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Decompose a CNOTDihedral element into a QuantumCircuit. For N <= 2 qubits this is based on optimal CX cost decomposition from reference [1]. For N > 2 qubits this is done using the general non-optimal compilation routine from reference [2].


elem (CNOTDihedral) – a CNOTDihedral element.


a circuit implementation of the CNOTDihedral element.

Return type



  1. Shelly Garion and Andrew W. Cross, Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates, Quantum 4(369), 2020(opens in a new tab)
  2. Andrew W. Cross, Easwar Magesan, Lev S. Bishop, John A. Smolin and Jay M. Gambetta, Scalable randomised benchmarking of non-Clifford gates, npj Quantum Inf 2, 16012 (2016).
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