Variational Quantum Algorithms for Steady States of Open Quantum Systems

Solving problems related to open quantum systems has attracted many interests. Here, we propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation, which can be efficiently evaluated with quantum circuits. Then we optimize the parameters of the quantum circuit to find the steady state. Numerical simulations are performed on the one-dimensional transverses field Ising model with dissipative channels. The result showed that the fidelity between the optimal mixed state and the true steady state is over 99\%. This algorithm is derived from the natural idea of expressing mixed states with purification and provides a reference for the study of open quantum systems.