On the Universality and Membership problems for quantum gates

• URL: http://arxiv.org/abs/2110.04210v2
• Date: Mon, 15 Nov 2021 19:24:49 GMT
• Title: On the Universality and Membership problems for quantum gates
• Authors: Lorenzo Mattioli and Adam Sawicki
• Abstract summary: We study the Universality and Membership Problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie groups theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the Universality and Membership Problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie groups theory. We also introduce an auxiliary problem called Subgroup Universality Problem, which helps in solving some instances of the Membership Problem, and can be of interest on its own. The resulting theorems are mainly formulated in terms of centralizers and the adjoint representations of a given set of quantum gates.

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