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Author De Vos, Alexis ♦ De Baerdemacker, Stijn
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2014
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Reversible computation ♦ Quantum computation
Abstract Quantum computation on $\textit{w}$ qubits is represented by the infinite unitary group $U(2^{w});$ classical reversible computation on $\textit{w}$ bits is represented by the finite symmetric group $S_{2}^{w}.$ In order to establish the relationship between classical reversible computing and quantum computing, we introduce two Lie subgroups $XU(\textit{n})$ and $ZU(\textit{n})$ of the unitary group $U(\textit{n}).$ The former consists of all unitary $\textit{n}$ × $\textit{n}$ matrices with all line sums equal to 1; the latter consists of all unitary diagonal $\textit{n}$ × $\textit{n}$ matrices with first entry equal to 1. Such a group structure also reveals the relationship between matrix calculus and diagrammatic zx-calculus of quantum circuits.
ISSN 15504832
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2014-11-01
Publisher Place New York
e-ISSN 15504840
Journal ACM Journal on Emerging Technologies in Computing Systems (JETC)
Volume Number 11
Issue Number 2
Page Count 11
Starting Page 1
Ending Page 11

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Source: ACM Digital Library