Time-Dependent Hamiltonian Simulation via Time-Independent Dynamics in a Larger Space

TL;DR

This paper introduces a quantum algorithm that simulates time-dependent Hamiltonian evolution by transforming it into a time-independent problem in a larger space, improving efficiency and matching state-of-the-art methods.

Contribution

It presents a novel approach using a larger space and Gaussian quadrature to efficiently simulate time-dependent Hamiltonians, improving upon previous methods.

Findings

Reduced dependence on evolution time and precision

Achieved complexity comparable to leading algorithms

Demonstrated efficiency of the time-independent framework

Abstract

In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian construction. A similar construction was first explored for this simulation problem by Watkins, Wiebe, Roggero, and Lee [PRX Quantum, 2024]. Our algorithm improves upon their work in terms of the dependence on evolution time and precision. In addition, the complexity matches the state-of-the-art simulation algorithms using other approaches. To achieve this improvement, we use Duhamel's principle to treat the clock and system Hamiltonians separately and exploit properties of Gaussian quadrature to reduce the simulation cost. Our approach demonstrates that time-dependent Hamiltonian simulation can be as efficient in a simpler framework and hence provides a new angle to model and simulate time-dependent systems.