Variational Quantum Algorithm for Markovian Open Quantum Systems

We propose a quantum-classical hybrid variational algorithm to simulate the non-equilibrium stationary states of Markovian open quantum systems, named the dissipative-system Variational Quantum Eigensolver (dVQE) [1]. In order to employ the variational optimization technique for a unitary quantum circuit, we first map a density matrix into a wavefunction with the doubled number of qubits, and then design the unitary quantum circuit so that the physical requirements for a mixed state are fulfilled. This allows us to define a cost function that consists of the time evolution generator of the Markovian quantum master equation. After the optimization, physical observables are evaluated by a quantum circuit with the original number of qubits. Our dVQE scheme is demonstrated by both numerical simulation on a classical computer and actual quantum simulation that makes use of the device provided in Rigetti Quantum Cloud Service.
[1] N. Yoshioka, Y. O. Nakagawa, K. Mitarai, and K. Fujii, arXiv:1908.09836 (2019).