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

Zhenhua Wang

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arXiv · 2306.13791

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

Zhenhua Wang

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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.

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BibTeX RIS

Zhenhua Wang. 2023-06-23. Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in Banach Algebras. https://arxiv.org/abs/2306.13791

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