Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems
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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 $${\mathcal {O}}(t\, \textrm{polylog}(t/\epsilon ))$$ O ( t polylog ( t / ϵ ) ) for evolution time t and precision $$\epsilon $$ ϵ . Our derivation of the succinct representation is based on stochastic Schrödinger equations, which could lead to new alternatives to deal with open quantum systems as well.