Lower bounds for the Trotter error

Hahn A, Hartung P, Burgarth D, Facchi P, Yuasa K (2025)

Publication Language: English

Publication Type: Journal article

Publication year: 2025

Journal

Physical Review A American Physical Society

Book Volume: 111

Article Number: 022417

Journal Issue: 2

DOI: 10.1103/PhysRevA.111.022417

Abstract

In analog and digital simulations of practically relevant quantum systems, the target dynamics can only be implemented approximately. The Trotter product formula is the most common approximation scheme as it is a generic method which allows tuning accuracy. The Trotter simulation precision will always be inexact for noncommuting operators, but it is currently unknown what the minimum possible error is. This is an important quantity because upper bounds for the Trotter error are known to often be vast overestimates. Here we present explicit lower bounds on the error, in norm and on states, allowing to derive minimum resource requirements. Numerical comparison with the true error shows that our bounds offer accurate and tight estimates.

Authors with CRIS profile

Daniel Burgarth Professur für Theoretische Physik

Involved external institutions

Macquarie University AU Australia (AU) University of Bari Aldo Moro / Università degli Studi di Bari Aldo Moro IT Italy (IT) Waseda University / 早稲田大学 JP Japan (JP)

How to cite

APA:

Hahn, A., Hartung, P., Burgarth, D., Facchi, P., & Yuasa, K. (2025). Lower bounds for the Trotter error. Physical Review A, 111(2). https://doi.org/10.1103/PhysRevA.111.022417

MLA:

Hahn, Alexander, et al. "Lower bounds for the Trotter error." Physical Review A 111.2 (2025).

BibTeX: Download