  Hybrid quantum-classical algorithms are among the most promising systems to
implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ)
technology. In this paper, at first, we investigate a quantum dynamics
algorithm for the density matrix obeying the von Neumann equation using an
efficient Lagrangian-based approach. And then, we consider the dynamics of the
ensemble-averaged of disordered quantum systems which is described by
Hamiltonian ensemble with a hybrid quantum-classical algorithm. In a recent
work [Phys. Rev. Lett. 120, 030403], the authors concluded that the dynamics of
an open system could be simulated by a Hamiltonian ensemble because of nature
of the disorder average. We investigate our algorithm to simulating incoherent
dynamics (decoherence) of open system using an efficient variational quantum
circuit in the form of master equations. Despite the non-unitary evolution of
open systems, our method is applicable to a wide range of problems for
incoherent dynamics with the unitary quantum operation.
