### Matrix Calculus for Classical and Quantum CircuitsMatrix Calculus for Classical and Quantum Circuits

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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