Global sensitivity analysis for optimization of the Trotter-Suzuki decomposition

TL;DR

This paper introduces a global sensitivity analysis method to optimize the Trotter-Suzuki decomposition in quantum simulations, reducing computational complexity by identifying and truncating insignificant Hamiltonian terms.

Contribution

It develops a novel application of Sobol sensitivity analysis for optimizing quantum simulation decompositions, enabling more efficient quantum computations.

Findings

Reduced number of exponentiations in the decomposition

Quantitative method for truncating unimportant Hamiltonian terms

Demonstrated effectiveness with a proof-of-concept example

Abstract

The Trotter-Suzuki decomposition is one of the main approaches for realization of quantum simulations on digital quantum computers. Variance-based global sensitivity analysis (the Sobol method) is a wide used method which allows to decompose output variance of mathematical model into fractions allocated to different sources of uncertainty in inputs or sets of inputs of the model. Here we developed a method for application of the global sensitivity analysis to the optimization of Trotter-Suzuki decomposition. We show with a proof-of-concept example that this approach allows to reduce the number of exponentiations in the decomposition and provides a quantitative method for finding and truncation 'unimportant' terms in the system Hamiltonian.