Hamiltonian Simulation Using Linear Combinations of Unitary Operations

TL;DR

This paper introduces a novel Hamiltonian simulation method using linear combinations of unitaries, offering improved efficiency and error scaling over traditional product-based algorithms.

Contribution

It develops a nearly deterministic implementation of linear combinations of unitaries, outperforming existing simulation techniques in efficiency and error scaling.

Findings

Superior performance compared to product formula methods

Better scaling with simulation error

Optimal implementation among similar approaches

Abstract

We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably, scales better with the simulation error than any known Hamiltonian simulation technique. Our main tool is a general method to nearly deterministically implement linear combinations of nearby unitary operations, which we show is optimal among a large class of methods.