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Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.87
Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion

Authors: Xiantao Li and Chunhao Wang

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

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

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)

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@InProceedings{li_et_al:LIPIcs.ICALP.2023.87,
  author =	{Li, Xiantao and Wang, Chunhao},
  title =	{{Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{87:1--87:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.87},
  URN =		{urn:nbn:de:0030-drops-181395},
  doi =		{10.4230/LIPIcs.ICALP.2023.87},
  annote =	{Keywords: Quantum algorithms, open quantum systems, Lindblad simulation}
}
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