Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates

• URL: http://arxiv.org/abs/2006.12042v2
• Date: Thu, 3 Dec 2020 15:51:00 GMT
• Title: Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates
• Authors: Shelly Garion and Andrew W. Cross
• Abstract summary: We present explicit canonical forms for all the elements in the two-qubit CNOT-Dihedral group, with minimal numbers of controlled-S (CS) and controlled-X ( CX) gates. We provide an algorithm to successively construct the n-qubit CNOT-Dihedral group, asserting an optimal number of controlled-X ( CX) gates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this note we present explicit canonical forms for all the elements in the two-qubit CNOT-Dihedral group, with minimal numbers of controlled-S (CS) and controlled-X (CX) gates, using the generating set of quantum gates [X, T, CX, CS]. We provide an algorithm to successively construct the n-qubit CNOT-Dihedral group, asserting an optimal number of controlled-X (CX) gates. These results are needed to estimate gate errors via non-Clifford randomized benchmarking and may have further applications to circuit optimization over fault-tolerant gate sets.

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