  We provide a general method for efficiently simulating time-dependent
Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is
based on approximating the truncated Dyson series of the evolution operator,
extending the earlier proposal by Berry to evolution generated by explicitly
time-dependent Hamiltonians. Two alternative strategies are proposed to
implement time ordering while exploiting the superposition principle for
sampling the Hamiltonian at different times. The resource cost of our
simulation algorithm retains the optimal logarithmic dependence on the inverse
of the desired precision.

Quantum Physics