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

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 polylog(t/is an element of)) for evolution time t and precision is an element of. Our derivation of the succinct representation is based on stochastic Schrodinger equations, which could lead to new alternatives to deal with open quantum systems as well.