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

Abstract

Non-Markovian open quantum systems are 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 of 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/ǫ)) for evolution time t and precision ǫ. Our derivation of the succinct representation is based on stochastic Schrödinger equations, which could lead to new alternatives to deal with other types of open quantum systems.

Description and complexity of Non-markovian open quantum dynamics

“…While the quantum simulatability of Markovian manybody open quantum systems [31][32][33][34], and many-body closed quantum systems [35][36][37][38] have been extensively studied, non-Markovian open quantum systems have remain relatively unexplored. A recent work developed an efficient quantum algorithm for non-Markovian dynamics where a chain Markovian dilation is known [39]. For spin-boson models with rapidly decaying spectral density functions, a Markovian dilation with finite Lieb-Robinson velocity has previously been established [40,41] which implies quantum simulatability of the model.…”