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Numerical scheme for the solution of the Dirac equation on classical and quantum computers Fillion-Gourdeau, Francois
Description
A numerical scheme that solves the time-dependent Dirac equation is presented in which the time evolution is performed by an operator-splitting decomposition technique combined with the method ofcharacteristics. On a classical computer, this numerical method has some nice features: it is very versatile and most notably, it can be parallellized efficiently. This makes for an interesting numerical tool for the simulation of quantum relativistic dynamical phenomena such as the electron dynamics in very high intensity lasers. Moreover, this numerical scheme can be implemented on a digital quantum computer due to its simple structure: the operator splitting is a sequence of streaming operators followed by rotations in spinor space. This structure is actually reminiscent of quantum walks, which can be implemented efficiently on quantum computers. We determine the resource requirements of the resulting quantum algorithm and show that under some conditions, it has an exponential speedup over the classical algorithm. Finally, an explicit decomposition of this algorithm into elementary gates from a universal set is carried out using the software Quipper. It is shown that a proof-of-principle calculation may be possible with actual quantum technologies.
Item Metadata
Title |
Numerical scheme for the solution of the Dirac equation on classical and quantum computers
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-08-14T15:04
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Description |
A numerical scheme that solves the time-dependent Dirac equation is presented in
which the time evolution is performed by an operator-splitting decomposition technique combined with the method ofcharacteristics. On a classical computer, this numerical method has some nice features: it is very versatile and most notably, it can be parallellized efficiently. This makes for an interesting numerical tool for the simulation of quantum relativistic dynamical phenomena such as the electron dynamics in very high intensity lasers. Moreover, this numerical scheme can be implemented on a digital quantum computer due to its simple structure: the operator splitting is a sequence of streaming operators followed by rotations in spinor space. This structure is actually reminiscent of quantum walks, which can be implemented efficiently on quantum computers. We determine the resource requirements of the resulting quantum algorithm and show that under some conditions, it has an exponential speedup over the classical algorithm. Finally, an explicit decomposition of this algorithm into elementary gates from a universal set is carried out using the software Quipper. It is shown that a proof-of-principle calculation may be possible with actual quantum technologies.
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Extent |
33 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: INRS-EMT
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Series | |
Date Available |
2018-02-10
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0363487
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Other
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International