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Circuit synthesis for the CNOTDihedral class for all-to-all connectivity.
)QuantumCircuit) CNOTDihedral) synth_cnotdihedral_two_qubits)synth_cnotdihedral_generalelemreturnc X | j }|dk rt | S t | S )a{ Decompose a :class:`.CNOTDihedral` element into a :class:`.QuantumCircuit`.
For :math:`N \leq 2` qubits this is based on optimal CX-cost decomposition from reference [1].
For :math:`N > 2` qubits this is done using the general non-optimal compilation
routine from reference [2].
Args:
elem: A :class:`.CNOTDihedral` element.
Returns:
A circuit implementation of the :class:`.CNOTDihedral` element.
References:
1. Shelly Garion and Andrew W. Cross, *Synthesis of CNOT-Dihedral circuits
with optimal number of two qubit gates*, `Quantum 4(369), 2020
`_
2. Andrew W. Cross, Easwar Magesan, Lev S. Bishop, John A. Smolin and Jay M. Gambetta,
*Scalable randomized benchmarking of non-Clifford gates*,
npj Quantum Inf 2, 16012 (2016).
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