发表机构
Graduate School of Quantum Science and Technology, Korea Advanced Institute of Science and Technology (KAIST); Center for Quantum Enabled-Computing, Center for Theoretical Physics of the Polish Academy of Sciences; University of Helsinki; HUN-REN Wigner Research Centre for Physics; Algorithmiq Ltd; Department of Physics, Korea Advanced Institute of Science and Technology（韩国科学技术院量子科学与技术研究生院; 波兰科学院理论物理中心量子使能计算中心; 赫尔辛基大学; 匈牙利研究与教育网络维格纳物理研究中心; Algorithmiq有限公司; 韩国科学技术院物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非高斯输入的自由费米子电路，提出精确采样与期望值估计的经典算法，涵盖被动与主动动力学，并改进马约拉纳单项式期望值的精确计算，为费米子量子模拟提供经典基准。
AI 中文摘要
模拟自由费米子（匹配门）电路的经典成本取决于输入态和计算任务。我们针对非高斯输入的电路开发了经典算法，处理精确采样以及期望值的加性误差和精确估计。对于由四模魔法态的n个副本组成的输入，我们给出了精确采样算法，将用于玻色采样的Clifford和Clifford算法推广到被动和主动自由费米子动力学，每个样本的最坏情况算术成本为O(2^n)，没有任何乘法多项式前因子。被动算法能够对近期 trapped-ion 实验的非相互作用区域进行精确模拟。我们还将最近开发的数关联器及相关可观测量的加性误差估计从被动动力学扩展到主动动力学，其运行时间在n和逆加性误差上为多项式，适用于由n个四模偶宇称态的乘积形成的输入态。我们的估计器使用适应于每个采样态的高斯态分解来控制其二阶矩。这包括对单个输出概率的估计。最后，我们证明对于由常数大小块组成的偶宇称乘积输入，对数权重的马约拉纳单项式的期望值可以在多项式时间内精确计算，改进了先前具有拟多项式运行时间的马约拉纳传播风格算法。精确算法通过动态规划处理输入块，在马约拉纳因子的子集之间共享计算。我们的算法套件为广泛的量子费米子模拟计算任务提供了经典基准。
英文摘要
The classical cost of simulating free-fermion (matchgate) circuits depends on both the input state and the computational task. We develop classical algorithms for circuits with non-Gaussian inputs, addressing exact sampling and both additive-error and exact estimation of expectation values. For inputs consisting of $n$ copies of the four-mode magic state, we give exact sampling algorithms, generalizing the Clifford and Clifford algorithm for Boson sampling, for passive and active free-fermion dynamics with worst-case arithmetic cost $O(2^n)$ per sample, without any multiplicative polynomial prefactor. The passive algorithm enables an exact simulation of the non-interacting regime of a recent trapped-ion experiment. We also extend recently developed additive-error estimation of number correlators and related observables from passive to active dynamics with runtime polynomial in $n$ and the inverse additive-error, for input states formed by products of $n$ four-mode even parity states. Our estimator uses a Gaussian-state decomposition adapted to each sampled state to control its second moment. This includes estimation of individual output probabilities. Finally, we show that for even-parity product inputs composed of constant-size blocks, expectation values of Majorana monomials of logarithmic weight can be computed exactly in polynomial time, improving on prior Majorana propagation-style algorithms with quasi-polynomial runtime. The exact algorithm processes the input blocks by dynamic programming, sharing calculations across subsets of Majorana factors. Our suite of algorithms provide classical benchmarks for fermionic quantum simulations across a broad spectrum of computational tasks.
Comments16 pages, 5 figures
