Reduce doc build time for learning representations

[Misty-W]

Description

Fixes #2075

Use cached PEC data and skip PEC executions in optimization loop, to speed up doc build time for learning-depolarizing-noise.md

Local execution time: ~100 seconds --> ~4 seconds

Problem with optimization fixed (tested locally and on RTD)- was comparing ideal values of the wrong circuit. Now that the circuit matches the one used to generate the data, the optimizer converges to the correct value.

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License

• I license this contribution under the terms of the GNU GPL, version 3 and grant Unitary Fund the right to provide additional permissions as described in section 7 of the GNU GPL, version 3.

Before opening the PR, please ensure you have completed the following where appropriate.

• I added unit tests for new code.
• I used type hints in function signatures.
• I used Google-style docstrings for functions.
• I updated the documentation where relevant.
• Added myself / the copyright holder to the AUTHORS file

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (68af75d) 98.20% compared to head (a83f059) 98.26%.
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2165      +/-   ##
==========================================
+ Coverage   98.20%   98.26%   +0.06%     
==========================================
  Files          88       88              
  Lines        4170     4146      -24     
==========================================
- Hits         4095     4074      -21     
+ Misses         75       72       -3     

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[natestemen]

Nice work! We love fast docs!

The one (nonblocking) question I have is if someone downloads this notebook (as a markdown file) and converts it a python notebook, will it run out of the box, or create an error looking for the PEC data file? Either way, I'm okay to merge. Just something I think we should be aware of/know the answer to.

[natestemen]

Why is it that this change does not require a change to the data that is loaded in further into the file? Naively, I would have thought if we are changing the circuit, then the PEC data would need to change as well. Does the PEC data consist of representations of the gates, which does not change here?

[Misty-W]

The change is to match the circuits used to generate the file. The file was generated separately from this notebook and is already used in test_learning.py to make the tests run efficiently.

[natestemen]

Ahh okay that makes sense! Thanks for the clarification. Can you comment on what's in the data file? (just for the sake of me learning!)

[Misty-W]

An array of values of execute_with_pec for different values of depolarizing noise strength epsilon (equally spaced apart by ??). The zeroth column is the value of epsilon used in the representations for PEC.

[natestemen]

Makes sense! And the circuit used in the data is the the same as the one defined here?

mitiq/docs/source/examples/learning-depolarizing-noise.md

Lines 52 to 54 in a83f059

	circuit = random_x_z_cnot_circuit(
	LineQubit.range(2), n_moments=5, random_state=np.random.RandomState(1)
	)

[Misty-W]

Yep!

[Misty-W]

The one (nonblocking) question I have is if someone downloads this notebook (as a markdown file) and converts it a python notebook, will it run out of the box, or create an error looking for the PEC data file? Either way, I'm okay to merge. Just something I think we should be aware of/know the answer to.

If they "run all cells" it will error out if they don't have the data files, and it's a shame the "hidden" cell shows in the Jupyter notebook. But they can (and should) run the next cell, which does the real workflow with execute_with_pec. We just don't want to run it every docs build.