Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

• URL: http://arxiv.org/abs/2111.03240v2
• Date: Mon, 27 Feb 2023 21:23:01 GMT
• Title: Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems
• Authors: Xiantao Li, Chunhao Wang
• Abstract summary: Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. We provide a succinct representation of the dynamics of non-Markovian open quantum systems with quantifiable error. We also develop an efficient quantum algorithm for simulating such dynamics.
• Score: 1.713291434132985
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases, such as Hamiltonian evolution and Lindblad evolution, quantum simulation algorithms have been extensively studied, efficient quantum simulations for the dynamics of non-Markovian open quantum systems remain underexplored. The most immediate obstacle for studying such systems is the lack of a universal succinct description of their dynamics. In this work, we fulfill the gap of studying such dynamics by 1) providing a succinct representation of the dynamics of non-Markovian open quantum systems with quantifiable error, and 2) developing an efficient quantum algorithm for simulating such dynamics with cost $O(t\, \mathrm{polylog}(t/\epsilon))$ for evolution time $t$ and precision $\epsilon$. Our derivation of the succinct representation is based on stochastic Schr\"odinger equations, which could lead to new alternatives to deal with open quantum systems as well.

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