Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates
arXiv:2006.12042 · doi:10.22331/q-2020-12-07-369
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.
arXiv comment9 pages. Accepted to Quantum on 30 Nov 2020
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- Estimating the bias of CX gates via character randomized benchmarking
- Generators and Relations for 3-Qubit Clifford+CS Operators
- Crosstalk-Based Parameterized Quantum Circuit Approximation
- Hardware-efficient random circuits to classify noise in a multi-qubit system