optimize FidelityQuantumKernel parameterization

[MoritzWillmann]

Summary

This PR optimizes the way indices, right_parameters and left_parameters are created in _get_symmetric_parameterization and _get_parameterization of the FidelityQuantumKernel class.

Details and comments

The previous version used a heavy amount of dynamic memory allocation which resulted in a very long runtime. This new version runs way faster for bigger instances by not using dynamic memory allocation. I didn't add any additional tests, since this doesn't introduce any new functionality.

I'm happy to incorporate comments and hope this can be merged soon 😄

[adekusar-drl]

Can you please measure how faster the implementation becomes with this PR?

[coveralls]

Pull Request Test Coverage Report for Build 7049710944

• 10 of 10 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-0.03%) to 92.66%

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Totals
Change from base Build 7049706485:	-0.03%
Covered Lines:	1843
Relevant Lines:	1989

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💛 - Coveralls

[MoritzWillmann]

Can you please measure how faster the implementation becomes with this PR?

This is the runtime of the respective functions in seconds as benchmarked with timeit with x_vec.shape==y_vec.shape==(100,2) and evaluate_duplicates=="all" and 100 executions:

get_parameterization            Old     11.828130300000339
get_parameterization            New     0.4398030000011204
get_symmetric_parameterization  Old     4.378354100001161
get_symmetric_parameterization  New     0.23957780000091589

[adekusar-drl]

Thanks, this is interesting. Can you please additionally measure an overall impact on qk.evaluate(), especially if there are more than 5 features/qubits?

[MoritzWillmann]

With x_vec.shape==y_vec.shape==(100,7), ZFeatureMap(7, reps=2), ComputeUncompute(Sampler()), evaluate_duplicates="all" and timeit with 10 executions, in seconds:

Old asymmetric  734.5568785999985
New asymmetric  702.9984134999995
Old symmetric   348.1263235000006
New symmetric   346.7739440999994

[adekusar-drl]

So, performance gain is not that large on a decent number of qubits, but still there is.

[adekusar-drl]

Thanks, looks good