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Cited by 33Quantum Computing Algorithms and ArchitectureQuantum many-body systemsNumerical methods for differential equations

Algorithm for the solution of the Dirac equation on digital quantum computers

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Fillion-Gourdeau, François, MacLean, Steve, Laflamme, Raymond·2017·Physical Review A
DOI 10.1103/physreva.95.042343
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Abstract

A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator-splitting decomposition technique that allows for a mapping of the Dirac operator to a quantum walk supplemented by unitary rotation steps in spinor space. Every step of the splitting method is decomposed into sets of quantum gates. It is demonstrated that the algorithm has an exponential speed-up over the implementation of the same numerical scheme on a classical computer, as long as certain conditions are satisfied. Finally, an explicit decomposition of this algorithm into elementary gates from a universal set is carried out to determine the resource requirements. It is shown that a proof-of-principle calculation may be possible with actual quantum technologies.

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Authors
Fillion-Gourdeau, F., MacLean, S., & Laflamme, R.
Affiliations
  • University of Waterloo (CA)
  • Canadian Institute for Advanced Research (CA)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2017-04-28
Volume
95
Issue
4
ISSN
  • 0556-2791 (ISSN-L)
  • 2469-9926
  • 2469-9934
DOI
10.1103/physreva.95.042343
OpenAlex
W2608164063
Cited by
33
References
94
Citations by year
2025: 3 · 2024: 6 · 2023: 4 · 2022: 5 · 2021: 4 · 2020: 5 · 2019: 4 · 2018: 2
FWCI
1.79
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
Keywords
Dirac equation, quantum algorithms, time-dependent Dirac equation, operator splitting, quantum walks, quantum gate decomposition, quantum advantage, resource requirements, relativistic quantum mechanics

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