Adaptive random compiler for Hamiltonian simulation

TL;DR

This paper introduces an adaptive randomized compilation method for Hamiltonian simulation that dynamically updates sampling weights based on moment measurements, improving accuracy especially for systems with unbounded operators.

Contribution

It presents a novel adaptive algorithm that enhances randomized compilation by using moment measurements, extending applicability to continuous-variable and hybrid systems.

Findings

Improves simulation accuracy with minimal additional gates

Extends randomized compilation to unbounded Hamiltonian systems

Numerical simulations confirm effectiveness

Abstract

Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application probabilities based on the strengths of Hamiltonian terms, as measured by the trace norm. However, relying solely on the trace norm to define sampling distributions may not be optimal, especially for continuous-variable and hybrid-variable systems involving unbounded operators, where quantifying Hamiltonian strengths is challenging. In this work, we propose an adaptive randomized compilation algorithm that dynamically updates sampling weights via low-order moment measurements of Hamiltonian terms, assigning higher probabilities to terms with greater uncertainty. This approach improves accuracy without significantly increasing gate counts and extends randomized compilation to continuous-variable and hybrid-variable systems by addressing the difficulties in characterizing the strengths of unbounded Hamiltonian terms. Numerical simulations demonstrate the effectiveness of our method.