Real-time Quantum Monte Carlo Algorithm for Open Quantum Systems

We present a real-time stochastic approach based on density matrix quantum Monte Carlo (QMC) to simulate the dynamics of open quantum systems coupled to infinite-dimensional quantum baths. This approach stochastically samples the time-dependent density matrix of a many-body system evolving under a Markovian or non-Markovian master equation, enabling a comprehensive investigation of the dynamics of open quantum systems within the field of Hamiltonian quantum computing, including both gate-model quantum computing and quantum annealing. Through comparative analysis with exact solutions of quantum master equations, we demonstrate that QMC exhibits excellent agreement and showcases significant improvements in computational time and memory overhead. Additionally, the method's inherent ability to access the density matrix enables the efficient computation of various quantum information metrics, such as entanglement entropy and purity, during time evolution. As QMC is unconstrained by entanglement, this paves the way for larger scale simulations of various time-dependent system behaviors such as quantum quenches than is possible using alternative methods.