Speed-up SparsePauliOp.simplify

[t-imamichi]

Summary

SparsePauliOp.simplify is very slow if there are so many Pauli strings. I optimized some numpy codes.

Details and comments

micro benchmark

import random
from timeit import timeit

from qiskit.quantum_info import SparsePauliOp

k = 10
n = 10_000

random.seed(123)
op = SparsePauliOp.from_list([(''.join(random.choices('IXYZ', k=k)), 1) for _ in range(n)])
print(f'{timeit(lambda: op.simplify(), number=10)} sec')

main (06795bf)

2.9950154619999996 sec

this PR v1 (418c55b6)

0.2740141010000001 sec

this PR v2 (8492a26e)

0.162777092 sec

this PR v3 (aa134b0)

0.07564510999999996 sec

this PR v4 (f09d662) thanks to @jakelishman

0.04969994 sec

[t-imamichi]

@ikkoham Could you review this PR?

[ikkoham]

Thank you @t-imamichi . The first part is the performance regression I introduced in #6826.
I think this PR should be merged before the next version is released.

LGTM.

[t-imamichi]

I notice that I can further speed-up this code. Let me check.
I applied a further optimization by packing bool vectors of paulis.x and paulis.z into np.int8 vectors.

[jakelishman]

Looks good, and a great speed up! I learned about np.packbits too, which I'd not come across before.