  Quantum simulation is one of the key applications of quantum computing, which
accelerates research and development in the fields such as chemistry and
material science. The recent development of noisy intermediate-scale quantum
(NISQ) devices urges the exploration of applications without the necessity of
quantum error correction. In this paper, we propose an efficient method to
simulate quantum dynamics driven by a static Hamiltonian on NISQ devices, named
subspace variational quantum simulator (SVQS). SVQS employs the subspace-search
variational quantum eigensolver (SSVQE) to find a low-lying eigensubspace and
extends it to simulate dynamics within the subspace with lower overhead
compared to the existing schemes. We experimentally simulate the time-evolution
operator in a low-lying eigensubspace of a hydrogen molecule. We also define
the subspace process fidelity as a measure between two quantum processes in a
subspace. The subspace time evolution mimicked by SVQS shows the subspace
process fidelity of $0.88$-$0.98$.
