Speed-up QubitMapper.mode_based_mapping

[t-imamichi]

Summary

This PR improves performance of JW transformation by

• computing SparsePauliOp of "+", "-", "E", "N" beforehand
• reducing the overhead of SparsePauliOp._add

If we introduce a specialized function to compute the sum of SparsePauliOp (e.g., SparsePauliOp.sum(list[SparsePauliOp]) -> SparsePauliOp, we can further improve the performance around 2x. But, we need discussion to introduce a new public API to Terra.

Update: SpasePauliOp.sum is merged Qiskit/qiskit#7202. So, I replaced the workaround of sum with SparsePauliOp.sum.

Details and comments

I also prepared separate PRs to improve the performance of JW as follows:

• Speed-up SparsePauliOp.simplify Qiskit/qiskit#7122
• Speed-up SparsePauliOp.compose Qiskit/qiskit#7126
• Speed-up SparsePauliOp._add Qiskit/qiskit#7138

I notice that SparsePauliOp.simplify has a critical performance issue, which is addressed at Qiskit/qiskit#7122, so, this PR with terra main still takes a long time.

Microbenchmark

Nature branch	Terra branch	Time
main	main	61.88646222 sec
this PR	main	53.311054609 sec
main	stable	12.960038270999998 sec
this PR	stable	10.459337683 sec
main	Qiskit/qiskit#7122	12.132281858 sec
this PR	Qiskit/qiskit#7122	4.158444311 sec
this PR	7122 + 7126 + 7138	1.7728687539999999 sec

Update: the final version with SparsePauliOp.sum takes 1.63 sec.

import random
from timeit import timeit

from qiskit_nature.converters.second_quantization import QubitConverter
from qiskit_nature.mappers.second_quantization import JordanWignerMapper
from qiskit_nature.operators.second_quantization import FermionicOp

random.seed(123)
k = 10
n = 100

op = sum(
    (FermionicOp(''.join(random.choices('+-ENI', k=k)), display_format="dense") * random.random())
    for _ in range(n))
mapper = JordanWignerMapper()
qubit_conv = QubitConverter(mapper)
print(f"{timeit(lambda: qubit_conv.convert(op), number=1)} sec")

[mrossinek]

Thanks @t-imamichi!

[pbark]

This LGTM! Thanks @t-imamichi

[t-imamichi]

Because Qiskit/qiskit#7202 is merged, I replace the workaround of sum with SpasePauliOp.sum. It gets intuitive and faster.

[mrossinek]

LGTM!

@t-imamichi we can merge this when you can enable Allow edit by maintainers so that we can keep this branch updated with main 👍

[t-imamichi]

Thanks. I forgot to enable it. I did it now.

[mrossinek]

@woodsp-ibm Offline you mentioned that you might have some more comments on this PR. Is that still the case or can this be merged?