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Generators and Roots of Quantum Logic Gates

R. Muradian·Diego Frias
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Abstract

This is an exposition of some basic mathematical aspects of quantum logic gates. At first we established some general formulas for the case of arbitrary quantum gate A with unique restriction A^2=I. The explicit form of the generators and roots of matrix A have been found . Then we apply general results to the particular cases of one-qubit and multi-qubit quantum gates. Some interesting properties of square roots of basic Pauli and Hadamard gates are demonstrated.

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R. Muradian, Diego Frias. 2005-11-28. Generators and Roots of Quantum Logic Gates. https://arxiv.org/abs/quant-ph/0511250

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