removed deprecated PauliTable, StabilizerTable and tests

[adigaboy]

Summary

Removed Deprecated code:
PauliTable
StabilizerTable
deprecated functions
and tests

Details and comments

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[Raghav-Bell]

@adigaboy Please check lint tests locally (refer to contribution guide) and add release note. Also remove tests from test_pauli_sum_op.py. As of now (latest), 0.22 deprecated code removal is requested (issue #10810 ). I don't think maintainers are going to remove deprecated code for 0.24 soon , let us wait for the review from maintainers.

[ikkoham]

@adigaboy Thank you very much. This is really important PR. Could you resolve the conflicts?

[ikkoham]

This PR requires a release note for removal.

[ikkoham]

LGTM!

[jakelishman]

Thanks for doing this, and thanks Hamamura-san for the reviewing and helping to fix up the last bits. I just had one super minor comment about the release note, but otherwise let's get this merged.

[coveralls]

Pull Request Test Coverage Report for Build 6540287880

• 2 of 2 (100.0%) changed or added relevant lines in 2 files are covered.
• 10 unchanged lines in 3 files lost coverage.
• Overall coverage decreased (-0.008%) to 87.063%

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Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	2	91.16%
qiskit/extensions/quantum_initializer/squ.py	2	84.15%
crates/qasm2/src/parse.rs	6	97.6%

Totals
Change from base Build 6539695207:	-0.008%
Covered Lines:	74015
Relevant Lines:	85013

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💛 - Coveralls