Accelerated implementation of objective function class for approximate quantum compiling

[A-tA-v]

Summary

Accelerated implementation of objective function class for approximate quantum compiling

Details and comments

The objective function itself remains the same as in the current version (Frobenius norm of the difference between the target matrix and approximating circuit). However, the new implementation is significantly faster. It can be optionally selected along with the current version.

[ajavadia]

Thanks for the contribution. Is this a drop-in replacement or there are some trade-offs? If it's simply faster then I don't think we need to keep the old objective function. Also do you have some numbers about how much faster it is on an example input?

[A-tA-v]

Hi Ali, thank you for your reponse. The default implementation might be interesting because it is easy to understand, if someone would like to see some technical details how the method does work. The accelerated code is harder to comprehend as it uses a lot of caching and transformations. Also, it uses more memory. Otherwise, you are right.
We are working on simplification of the accelerated implemenetation, but it will take quite a time to complete.
As for comparison, we can provide a speed-up vs number of qubits plot.

[ajavadia]

Ok sounds good. Yes I think we can keep the old one around then for now. I had a look through the PR and it all looks pretty good. Once you put some benchmarking numbers here then I think we can merge.

[A-tA-v]

This is the benchmarking result: accelerated implementation vs default (straightforward) one. The actual speedup may depend on Numpy version, number of CPU cores and hardware generation, whether the code is executed with multi-threading enabled or not, and so on. However, the performance of accelerated version is always consistently higher. On the chart you can see the speedup (averaged over various circuit depths) as a function of the number of qubits. We also show the dispersion of speedup measurements (plus/minus standard deviation around the mean).

[coveralls]

Pull Request Test Coverage Report for Build 3341797110

• 420 of 435 (96.55%) changed or added relevant lines in 8 files are covered.
• 43 unchanged lines in 3 files lost coverage.
• Overall coverage increased (+0.02%) to 84.427%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/transpiler/synthesis/aqc/fast_gradient/layer.py	128	130	98.46%
qiskit/transpiler/synthesis/aqc/fast_gradient/fast_gradient.py	111	115	96.52%
qiskit/transpiler/synthesis/aqc/fast_gradient/pmatrix.py	99	103	96.12%
qiskit/transpiler/synthesis/aqc/fast_gradient/fast_grad_utils.py	74	79	93.67%

Files with Coverage Reduction	New Missed Lines	%
src/optimize_1q_gates.rs	1	95.16%
src/sampled_exp_val.rs	14	63.93%
src/results/marginalization.rs	28	72.41%

Totals
Change from base Build 3339680957:	0.02%
Covered Lines:	62113
Relevant Lines:	73570

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💛 - Coveralls

[A-tA-v]

Dear reviewers, could have a look at this pull request?