Robust high-order quantum simulation using finite-width pulses

TL;DR

This paper introduces a comprehensive framework for enhancing quantum simulation pulse sequences to higher orders, ensuring robustness against finite pulse-width effects and improving error scaling.

Contribution

The authors develop a method to convert first-order pulse sequences into higher-order, robust sequences using Trotter formulas and dynamically corrected gates, applicable to various quantum simulations.

Findings

Sequences achieve arbitrarily high-order error scaling.

Framework maintains robustness against finite pulse-width effects.

Numerical verification confirms predicted error scalings.

Abstract

We present a general framework for promoting first-order pulse sequences in quantum simulation to higher-order sequences that maintain robustness in the presence of finite pulse-width effects. Our approach maps a given first-order pulse sequence to a first-order Trotter formula, applies higher-order Trotter-formula constructions, and then compiles the resulting evolution back into physically implementable finite-width pulses via dynamically corrected gates. The resulting sequences achieve arbitrarily high-order error scaling with respect to the control cycle time of the underlying first-order sequence while maintaining robustness to finite pulse-width effects. The framework also enables the use of multi-product formulas for more efficient constructions. We apply the framework to several physically motivated quantum-simulation tasks and numerically verify the predicted error scalings.