Decomposition of Clifford Gates

• URL: http://arxiv.org/abs/2102.11380v1
• Date: Fri, 5 Feb 2021 10:32:09 GMT
• Title: Decomposition of Clifford Gates
• Authors: Tefjol Pllaha, Kalle Volanto, Olav Tirkkonen
• Abstract summary: We provide a fast algorithm that decomposes any Clifford gate as a $textitminimal$ product of Clifford transvections. The algorithm can be directly used for finding all Pauli matrices that commute with any given Clifford gate.
• Score: 3.7900158137749322
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a $\textit{minimal}$ product of Clifford transvections. The algorithm can be directly used for finding all Pauli matrices that commute with any given Clifford gate. To achieve this goal, we exploit the structure of the symplectic group with a novel graphical approach.

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