  Hybrid quantum-classical (HQC) algorithms make it possible to use near-term
quantum devices supported by classical computational resources by useful
control schemes. In this paper, we develop an HQC algorithm using an efficient
variational optimization approach to simulate open system dynamics under the
Noisy-Intermediate Scale Quantum(NISQ) computer. Using the time-dependent
variational principle (TDVP) method and extending it to McLachlan TDVP for
density matrix which involves minimization of Frobenius norm of the error, we
apply the unitary quantum circuit to obtain the time evolution of the open
quantum system in the Lindblad formalism. Finally, we illustrate the use of our
methods with detailed examples which are in good agreement with analytical
calculations.
