Add label assigned check in SparsePauliOp

[daimurat]

Summary

Added a check process discussed in #7916.

Details and comments

• If the qubit designated from input Pauli list is already assigned (not I), .from_sparse_list raise QiskitError.
• For performance added do_check flag to be able to turn off the check.

Note: This is a part of QAMP spring 22

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[Cryoris]

I think I should be checked too, otherwise it's unclear how we interpret using an index multiple times 🙂 Could you add that?

[daimurat]

Thank you @Cryoris.
How about not to being allowed input I instead of checking I ?
I think there seems to be no use case that input I should be applied.

[ikkoham]

It is true that there is no reason to pass I with sparse format, so I don't think we need to allow I.

[Cryoris]

Yes that's true, strictly speaking there's not reason to pass I. But it might be restrictive to explicitly forbid it because (1) if a user happens to have strings with I in them they would have to clean the string, which can be cumbersome (maybe the string is automatically constructed) and (2) we would have to add a check whether I is included. I think it would be easier for both users and us if we just allow any Pauli string.

We could of course clean the input strings and only store the non-I ones, that might be good though!

[ikkoham]

Then I feel that it is ok to not check I for the first version. Personally, I am concerned that it would complicate the implementation. As long as we make errors as long as the output is clearly strange (as issue pointed out), we don't have problems.

[Cryoris]

There are a few ways to implement it which a not complicating the implementation I think 🙂 For example one of the following 2:

1. Just check if indices contains duplicated (that might be even simpler than the current code 🙂)

if do_checks and np.unique(indices).size == len(indices):
  # raise error

2. At the beginning, populate labels with None and use the check that you currently have. Then at the end replace all left Nones with "I" 🙂

[ikkoham]

Both has extra computational cost, but I'd prefer 1 using set.

[daimurat]

Thank you. I fixed the check condition. Could you review it?

[coveralls]

Pull Request Test Coverage Report for Build 2494403645

• 3 of 3 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.0005%) to 84.425%

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Totals
Change from base Build 2493889477:	0.0005%
Covered Lines:	54714
Relevant Lines:	64808

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💛 - Coveralls

[ikkoham]

@daiki0623 Thank you. LGTM. I'll wail @Cryoris's review.

[Cryoris]

LGTM thanks for the contribution @daiki0623!