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Abstract <p>We consider an <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11496_2025_9109_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\)</EquationSource> <!--PhysPart2570007Tsirulev-m1--> </InlineEquation>-qubit quantum system with a Hamiltonian, defined by an expansion in the Pauli basis, and propose a new algorithm for classical computing the exponential of the Hamiltonian. The algorithm is based on the representation of the exponential by the Dunford–Cauchy integral, followed by an efficient computation of the resolvent, and is suitable for Hamiltonians that are sparse in the Pauli basis. The practical efficiency of the algorithm is demonstrated by two illustrative examples.</p>

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Computation of Operator Exponentials Using the Dunford–Cauchy Integral

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  • 发表日期：

    2025年8月29日

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  • A. N. Tsirulev

摘要

Abstract

We consider an \(n\) -qubit quantum system with a Hamiltonian, defined by an expansion in the Pauli basis, and propose a new algorithm for classical computing the exponential of the Hamiltonian. The algorithm is based on the representation of the exponential by the Dunford–Cauchy integral, followed by an efficient computation of the resolvent, and is suitable for Hamiltonians that are sparse in the Pauli basis. The practical efficiency of the algorithm is demonstrated by two illustrative examples.