Improved Quantum Computing with the Higher-order Trotter Decomposition

TL;DR

This paper introduces higher-order Trotter decompositions to enhance quantum control simulations, improving efficiency and accuracy in quantum algorithms and optimization tasks.

Contribution

It presents a novel application of higher-order Trotter decompositions to reduce computational costs and improve performance in quantum control and variational quantum algorithms.

Findings

Speed gains in quantum control simulations

Enhanced performance in variational quantum algorithms

Applicability to various quantum optimization tasks

Abstract

In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is often hard to diagonalize. In this paper, we mitigate this issue by substituting the time evolution segments with their Trotter decompositions, which reduces the propagator into a combination of single-qubit operations and fixed-time system evolutions. The resulting procedure can provide substantial speed gain with acceptable costs in the propagator error. As a demonstration, we apply the proposed strategy to improve the efficiency of the gradient ascent pulse engineering algorithm for searching optimal control fields. Furthermore, we show that the higher-order Trotter decompositions can provide efficient Ans\"atze for the variational quantum algorithm, leading to improved performance in solving the ground-state problem. The strategy presented here is also applicable for many other quantum optimization and simulation tasks.