Faster quantum simulation by randomization

TL;DR

This paper introduces a randomized ordering method for product formulas in quantum simulation, leading to stronger theoretical bounds and improved empirical performance in simulating Hamiltonian dynamics.

Contribution

The authors demonstrate that randomizing the order of summands in product formulas yields better approximation bounds and more efficient quantum simulations than traditional methods.

Findings

Stronger approximation bounds for randomized product formulas.

Asymptotic improvement over previous bounds that consider commutation.

Numerical evidence shows better empirical performance of the randomized approach.

Abstract

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation for product formulas of any given order, and thereby give more efficient simulations. Indeed, we show that these bounds can be asymptotically better than previous bounds that exploit commutation between the summands, despite using much less information about the structure of the Hamiltonian. Numerical evidence suggests that the randomized approach has better empirical performance as well.