Add the ability to represent a clifford+T operation in Matsumoto-Amano normal form

[NoureldinYosri]

the to_sequence method in

Qualtran/qualtran/rotation_synthesis/matrix/clifford_t_repr.py

Line 82 in 7b81e72

def to_sequence(matrix: su2_ct.SU2CliffordT, fmt: str = 'xyz') -> tuple[str, ...]:

can represent a clifford+T operation in 2 forms

1. as a string of Tx/Ty/Tz gates followed by a clifford
2. An optional H followed by a string of alternating $T_x^{b_i}$ and $T_z^{b_i}$ with $b_i \in {-1, 1}$ followed by a clifford

A third form that clifford+T operations can be written in is the Matsumoto-Amano normal form

$$ U = T^{a_0} (\prod H S^{b_i} T) C $$

for some clifford $C$, it would be nice to have implement this form as well

references https://arxiv.org/abs/0806.3834 and https://arxiv.org/abs/1312.6584

[bopardikarsoham]

Hi @NoureldinYosri I’m a new contributor to Qualtran. Would you mind if I give this issue a try?

[NoureldinYosri]

sure, I assigned it to you @bopardikarsoham