Stochastic simulation of open quantum systems on NISQ Computers*

The unravelling of the quantum master equation (QME) based on quantum forking is proposed. Through the entanglement with log2(d) index qubits prepared in a superposition state, an initial quantum state can follow d quantum trajectories in superposition. An expectation value measurement on the target qubit at the end of the simulation yields the convex combination of the results from all possible paths, providing the ensemble-averaged solution of the QME. Regardless of the number of independent quantum trajectories needed in the unravelling, our method uses only a constant number of quantum circuit executions as well as the initial wave function. To simulate a generic stochastic Schrödinger equation, one needs to be able to perform an arbitrary non-Hermitian evolution. We also describe how this can be done systematically using projective measurement and post-selection. As proof of concept, we demonstrate the parallel unravelling using IBMQ hardware. We implement unravelling of various single-qubit and two-qubit master equations.