通过拼接与合并实现晶格林德布拉德模拟
Lattice Lindbladian simulation by patching and merging
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中文总结 AI 辅助
本文提出利用局域性的拼接与合并技术，为晶格林德布拉德动力学开发近乎最优的量子算法，显著降低门计数，实现耗散多体系统的快速模拟。
中文摘要 AI 辅助
模拟由局部林德布拉德算符控制的耗散量子多体系统的动力学是量子计算中的一项基本任务。虽然哈密顿量模拟已实现了近乎最优的门计数，但林德布拉德模拟的类似结果仍然难以实现。在本工作中，我们通过利用晶格林德布拉德算符的局域性来开发量子算法。首先，我们考虑稀疏耗散系统，其中耗散稀疏地分布，包括边界驱动系统。我们为其动力学建立了一个近乎最优的量子算法，门计数为 $O(Nt \\, \mathrm{polylog}(Nt/\varepsilon))$，其中 $N$ 是系统大小，$t$ 是演化时间，$\varepsilon$ 是允许误差。然后，我们考虑具有有限范围相互作用和耗散的通用晶格林德布拉德算符，并开发了一种算法来模拟时间演化的可观测量，每个样本的门计数为 $O((Nt)^{4/3} \\, \mathrm{polylog}(Nt/\varepsilon))$，采样复杂度为 $\Theta(\varepsilon^{-2})$。在保留对 $1/\varepsilon$ 的多对数依赖的算法中，该门计数对系统大小的依赖关系是已知最小的。我们的算法基于两种利用局域性的技术：拼接和合并。拼接将耗散动力学分解为子系统上的动力学，误差呈指数级小，推广了Haah-Hastings-Kothari-Low算法中用于近乎最优哈密顿量模拟的关键思想。合并将反向耗散动力学吸收到演化的其他部分，大幅减少了与准概率采样相关的开销。这些结果表明，可以充分利用局域性来实现耗散多体动力学的快速量子模拟，为预测非平衡现象和制备所需量子态等应用开辟了道路。
英文摘要
Simulating the dynamics of dissipative quantum many-body systems governed by local Lindbladians is a fundamental task in quantum computation. While the near-optimal gate count has been achieved for Hamiltonian simulation, comparable results for Lindbladian simulation remain elusive. In this work, we develop quantum algorithms for lattice Lindbladians by exploiting their locality. First, we consider sparsely dissipative systems, in which the dissipation is sparsely located, including boundary-driven systems. We establish a near-optimal quantum algorithm for their dynamics with gate count $O(Nt \, \mathrm{polylog}(Nt/\varepsilon))$, where $N$ is the system size, $t$ is the evolution time, and $\varepsilon$ is the allowable error. We then consider generic lattice Lindbladians with finite-range interactions and dissipation, and develop an algorithm for simulating time-evolved observables with gate count $O((Nt)^{4/3} \, \mathrm{polylog}(Nt/\varepsilon))$ per sample with the sampling complexity $Θ(\varepsilon^{-2})$. The gate count has the smallest known dependence on the system size among algorithms retaining polylogarithmic dependence on $1/\varepsilon$. Our algorithms are based on two techniques that exploit locality: patching and merging. Patching decomposes dissipative dynamics into dynamics on subsystems with exponentially small error, generalizing a key idea underlying the Haah-Hastings-Kothari-Low algorithm for near-optimal Hamiltonian simulation. Merging absorbs reversed dissipative dynamics into other parts of the evolution, substantially reducing the overhead associated with quasi-probabilistic sampling. These results demonstrate that locality can be fully exploited to achieve fast quantum simulation of dissipative many-body dynamics, opening the way to applications such as predicting nonequilibrium phenomena and preparing desirable quantum states.
发表机构
- The University of Osaka（大阪大学）
- Department of Applied Physics, Graduate School of Engineering, The University of Tokyo（东京大学工学研究科应用物理系）
- RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）
机构由 AI 辅助整理，请以论文原文为准。
