的情况下，它们能保持量子码的有效距离。该工作为设计具有高效逻辑门的qLDPC码提供了新方法，特别适用于具备长程连接能力的量子计算平台。 English Research Briefing Research Briefing: Automorphism gadgets in homological product codes 1. The Core Contribution This paper presents a comprehensive and constructive framework for designing logical operations in homological product codes, a powerful family of quantum low-density parity-check (qLDPC) codes. The central thesis is that permutation symmetries (automorphisms) of the classical or quantum input codes can be systematically “lifted” to create logical gates on the resulting output code. The primary conclusion is that this method yields a rich set of “automorphism gadgets”—logical operations implemented by physical qubit permutations combined with subsystem-level circuits. Crucially, the authors prove that these gadgets can be inherently fault-tolerant, preserving the effective distance of the code under the assumption of error-free permutations. This work provides a general-purpose recipe for enriching the gate sets of qLDPC codes, moving beyond topological constraints and offering a practical path toward fault-tolerant computation in architectures with long-range connectivity. ...

中文速览 本文提出了一种名为“多项式深度对偶变换”的新概念。这种变换利用一个深度为系统尺寸多项式的量子线路，将一类复杂的量子哈密顿量（如二维环面码）精确地映射到结构简单的经典哈密顿量（如两条解耦的经典伊辛链）。作者们形式化地证明了二维环面码与伊辛链的这种对偶关系，并由此提出了一种高效制备其任意温度下吉布斯态的算法，其线路复杂度为 \(O(L^3)\)，在效率和简洁性上优于先前方法。此外，论文通过计算证据推测，该方法可推广至多种稳定子码模型（如三维环面码、Haah码等）。最后，作者将此对偶概念扩展至林德布拉德算子（Lindbladians），证明了混合时间等关键动力学性质在对偶变换下保持不变。 English Research Briefing Research Briefing: Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains 1. The Core Contribution This paper introduces the concept of polynomial-depth duality, where a complex quantum Hamiltonian is shown to be equivalent to a simple classical Hamiltonian via a unitary transformation that can be implemented by a polynomial-depth quantum circuit. The central thesis is that if a quantum Hamiltonian is poly-depth dual to an efficiently samplable classical model, then its Gibbs state can also be prepared efficiently. As its primary conclusion and proof-of-concept, the paper provides a formal proof that the 2D toric code Hamiltonian is poly-depth dual to two decoupled 1D classical Ising chains. This discovery leads to a direct and highly efficient algorithm for preparing the Gibbs state of the 2D toric code at any temperature, with a circuit complexity of \(O(L^3)\), surpassing the efficiency and simplicity of previous approaches. ...

中文速览 本文的核心思想在于，它弥合了近似酉设计（approximate unitary designs）和自由概率（free probability）这两个量子理论中的重要概念。研究人员引入并分析了一种名为“随机矩阵乘积酉算子（RMPU）”的高效可构造的随机量子线路模型。他们证明，该模型仅需多项式级别的资源（即多项式大小的“键维” \(\chi\)），便能为局域且有迹的观测量复现出高阶乱时序关联函数（OTOCs）在完全随机（Haar随机）情况下的取值。这一结果的关键在于，它表明RMPU能够生成“自由独立性”——这是随机矩阵理论中描述非对易随机变量统计无关性的核心性质，也是量子混沌系统中热化行为的深层特征。因此，该工作揭示了某些复杂的量子混沌和随机性特征，其生成所需的计算复杂度可能比之前预想的要低，为理解量子热化机制和设计具有量子优势的算法指明了新的方向。 English Research Briefing Research Briefing: Free Independence and Unitary Design from Random Matrix Product Unitaries 1. The Core Contribution This paper’s central thesis is that an efficiently constructible random quantum circuit model, the Random Matrix Product Unitary (RMPU), can generate features of profound quantum randomness previously associated only with computationally intractable, fully Haar-random unitaries. The primary conclusion is that RMPUs with a bond dimension \(\chi\) that scales polynomially with system size are sufficient to reproduce the Haar-random values of higher-order out-of-time-ordered correlators (OTOCs) for a physically relevant class of observables—namely, local operators with a non-zero trace. This demonstrates that free independence, the non-commutative analogue of statistical independence and a key signature of quantum chaos, can emerge from structured, shallow-complexity unitary ensembles. This finding bridges the gap between the theory of unitary designs and free probability, suggesting that certain complex aspects of thermalization are “easier” to achieve than a generic analysis might imply. ...

中文速览 本文的核心思想是提出一个基于霍普夫代数（Hopf Algebra）的全新数学框架，用于统一和形式化地描述量子纠错中的核心操作——编码“手术”（Quantum Code Surgery）。传统上，编码手术依赖于对特定拓扑编码（如表面码）的几何直觉，通过融合与分裂编码区域来实现逻辑门。本研究通过引入霍普夫代数的代数结构，将这些几何操作转化为严谨的代数运算（如乘法与余乘法）。这种方法不仅为现有手术技术提供了更深刻的理论基础，将其与编码的同调（Homology）性质联系起来，还可能催生出全新的、可被自动发现和验证的容错量子计算协议，从而为构建可扩展的容错量子计算机开辟了一条新的理论路径。 English Research Briefing Research Briefing: Homology, Hopf Algebras and Quantum Code Surgery 1. The Core Contribution This paper introduces a novel and highly abstract algebraic framework based on Hopf algebras to describe and generalize the operations of quantum code surgery. The central thesis is that the geometric and often ad-hoc procedures for merging and splitting topological code patches—the basis of surgery-based quantum computation—can be rigorously formalized as operations within a Hopf algebra. The primary conclusion is that this framework notifies the description of fault-tolerant gadgets, connecting the homological nature of logical operators directly to algebraic operations, thereby creating a powerful new language for designing and verifying complex fault-tolerant protocols. ...

中文速览 本文提出了一种通用的理论框架，用于构建和分析混合量子处理器中的稳定子态和纠错码，这类处理器由连续变量的谐振子（oscillator）和离散变量的量子比特（qudit）组成。作者推广了戈特斯曼-基塔耶夫-普瑞斯基尔（GKP）码的格点形式，引入了一类新的、被称为“局部紧阿贝尔（LCA）”的稳定子态。其核心思想是将量子比特的离散相空间“吸收”到谐振子的连续相空间中，形成一个完全由连续变量参数化的混合相空间。这些LCA态是纠缠的，且无法通过标准的辛（高斯-克利福德）操作从可分离的初态制备，因此代表了一种超越传统GKP态和量子比特稳定子态的新型非高斯量子资源。该框架不仅能够构建出可探测位移范围远超GKP态的量子态（放大因子为\(\sqrt{c}\)，其中\(c\)为量子比特的维度），还利用非交换几何中的森田等价（Morita equivalence）等数学工具，为设计通用的混合量子纠错码及其逻辑操作提供了系统性的方法。 English Research Briefing Research Briefing: Hybrid oscillator-qudit quantum processors: stabilizer states and symplectic operations 1. The Core Contribution This paper introduces a comprehensive and platform-agnostic theoretical framework for stabilizer states and error-correcting codes in hybrid quantum systems composed of continuous-variable (CV) oscillators and discrete-variable (DV) qudits. The central thesis is the development of a new class of stabilizer states, termed Locally Compact Abelian (LCA) states, which unify and generalize the Gottesman-Kitaev-Preskill (GKP) formalism. The paper’s primary conclusion is that these intrinsically entangled states constitute a novel class of non-Gaussian resources, fundamentally distinct from simple tensor products of oscillator and qudit stabilizer states. This distinction arises because LCA states cannot be generated by symplectic (Gaussian-Clifford) operations, and they offer practical advantages, such as an enhanced range for sensing displacements and a systematic method for constructing powerful hybrid quantum error-correcting codes. ...

中文速览 本文深入研究了用于量子低密度奇偶校验（LDPC）码的线性规划（LP）解码器，并揭示了其能力与局限。研究的核心贡献在于两个方面：首先，论文从理论上证明了标准LP解码器存在一个关键缺陷，即对于许多常见的量子LDPC码（如超图乘积码和双变量循环码），存在一些恒定权重（其大小不随码长增长）的特定错误模式，这些模式会导致LP解码器输出无法直接使用的非整数“分数解”，从而根本上阻碍了该解码器达到一个有效的纠错阈值。其次，为解决此问题，作者提出了一种创新的混合解码算法，即在LP解码后引入“有序统计解码”（Ordered Statistics Decoding, OSD）作为后处理步骤（称为LP+OSD）。该方法巧妙地将LP输出的分数值解释为量子比特的出错概率，并利用OSD进行系统性搜索，从而高效地找到一个满足测量结果（syndrome）的、低权重的整数纠错方案。数值模拟结果有力地表明，对于中等规模（可达数百个量子比特）的量子码，LP+OSD解码器的性能优于当前流行的“置信传播+OSD”（BP+OSD）解码器。这一发现指出，配备了高效后处理技术的LP解码器是近期量子纠错应用中一个极具竞争力的解码策略。 English Research Briefing Research Briefing: Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes 1. The Core Contribution This paper makes a two-fold contribution to the field of quantum decoding. First, it identifies and proves a fundamental limitation of standard Linear Programming (LP) decoders when applied to quantum Low-Density Parity-Check (LDPC) codes: the existence of generic, constant-weight error patterns that inevitably lead to ambiguous fractional solutions, preventing the decoder from achieving a performance threshold. Second, it proposes a powerful solution to this problem by augmenting the LP decoder with Ordered Statistics Decoding (OSD) as a post-processing step. The central conclusion is that this new hybrid decoder, LP+OSD, can outperform the state-of-the-art Belief Propagation with OSD (BP+OSD) decoder for intermediate-sized codes of up to a few hundred qubits, establishing it as a leading candidate for near-term quantum error correction. ...