本文研究量子魔法分布对电路经典可模拟性的影响，发现 Pauli 求值任务在魔法深度变化时出现从 P 到 GapP-完全的复杂性相变，并给出魔法深度一电路在加性误差下的多项式时间经典模拟算法。
摘要：
量子魔法是量子计算机无法被经典计算机高效模拟的必要资源。已有结果将量子魔法的数量（以 $T$ 门数量或稳定子秩刻画）与经典可模拟性联系起来。然而，量子魔法的分布如何影响量子电路模拟的难度仍然是一个未解决的问题。在本工作中，我们研究了具有交替 Clifford 层和 $T$ 层的量子电路在三个任务上的经典可模拟性：振幅估计、采样和 Pauli 可观测量求值。在所有 $T$ 门都分布在单层的情况下，在合理假设下，以乘法误差进行振幅估计和采样已经是经典不可解的，但 Pauli 可观测量却容易求值。令人惊讶的是，仅增加一个 $T$ 门层，或者仅仅把所有 $T$ 门替换为 $T^{\frac{1}{2}}$，Pauli 求值任务就表现出从 P 到 GapP-完全的急剧复杂性转变。然而，当精度要求放宽到 1/poly($n$) 加性误差时，我们能够给出一个多项式时间经典算法，用于计算任意可分解为对角门乘积的魔法深度一电路的振幅、Pauli 可观测量，以及从 $\log(n)$ 大小的边际分布中采样。我们的研究提供了模拟高魔法电路的新技术，同时揭示了它们的复杂性及其对魔法深度的显著依赖性。
英文摘要：
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to classical simulability. However, the effect of the distribution of quantum magic on the hardness of simulating a quantum circuit remains open. In this work, we investigate the classical simulability of quantum circuits with alternating Clifford and $T$ layers across three tasks: amplitude estimation, sampling, and evaluating Pauli observables. In the case where all $T$ gates are distributed in a single layer, performing amplitude estimation and sampling to multiplicative error are already classically intractable under reasonable assumptions, but Pauli observables are easy to evaluate. Surprisingly, with the addition of just one $T$ gate layer or merely replacing all $T$ gates with $T^{\frac{1}{2}}$, the Pauli evaluation task reveals a sharp complexity transition from P to GapP-complete. Nevertheless, when the precision requirement is relaxed to 1/poly($n$) additive error, we are able to give a polynomial time classical algorithm to compute amplitudes, Pauli observable, and sampling from $\log(n)$ sized marginal distribution for any magic-depth-one circuit that is decomposable into a product of diagonal gates. Our research provides new techniques to simulate highly magical circuits while shedding light on their complexity and their significant dependence on the magic depth.
Classical simulability of quantum circuits followed by sparse classical post-processing
Institute of Systems and Information Engineering, University of Tsukuba（筑波大学系统信息工程学院）；Tsukuba Institute for Advanced Research, University of Tsukuba（筑波大学筑波先进研究所）
Advantage of utilizing nonlocal magic resource in Haar-random circuits
South China University of Technology（华南理工大学）；State Key Laboratory of Luminescent Materials and Devices, South China University of Technology（发光材料与器件国家重点实验室，华南理工大学）
Classical simulation of a quantum circuit with noisy magic inputs
Graduate School of Quantum Science and Technology, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院量子科学与技术研究生院）；Department of Physics, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院物理系）
Scuola Superiore Meridionale（南方高等学院）；INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Dipartimento di Fisica ‘Ettore Pancini’, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）；NFN, Sezione di Napoli（那不勒斯国家核物理研究所）
Magic-induced computational separation in entanglement theory
Harvard University（哈佛大学）；Scuola Normale Superiore and Istituto Nanoscienze, Consiglio Nazionale delle Ricerche（意大利高等师范学院与纳米科学研究所，国家研究委员会）；Freie Universität Berlin（柏林自由大学）
Efficient fidelity simulation of high-rate magic distillation circuits
QuEra Computing Inc.（QuEra 计算公司）；Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算机科学联合中心）；Simons Institute for the Theory of Computing, University of California at Berkeley（加州大学伯克利分校西蒙斯计算理论研究所）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Department of Physics, Harvard University（哈佛大学物理学系）
Gauge and diffeomorphism invariance from quantum information principles
Institut Cartogràfic i Geològic de Catalunya（加泰罗尼亚地图与地质研究所）；Departamento de Física Teórica, Centro de Astropartículas y Física de Altas Energías (CAPA), Universidad de Zaragoza（萨拉戈萨大学理论物理系高能粒子与天体物理中心）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Barcelona Supercomputing Center (BSC)（巴塞罗那超级计算中心）
Shallow Quantum Circuits for Deep Chemistry via Valence Bond Embeddings
Institute for Computer Science, University of Augsburg（奥格斯堡大学计算机科学研究所）；Center for Advanced Analytics and Predictive Sciences, University of Augsburg（奥格斯堡大学高级分析与预测科学中心）
Limitations of Noisy Geometrically Local Quantum Circuits
University of Maryland（马里兰大学）；Joint Center for Quantum Information & Computer Science, University of Maryland and NIST（马里兰大学与美国国家标准与技术研究院联合量子信息与计算中心）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Shallow quantum circuit for generating extremely low-entangled approximate state designs
Pohang University of Science and Technology（浦项科技大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究院）；Korea Institute for Advanced Study（韩国高等研究院）
Entanglement geometry separates circuit cutting, classical hardness, and trainability
Quantum Software Lab（量子软件实验室）；University of Edinburgh, UK（爱丁堡大学）；IBM Research（IBM研究院）；Centre for Quantum Technologies（量子技术中心）；National University of Singapore（新加坡国立大学）
Numerical Evaluation of ZX Calculus Optimization for Solovay Kitaev Quantum Circuit Synthesis
University of Colombo（科伦坡大学）；The University of Western Australia（西澳大学）；University Paris City and University of Reunion（巴黎城市大学与留尼汪大学）；PEACCEL, AI for Biologics（PEACCEL生物制剂人工智能）
