Simulating the dynamics of time-dependent Hamiltonians with a truncated Dyson series

Understand

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.