Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in Banach Algebras

TL;DR

This paper develops new error estimates for Lie-Trotter formulas in Banach algebras using Jordan products, introduces generalized formulas, and derives Suzuki symmetrized approximations, enhancing quantum computational methods.

Contribution

It introduces novel error bounds and generalized formulas for Lie-Trotter products in Banach algebras, connecting to Suzuki symmetrization techniques.

Findings

Two new error estimates for Lie-Trotter formulas

Introduction of generalized Lie-Trotter formulas

Derivation of Suzuki symmetrized approximation

Abstract

The Lie-Trotter formula has been a fundamental tool in quantum mechanics, quantum computing, and quantum simulations. The error estimations for the Lie-Trotter product formula play a crucial role in achieving scalability and computational efficiency. In this note, we present two error estimates of Lie-Trotter product formulas, utilizing Jordan product within Banach algebras. Additionally, we introduce two generalized Lie-Trotter formula and provide two explicit estimation formulas. Consequently, the renowned Suzuki symmetrized approximation for the exponentiated sums follows directly from our main Theorem.