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The Decomposition of U(n) into XU(n) and ZU(n)
Alexis De Vos and Stijn De Baerdemacker

Any matrix of the unitary group U(n) can be decomposed into matrices from two subgroups, denoted XU(n) and ZU(n). This leads to decompositions of an arbitrary quantum circuit into NEGATOR circuits and PHASOR circuits. The NEGATOR circuits are closely related to classical reversible computation.

Keywords: Unitary group, subgroup, reversible computing, quantum computing

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