Simulating Markovian open quantum systems using higher-order series expansion

• URL: http://arxiv.org/abs/2212.02051v2
• Date: Sun, 9 Jul 2023 13:12:36 GMT
• Title: Simulating Markovian open quantum systems using higher-order series expansion
• Authors: Xiantao Li, Chunhao Wang
• Abstract summary: We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. Our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding.
• Score: 1.713291434132985
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution time and poly-logarithmically in inverse precision. However, our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding. Our approach is based on a novel mathematical treatment of the evolution map, which involves a higher-order series expansion based on Duhamel's principle and approximating multiple integrals using scaled Gaussian quadrature. Our method easily generalizes to simulating quantum dynamics with time-dependent Lindbladians. Furthermore, our method of approximating multiple integrals using scaled Gaussian quadrature could potentially be used to produce a more efficient approximation of time-ordered integrals, and therefore can simplify existing quantum algorithms for simulating time-dependent Hamiltonians based on a truncated Dyson series.

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