We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization technique for a unitary quantum circuit, we map a mixed state into a pure state with a doubled number of qubits and design the unitary quantum circuit to fulfill the requirements for a density matrix. This allows us to define a cost function that consists of the time evolution generator of the quantum master equation. Evaluation of physical observables is, in turn, carried out by a quantum circuit with the original number of qubits. We demonstrate our dVQE scheme by both numerical simulation on a classical computer and actual quantum simulation that makes use of the device provided in Rigetti Quantum Cloud Service.
@article{arxiv.1908.09836,
title = {Variational Quantum Algorithm for Non-equilibrium Steady States},
author = {Nobuyuki Yoshioka and Yuya O. Nakagawa and Kosuke Mitarai and Keisuke Fujii},
journal= {arXiv preprint arXiv:1908.09836},
year = {2020}
}