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

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 Schrödinger equations, which could lead to new alternatives to deal with open quantum systems as well.

39 pages, no figures. To appear in Communications in Mathematical Physics

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• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory
• Accuracy guarantees and quantum advantage in analogue open quantum simulation with and without noise
• Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers
• Quantum algorithms based on quantum trajectories
• Quantum Simulation of Two-Level $PT$-Symmetric Systems Using Hermitian Hamiltonians