No. 07
光晶格中任意相干原子重排的构建Constructing Arbitrary Coherent Rearrangements in Optical Lattices
提出超冷原子任意相干重排方案：借光超晶格动力学与离散线性光学的类比，用 Clements 方案由双阱阵列中的隧穿与位点分辨相移构造任意 N 维单粒子幺正变换，并数值评估强度噪声与寻址串扰的影响；推广到二维可实现深度随原子数亚线性增长的全对全重排。
光晶格中超冷原子运动自由度的相干控制，为利用大质量粒子实现可编程量子动力学提供了一条有前景的途径。我们提出并分析了一种实现超冷原子相干重排的方案，它对应于单粒子运动态上的任意幺正变换。利用光超晶格中的动力学与离散线性光学之间的类比，我们采用 Clements 方案，从双阱阵列中的隧穿与相移系统地构造任意全局 N 维单粒子幺正变换。隧穿被全局控制，而局部操作通过位点分辨的势移实现。我们数值研究了该方案对强度噪声和寻址串扰的敏感性。我们确定了这一幺正构造所支持的关键子程序，包括离散傅里叶变换和非原生哈密顿量的实现。将方案推广到二维，可实现电路深度随原子数亚线性标度的全对全原子重排，为原子重排提供高密度、高度可扩展的途径。
Abstract (English)
Coherent control of motional degrees of freedom of ultracold atoms in optical lattices offers a promising route toward programmable quantum dynamics with massive particles. We propose and analyze a scheme for implementing coherent rearrangement of ultracold atoms, corresponding to arbitrary unitary transformations on single-particle motional states. Exploiting an analogy between dynamics in optical superlattices and discrete linear optics, we employ the Clements scheme to systematically construct any global N -dimensional single-particle unitary from tunneling and phase shifts in arrays of double wells. Tunneling is controlled globally, while local operations are achieved through site-resolved potential shifts. We numerically investigate the susceptibility of the scheme to intensity noise and addressing crosstalk. We identify key subroutines enabled by this unitary construction, including the discrete Fourier transform and the implementation of non-native Hamiltonians. Extending the scheme to two dimensions enables all-to-all atomic rearrangement with a circuit depth that scales sublinearly with the atom number, providing a high-density and highly scalable approach to atom rearrangement. See 1 more figures
Alexander Roth, Liyang Qiu, Timon Hilker, Titus Franz, and Philipp M. Preiss
PRX Quantum 7, 043021 (2026)
10.1103/jsr3-2r5t
No. 08
超导 GKP 量子比特逻辑门与读出的建模Modeling Logical Gates and Readout of Superconducting Gottesman-Kitaev-Preskill Qubits
针对 GKP 码理论噪声模型与实际超导器件条件之间的脱节，用随机位移通道近似损耗与退相位对近似 GKP 码态的影响，分析 Clifford 门的误差扩散并提出可将门不保真度降低多个数量级的解码器修正，还用量子轨迹理论分析提高零拍读出效率的方案。
Gottesman-Kitaev-Preskill（GKP）码是实现容错量子计算的一条令人振奋的途径，因为高斯资源与 GKP 泡利本征态制备就足以实现通用量子计算。然而，GKP 量子比特理论上要纠的噪声模型——均匀随机位移误差——与实际超导器件中影响 GKP 量子比特的条件（真实噪声通道、逻辑门和低效测量）之间存在脱节。本工作从三方面弥合这一差距。首先，我们用随机位移通道近似损耗与退相位对近似 GKP 码态的影响，并表明该近似与数值结果吻合良好。其次，我们分析 GKP Clifford 门的误差扩散性质，并描述在每个门实现之后修改解码器如何能将门的不保真度降低多个数量级。最后，我们考虑零拍测量低效对逻辑态读出的影响，并分析一种利用量子轨迹理论提高测量效率的方案。
Abstract (English)
The Gottesman-Kitaev-Preskill (GKP) code is an exciting route to fault-tolerant quantum computing since Gaussian resources and GKP Pauli-eigenstate preparation are sufficient to achieve universal quantum computing. However, there is a disconnect between the noise model that GKP qubits are in theory designed to correct—uniform random displacement errors—and the conditions that affect GKP qubits in superconducting devices in practice: realistic noise channels, logical gates, and inefficient measurements. In this work we bridge this gap in three ways. First, we approximate the effect loss and dephasing on approximate GKP codestates using a random displacement channel, and show that this approximation matches well with numerics. Second, we analyze the error-spreading properties of GKP Clifford gates and describe how a modification in the decoder following the implementation of each gate can reduce the gate infidelity by multiple orders of magnitude. Finally, we consider the effect of homodyne measurement inefficiencies on logical state readout and analyze a scheme to improve the measurement efficiency using the theory of quantum trajectories. See 14 more figures
Mackenzie H. Shaw, Andrew C. Doherty, and Arne L. Grimsmo
PRX Quantum 7, 043020 (2026)
10.1103/k1tk-wh93
No. 09
借助里德堡阻塞在光镊中快速制备单原子Fast Single-Atom Preparation in Optical Tweezers via Rydberg Blockade
利用光镊内的里德堡阻塞与自电离，在微秒尺度上从多占据光镊中逐个移除原子：Yb-171 中经双光子激发在 64.8 μs 内把多原子概率降至 1%，比光辅助碰撞快两个数量级；从亚稳态单光子激发时填充率可达 74.8%。
持续补充的光镊阵列将解锁中性原子量子比特的无深度限制量子电路。限制这类系统循环时间的一个关键瓶颈是：把原子从最初装载了多个原子的光镊中移除。在光辅助碰撞这一传统技术中，缓慢的碰撞动力学把移除多余原子的时间尺度限制在数毫秒。在此，我们提出并演示了一种利用镊内里德堡阻塞和自电离，在微秒时间尺度上从多占据光镊中一次选择性移除一个原子的方案。我们在 Yb-171 中于两种互补情形下演示了该协议。从基态进行双光子里德堡激发时，我们在 64.8 μs 内将多原子概率降至 1%，同时在 58.2(2)% 的光镊中保留单原子，这与相同实验条件下光辅助碰撞达到的填充率相当，但速度快了两个数量级以上。从亚稳态 3P0 进行单光子激发时，单原子损耗降低使填充率提高到 74.8(3)%，代价是制备 3P0 态原子所需的额外时间开销。最终填充率受一种尚未解释的两体损耗机制限制；若能解决，将可实现快速、准确定性的装载。
Abstract (English)
Continuously replenished optical tweezer arrays will unlock unlimited-depth quantum circuits with neutral atom qubits. A key bottleneck limiting the cycle time of these systems is removing atoms from tweezers initially loaded with more than one atom. In the conventional technique of light-assisted collisions, slow collisional dynamics limit the timescale for removing excess atoms to several milliseconds. Here, we propose and demonstrate a scheme for selectively removing one atom at a time from multiply occupied tweezers on a microsecond timescale, using intra-tweezer Rydberg blockade and autoionization. We demonstrate the protocol in Yb 171 in two complementary regimes. With two-photon Rydberg excitation from the ground state, we reduce the multi-atom probability to 1% in 64.8 μ s , while retaining single atoms in 58.2 ( 2 ) % of the tweezers, which is comparable to the filling fraction achieved with light-assisted collisions under the same experimental conditions, but over two orders of magnitude faster. With single-photon excitation from the metastable state P 0 3 , reduced single-atom loss enables a higher filling fraction of 74.8 ( 3 ) % , at the cost of additional temporal overhead to prepare the atoms in P 0 3 . The final filling fraction is limited by an unexplained two-body loss mechanism, which, if solved, could enable fast, quasi-deterministic loading.
Yiyi Li, Vernon M. Hughes, Michael Peper, Yicheng Bao, Chenyuan Li, Sanzhar Bissenali, and Jeff D. Thompson
PRX Quantum 7, 043019 (2026)
10.1103/8t3p-x6s7
No. 10
里德堡原子阵列中伊辛临界奇异对称性的介子谱学Meson Spectroscopy of Exotic Symmetries of Ising Criticality in Rydberg Atom Arrays
在里德堡原子量子处理单元中利用可调几何构型同时实现单链与梯子，识别出与 E8 一致的质量谱，并在弱耦合梯子中首次给出伊辛激发重组为 D8(1) 预言的束缚态谱的迹象，为研究准粒子相互作用、几何与临界性的交织提供直接窗口。
伊辛模型是探索量子临界系统中涌现对称性的标准平台。一维伊辛链的临界点由共形伊辛场论描述，该场论在存在磁微扰时仍可积，从而产生与例外李代数 E8 相关联的有质量粒子。将两条伊辛链弱耦合为梯子会破坏可积性，并预言会使解耦链的基本扭结激发束缚，产生由 D8(1) 理论描述的更丰富的激发谱。E8 激发的实验迹象可以说已在自旋链材料 CoNb2O6 的散射研究中被观察到，但链间耦合产生的束缚态谱一直难以直接观测。在此，我们在里德堡原子量子处理单元中探测这些涌现对称性，利用其可调几何构型实现链与梯子两种构型。我们在单链临界点识别出与 E8 一致的质量谱，并在弱耦合梯子中首次报告伊辛激发重组为 D8(1) 对称性所预言的束缚态谱的迹象。我们的结果展示了里德堡平台在研究量子多体系统对称性涌现方面的能力，并为准粒子相互作用、几何与临界性之间的相互作用提供了直接窗口。
Abstract (English)
The Ising model serves as a canonical platform for exploring emergent symmetry in quantum critical systems. The critical point of the 1D Ising chain is described by a conformal Ising field theory, which remains integrable in the presence of a magnetic perturbation, leading to massive particles associated with the exceptional Lie algebra E 8 . Weakly coupling two Ising chains into a ladder breaks this integrability and is predicted to bind the elementary kink excitations of the decoupled chains, giving rise to a richer spectrum of excitations described by the D 8 ( 1 ) theory. Experimental signatures of E 8 excitations have arguably been observed in scattering studies of the spin chain material CoNb 2 O 6 , but direct observation of the bound-state spectrum emerging from interchain coupling has remained elusive. Here, we probe these emergent symmetries in a Rydberg atom quantum processing unit, leveraging its tunable geometry to realize both chain and ladder configurations. We identify mass spectra consistent with E 8 at the single-chain critical point and, in the weakly coupled ladder, report the first signatures of the reorganization of Ising excitations into the bound-state spectrum predicted by D 8 ( 1 ) symmetry. Our results demonstrate the power of Rydberg platforms for investigating symmetry emergence in quantum many-body systems and provide a direct window into the interplay of quasiparticle interactions, geometry, and criticality.
Joseph Vovrosh, Julius de Hond, Sergi Julià-Farré, Johannes Knolle, and Alexandre Dauphin
PRX Quantum 7, 043018 (2026)
10.1103/w3zn-7xht
No. 11
自由互信息与高阶乱序时序关联函数Free Mutual Information and Higher-Point Out-of-Time-Ordered Correlators
借鉴自由概率论提出自由互信息，用以刻画算符在双指数维度的算符空间中的扩散，并证明它可写成所有高阶乱序时序关联函数的加权和，从而为算符遍历性给出信息论解释。
我们引入一个称为自由互信息（FMI）的量，它借用自由概率论中的概念，作为量子混沌的一种新的物理度量。该量刻画时间演化后的算符在希尔伯特空间全部可能算符所构成的空间（其维数随自由度数目呈双指数增长）中的扩散，因而给出了比物理空间中已被充分理解的算符增长现象更精细的算符扩散图像。我们推导出适用于任意物理体系的两个核心结果：第一，给出两个可观测量 A(t) 与 B 的自由互信息的显式「库仑气体」公式，用乘积算符 A(t)B 的本征值表示；第二，给出一个一般关系，把自由互信息表示为所有高阶乱序时序关联函数（OTOC）的加权和。第二个结果为高阶 OTOC 提供了精确的信息论解释：它们集体地量化了算符遍历性以及向自由性的趋近。鉴于近期在高阶 OTOC 实验测量方面的进展，这一物理解释尤为有用。我们在多种混沌体系中（包括随机幺正线路与混沌自旋链）识别出自由互信息与高阶 OTOC 的普适行为，表明双指数算符空间中的扩散是量子多体混沌的一般特征。同时，自由互信息在各种非混沌体系（包括某些幺正设计）中的非普适行为表明，存在算符在物理空间中扩散但在算符空间中仍保持局域的情形。因此，自由互信息是比标准四点 OTOC 更敏锐的混沌判据。
Abstract (English)
We introduce a quantity called the free mutual information (FMI), adapted from concepts in free probability theory, as a new physical measure of quantum chaos. This quantity captures the spreading of a time-evolved operator in the space of all possible operators on the Hilbert space, which is doubly exponential in the number of degrees of freedom. It thus provides a finer notion of operator spreading than the well-understood phenomenon of operator growth in physical space. We derive two central results which apply in any physical system: first, an explicit “Coulomb gas” formula for the FMI of two observables A ( t ) and B in terms of the eigenvalues of the product operator A ( t ) B ; and second, a general relation expressing the FMI as a weighted sum of all higher-point out-of-time-ordered correlators (OTOCs). This second result provides a precise information-theoretic interpretation for the higher-point OTOCs as collectively quantifying operator ergodicity and the approach to freeness. This physical interpretation is particularly useful in light of recent progress in experimentally measuring higher-point OTOCs. We identify universal behaviors of the FMI and higher-point OTOCs across a variety of chaotic systems, including random unitary circuits and chaotic spin chains, which indicate that spreading in the doubly exponential operator space is a generic feature of quantum many-body chaos. At the same time, the non-generic behavior of the FMI in various non-chaotic systems, including certain unitary designs, shows that there are cases where an operator spreads in physical space but remains localized in operator space. The FMI is thus a sharper diagnostic of chaos than the standard four-point OTOC. See 17 more figures
Shreya Vardhan and Jinzhao Wang
PRX Quantum 7, 043017 (2026)
10.1103/wt7l-6385
No. 12
拓扑稳定子码能隙边界的算法构造：低开销平面量子LDPC码Algorithmic Construction of Gapped Boundaries for Topological Stabilizer Codes: A Route to Low-Overhead Planar qLDPC Codes
针对 qLDPC 码多定义于周期格点、而可扩展硬件偏好开放边界平面架构的矛盾，建立了构造二维拓扑稳定子码全部能隙边界与缺陷的算符代数框架，并在环面码、颜色码等多种码上验证。
量子低密度奇偶校验（qLDPC）码有望实现低开销的容错量子存储，但许多领先的构造天然定义在周期格点上，而可扩展的量子硬件更青睐具有开放边界的平面架构。本工作中，我们发展了一套一般的算符代数框架与计算算法，用于构造二维拓扑泡利稳定子码的全部能隙边界与缺陷。从截断的体码出发，我们的方法识别边界规范算符、边界任意子及其弦算符，进而通过任意子凝聚与拓扑序补全构造微观边界哈密顿量，从而消除边界附近的局域逻辑算符。我们建立了体任意子与反常边界子系统码激发之间的一一对应关系，使得聚变规则、拓扑自旋与编织统计可直接从边界算符代数中提取。对于平移不变码，洛朗多项式表示把这些任务化为基于 Hermite 与 Smith 标准形的有限矩阵计算，从而可对素数与合数维数的 Z_d qudit 实现自动化构造。我们在环面码、颜色码、双半子码、六半子码与反常三费米子码上演示了该框架，并将其应用于双变量自行车码，揭示出大的逻辑维数与任意子弦异常长的平移周期。通过系统地把体拓扑数据转换为显式的边界与缺陷哈密顿量，我们的框架可作为构造具有开放边界的低开销平面 qLDPC 码以及工程设计容错逻辑操作的基础。
Abstract (English)
Quantum low-density parity-check (qLDPC) codes promise low-overhead fault-tolerant quantum memory, but many leading constructions are naturally defined on periodic lattices, whereas scalable quantum hardware favors planar architectures with open boundaries. In this work, we develop a general operator-algebraic framework and computational algorithms for constructing all gapped boundaries and defects of two-dimensional topological Pauli stabilizer codes. Starting from a truncated bulk code, our method identifies boundary gauge operators, boundary anyons, and their string operators, and then constructs microscopic boundary Hamiltonians through anyon condensation and topological-order completion, thereby eliminating local logical operators near the boundary. We establish a one-to-one bulk-boundary correspondence between bulk anyons and excitations of the anomalous boundary subsystem code, enabling fusion rules, topological spins, and braiding statistics to be extracted directly from the boundary operator algebra. For translation-invariant codes, Laurent-polynomial representations reduce these tasks to finite matrix computations based on Hermite and Smith normal forms, enabling automated constructions for Z d qudits of both prime and composite dimension. We demonstrate the framework on toric, color, double-semion, six-semion, and anomalous three-fermion codes, and apply it to bivariate bicycle codes, revealing large logical dimensions and unusually long translation periods for anyon strings. By systematically converting bulk topological data into explicit boundary and defect Hamiltonians, our framework can serve as a foundation for constructing low-overhead planar qLDPC codes with open boundaries and for engineering fault-tolerant logical operations. See 33 more figures
Zijian Liang (梁子健), Bowen Yang (杨博闻), Joseph T. Iosue, and Yu-An Chen (陳昱安)
PRX Quantum 7, 043016 (2026)
10.1103/989h-xjqv
No. 13
利用局域层析高效学习全局量子信道Efficiently Learning Global Quantum Channels with Local Tomography
提出从局域到全局的重构框架，在条件互信息指数衰减的假设下以随系统尺寸多项式增长的样本量重构多比特信道，数值上可准确恢复多达 50 个比特信道的全局诊断量。
量子处理器可扩展的表征对于抑制噪声与不完美至关重要。随机测量协议能够高效获取局域可观测量，但推断多比特过程的全局一致描述仍然困难。这里我们提出一个面向一维多比特态与信道的从局域到全局的重构框架。只要以条件互信息量化的关联呈指数衰减，该方法就是高效的。特别地，我们证明在该假设下，所需样本数随系统尺寸以及所期望的全局重构误差（我们用真实与重构 Choi 态之间的迹范数距离来量化）的倒数呈多项式标度。我们的方法基于把局域影子层析与通过凸优化得到的局域最优恢复映射相结合。除这些严格保证外，我们还数值研究了该协议在局域 Lindblad 演化体系与含噪浅层线路上的性能。借助张量网络表示，我们重构了作用于多达 50 个比特的信道，并准确恢复过程保真度、Choi 态纯度以及按泡利权重分辨的过程矩阵元等全局诊断量。因此，我们的工作把局域影子层析这一强大工具箱扩展到可扩展的信道表征，并能获取全局性质。
Abstract (English)
Scalable characterization of quantum processors is crucial for mitigating noise and imperfections. While randomized measurement protocols enable efficient access to local observables, inferring a globally consistent description of multi-qubit processes remains challenging. Here we introduce a local-to-global reconstruction framework for one-dimensional multi-qubit states and channels. The method is efficient provided that correlations, as quantified by the conditional mutual information, decay exponentially. In particular, we prove that under this assumption, the required number of samples scales polynomially with the system size and the inverse of the desired global reconstruction error, which we quantify by the trace-norm distance between the true and the reconstructed Choi states. Our approach is based on combining local shadow tomography with locally optimal recovery maps obtained by convex optimization. We supplement these rigorous guarantees by studying the performance of the protocol numerically for a system evolving under a local Lindbladian and a noisy, shallow circuit. By employing a tensor network representation, we reconstruct channels acting on up to 50 qubits and accurately recover global diagnostics such as the process fidelity, the Choi state purity, and Pauli-weight-resolved process matrix elements. Our work thus extends the powerful toolbox of local shadow tomography to scalable channel characterization with access to global properties.
Zidu Liu and Dominik S. Wild
PRX Quantum 7, 043015 (2026)
10.1103/51mt-ghpn
No. 14
内禀平均力哈密顿量与强耦合量子热力学Intrinsic Hamiltonian of Mean Force and Strong-Coupling Quantum Thermodynamics
构建强耦合量子体系的热力学框架，确定可使热力学自洽的初态类别，仅用约化态与局域可及变量统一描述热力学过程与恒温性质，并给出最小功等操作性判据。
我们提出一个适用于与热库强耦合的量子体系的普适热力学框架，并确定了一类能够保证热力学行为自洽的初态。与其他方法不同，我们的框架统一描述了热力学过程与恒温性质，同时保持与标准弱耦合情形相同的规范自由度，并保留热力学熵的 von Neumann 表达式。此外，该表述完全以系统的约化态为出发点，仅依赖可通过局域微观操控获取的变量，因此与实验可及量直接相连，使得讨论受控系统的操作性问题成为可能——例如确定在存在强耦合热库时把系统驱动到两个指定态之间所需的最小功。我们用结构化的玻色热库这一典型模型验证了该方法。
Abstract (English)
We present a universal thermodynamic framework for quantum systems strongly coupled to thermal reservoirs, identifying the class of initial conditions required for consistent thermodynamic behavior. Unlike other approaches, our framework provides a unified description of both thermodynamic processes and thermostatic properties, while preserving the same gauge freedoms as in the standard weak-coupling regime and retaining the von Neumann expression for the thermodynamic entropy. Furthermore, the formulation is entirely in terms of the system’s reduced state, relying only on variables accessible through local microscopic control. It is therefore directly connected to experimentally accessible quantities, making it possible to address operational questions concerning the controlled system—such as determining the minimum work required to drive it between two prescribed states in the presence of a strongly coupled reservoir. We validate our approach using a paradigmatic model of a structured bosonic reservoir. See 4 more figures
Ignacio González, Sagnik Chakraborty, and Ángel Rivas
PRX Quantum 7, 043014 (2026)
10.1103/pwws-21cx
No. 15
巨型原子实现确定性被动量子态传输Enabling Deterministic Passive Quantum State Transfer with Giant Atoms
利用巨型原子与一维波导的耦合，通过设计耦合点位置与强度使发射波包具有时间反演对称性，两个耦合点即可把态传输保真度从 54% 提升到 87%，十个以上超过 99%。
以被动方式实现量子态传输可以成为可扩展量子网络的有力资源。这里我们展示，与一维波导耦合的巨型原子如何为这种被动、确定性的传输提供平台。具体而言，我们表明当巨型原子的尺度与所发射波包的宽度相当时，通过设计原子–波导耦合点的位置与强度，可以使该波包具有时间反演对称性。我们首先推导出一般性解析条件，在此条件下任意比特衰减可映射为依赖波矢的耦合，从而在无穷多耦合点的连续极限下保证完美态传输。随后，针对耦合点数目有限的实验相关构型，我们优化了耦合位置与耦合强度。我们证明传输保真度可以远超单耦合点的值（54%），仅用两个耦合点即可达到 87%，而十个及以上耦合点则超过 99%。我们进一步分析了该协议对耦合点无序以及比特频率波动的鲁棒性，并将形式体系推广到具有非线性色散的环境，表明色散引起的畸变可以通过精心选择的装置完全补偿。我们的结果确立了巨型原子作为实现高保真量子态传输的强大平台，并表明可以把含时控制转而编码进器件设计之中。
Abstract (English)
Achieving quantum state transfer in passive ways can become a powerful asset for scalable quantum networks. Here, we demonstrate how giant atoms coupled to 1D waveguides provide a platform for such a passive, deterministic transfer. Specifically, we show that when the giant atom’s extent is comparable to the width of the emitted wave packet, this wave packet can be designed to be time-reversal-symmetric by engineering the positions and strengths of atom-waveguide coupling points. We first derive general analytical conditions under which arbitrary qubit decays can be mapped to wave-vector-dependent couplings that guarantee perfect state transfer in the continuum limit of infinitely many coupling points. Then, for experimentally relevant configurations with a finite number of coupling points, we optimize the coupling positions and values. We demonstrate that the transfer fidelity can be boosted well beyond the value for a single coupling point (54%), reaching 87% with only two coupling points and exceeding 99% with ten or more. We further analyze the robustness of the protocol against disorder in the coupling points as well as frequency variations of the qubits and extend the formalism to environments with nonlinear dispersion, showing that dispersion-induced distortions can be fully compensated by judiciously chosen setups. Our results establish giant atoms as a powerful platform for realizing high-fidelity quantum state transfer and demonstrate how time-dependent control can be instead encoded into the device design.
Oliver Diekmann, Enrico Di Benedetto, Nicolas Jungwirth, Daniele De Bernardis, Zeyu Kuang, Francesco Ciccarello, Stefan Rotter, Peter Rabl, Alejandro González-Tudela, and Carlos Gonzalez-Ballestero
PRX Quantum 7, 043013 (2026)
10.1103/6wcb-nj42