Variational Quantum Simulations of the Lindblad Equation on Near-Term Quantum Computers

Studying the nonunitary dynamics of open quantum systems is of a paramount importance due to the inevitable presence of decoherence and dissipation in realistic strongly correlated systems. In this work, we introduce a variational hybrid quantum algorithm to simulate the Lindblad master equation for time-evolving Markovian open quantum systems on near-term quantum computers. We also illustrate how can it be implemented to solve the adjoint Lindblad equation for time-evolving quantum observables in the Heisenberg picture framework. We design and optimize low-depth variational quantum circuits that efficiently capture dynamics for open quantum systems, and highlight the difference between them and those used for capturing the dynamics of isolated quantum systems. We benchmark and test the algorithm on different system sizes, showing its potential and consistency with near-term hardware capabilities.