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arXiv · 2006.12042

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

Shelly Garion·Andrew W. Cross
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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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BibTeXRIS

Shelly Garion, Andrew W. Cross. 2020-06-22. Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates. https://doi.org/10.22331/q-2020-12-07-369

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