[2210.16195] CNOT circuits need little help to implement arbitrary Hadamard-free Clifford transformations they generate

A Hadamard-free Clifford transformation is a circuit composed of quantum Phase (P), CZ, and CNOT gates. It is known that such a circuit can be written as a three-stage computation, -P-CZ-CNOT-, where each stage consists only of gates of the specified type.