  We propose a neural-network variational quantum algorithm to simulate the
time evolution of quantum many-body systems. Based on a modified restricted
Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be
efficiently implemented in near-term quantum computers with low measurement
cost. Using a qubit recycling strategy, only one ancilla qubit is required to
represent all the hidden spins in an RBM architecture. The variational
algorithm is extended to open quantum systems by employing a stochastic
Schrodinger equation approach. Numerical simulations of spin-lattice models
demonstrate that our algorithm is capable of capturing the dynamics of closed
and open quantum many-body systems with high accuracy without suffering from
the vanishing gradient (or 'barren plateau') issue for the considered system
sizes.
