Suzuki type estimates for exponentiated sums and generalized Lie-Trotter formulas in JB-algebras

Sarah Chehade; Shuzhou Wang; Zhenhua Wang

doi:10.1016/j.laa.2023.10.004

Suzuki type estimates for exponentiated sums and generalized Lie-Trotter formulas in JB-algebras

Sarah Chehade, Shuzhou Wang, Zhenhua Wang

Quantum Computational Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Lie-Trotter-Suzuki product formulas are ubiquitous in quantum mechanics, computing, and simulations. Approximating exponentiated sums with such formulas are investigated in the JB-algebraic setting. We show that the Suzuki type approximation for exponentiated sums holds in JB-algebras, we give explicit estimation formulas, and we deduce three generalizations of Lie-Trotter formulas for arbitrary number elements in such algebras. We also extended the Lie-Trotter formulas in a Jordan Banach algebra from three elements to an arbitrary number of elements.

Original language	English
Pages (from-to)	156-169
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	680
DOIs	https://doi.org/10.1016/j.laa.2023.10.004
State	Published - Jan 1 2024

Funding

S. C. acknowledges DOE ASCR funding under the Quantum Computing Application Teams program, FWP number ERKJ347. This manuscript has been authored in part by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. The authors would like to thank the referee for the careful reading of the manuscript and valuable comments. S. C. acknowledges DOE ASCR funding under the Quantum Computing Application Teams program, FWP number ERKJ347 . This manuscript has been authored in part by UT-Battelle, LLC , under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan.

Keywords

JB-algebra
Jordan-Banach algebra
Lie-Trotter formula
Suzuki approximation

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10.1016/j.laa.2023.10.004

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title = "Suzuki type estimates for exponentiated sums and generalized Lie-Trotter formulas in JB-algebras",

abstract = "Lie-Trotter-Suzuki product formulas are ubiquitous in quantum mechanics, computing, and simulations. Approximating exponentiated sums with such formulas are investigated in the JB-algebraic setting. We show that the Suzuki type approximation for exponentiated sums holds in JB-algebras, we give explicit estimation formulas, and we deduce three generalizations of Lie-Trotter formulas for arbitrary number elements in such algebras. We also extended the Lie-Trotter formulas in a Jordan Banach algebra from three elements to an arbitrary number of elements.",

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author = "Sarah Chehade and Shuzhou Wang and Zhenhua Wang",

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N2 - Lie-Trotter-Suzuki product formulas are ubiquitous in quantum mechanics, computing, and simulations. Approximating exponentiated sums with such formulas are investigated in the JB-algebraic setting. We show that the Suzuki type approximation for exponentiated sums holds in JB-algebras, we give explicit estimation formulas, and we deduce three generalizations of Lie-Trotter formulas for arbitrary number elements in such algebras. We also extended the Lie-Trotter formulas in a Jordan Banach algebra from three elements to an arbitrary number of elements.

AB - Lie-Trotter-Suzuki product formulas are ubiquitous in quantum mechanics, computing, and simulations. Approximating exponentiated sums with such formulas are investigated in the JB-algebraic setting. We show that the Suzuki type approximation for exponentiated sums holds in JB-algebras, we give explicit estimation formulas, and we deduce three generalizations of Lie-Trotter formulas for arbitrary number elements in such algebras. We also extended the Lie-Trotter formulas in a Jordan Banach algebra from three elements to an arbitrary number of elements.

KW - JB-algebra

KW - Jordan-Banach algebra

KW - Lie-Trotter formula

KW - Suzuki approximation

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DO - 10.1016/j.laa.2023.10.004

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SN - 0024-3795

VL - 680

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EP - 169

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Suzuki type estimates for exponentiated sums and generalized Lie-Trotter formulas in JB-algebras

Abstract

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Keywords

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