A simple asymptotically optimal Clifford circuit compilation algorithm

• URL: http://arxiv.org/abs/2310.10882v1
• Date: Mon, 16 Oct 2023 23:27:59 GMT
• Title: A simple asymptotically optimal Clifford circuit compilation algorithm
• Authors: Timothy Proctor and Kevin Young
• Abstract summary: We present an algorithm that decomposes any $n$-qubit Clifford operator into a circuit consisting of three subcircuits. As with other derivationally optimal Clifford compilation algorithms, the resulting circuit contains $O(n2/log n)$ two-qubit gates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an algorithm that decomposes any $n$-qubit Clifford operator into a circuit consisting of three subcircuits containing only CNOT or CPHASE gates with layers of one-qubit gates before and after each of these subcircuits. As with other asymptotically optimal Clifford compilation algorithms, the resulting circuit contains $O(n^2/\log n)$ two-qubit gates. The derivation of our algorithm only requires the symplectic representation of Clifford gates, basic row and column matrix manipulations, and some known properties of general matrices over 0 and 1.

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