Variational Quantum Algorithms for the Steady States of Open Quantum Systems
Huan-Yu Liu1,2, Tai-Ping Sun1,2, Yu-Chun Wu1,2,3*, and Guo-Ping Guo1,2,3,4
1Key Laboratory of Quantum Information, Chinese Academy of Sciences, School of Physics, University of Science and Technology of China, Hefei 230026, China 2CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China 3Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230088, China 4Origin Quantum Computing Hefei, Hefei 230026, China
Abstract：The solutions of the problems related to open quantum systems have attracted considerable interest. 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. We then optimize the parameters of the quantum circuit to find the steady state. Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels. The result shows 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 it provides a reference for the study of open quantum systems.
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2021, Vol. 38 
