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Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion

Authors Xiantao Li, Chunhao Wang

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ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum algorithms
  • open quantum systems
  • Lindblad simulation

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Abstract

We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution time and poly-logarithmically in inverse precision. However, our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding. Our approach is based on a novel mathematical treatment of the evolution map, which involves a higher-order series expansion based on Duhamel’s principle and approximating multiple integrals using scaled Gaussian quadrature. Our method easily generalizes to simulating quantum dynamics with time-dependent Lindbladians. Furthermore, our method of approximating multiple integrals using scaled Gaussian quadrature could potentially be used to produce a more efficient approximation of time-ordered integrals, and therefore can simplify existing quantum algorithms for simulating time-dependent Hamiltonians based on a truncated Dyson series.

Cite As Get BibTex

Xiantao Li and Chunhao Wang. Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 87:1-87:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ICALP.2023.87

Author Details

Xiantao Li
  • Department of Mathematics, Pennsylvania State University, University Park, PA, USA
Chunhao Wang
  • Department of Computer Science and Engineering, Pennsylvania State University, University Park, PA, USA

Funding

Both XL and CW were supported by a seed grant from the Institute of Computational and Data Science (ICDS).
  • Li, Xiantao: XL’s research is supported by the National Science Foundation Grants DMS-2111221.
  • Wang, Chunhao: CW acknowledges support from National Science Foundation grant CCF-2238766 (CAREER).

Acknowledgements

We thank the anonymous reviewers for the valuable comments.

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