A quantum algorithm for finding the steady states of non-Markovian open quantum systems

Abstract

Finding new quantum algorithms for solving problems more efficiently than classical computers is at the forefront of research in quantum computing. Among fundamental problems, determining the steady states of general (i.e., non-Markovian) open quantum systems is crucial and presents significant challenges for classical methods. While recent quantum algorithms have been developed to time-evolve non-Markovian open quantum systems, they could become inefficient to obtain steady states when systems relax slowly. Here, we generalize the quantum algorithm developed by Ramusat and Savona to directly estimate steady states of Markovian open quantum systems to non-Markovian ones, by replacing the standard Liouvillian superoperator by the Hierarchical Equations Of Motion (HEOM) generator. We apply our algorithm to non-Markovian spin-only descriptions of the driven-dissipative one-mode and two-mode Rabi models, and compare our results to the ones obtained from the Markovian descriptions of the enlarged systems that include the modes. We show that our non-Markovian version of the algorithm provides an advantage in terms of (quantum) computational resources compared to Markovian embbedings.