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

TL;DR

This paper introduces an efficient quantum simulation method for time-dependent Hamiltonians using a truncated Dyson series, improving resource costs and implementing time ordering with superposition techniques.

Contribution

It extends Berry's approach by providing a general, resource-efficient simulation method for explicitly time-dependent Hamiltonians on quantum computers.

Findings

Achieves optimal logarithmic resource scaling with precision

Proposes two strategies for implementing time ordering

Extends Dyson series approximation to time-dependent cases

Abstract

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.