Reducing the number of gates in a quantum circuit

Rules for reduction:

$XX = YY = ZZ = HH = I$,

$S^\dagger \cdot S = S \cdot S^\dagger = I$,

$CX \cdot CX = II$,

$HZH = X$,

$HXH = Z$,

$SS = S^\dagger \cdot S^\dagger = Z$

Status

This code is complete.

How to use

Please refer to the file example_use.ipynb