Noise Scaling for LRE

[purva-thakre]

Fixes #2307

Description

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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

[purva-thakre]

When this PR is close to being merged, replace mitiq/lre with the seealso directive from Sphinx.

https://www.sphinx-doc.org/en/master/usage/restructuredtext/directives.html#directive-seealso

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.25%. Comparing base (b58f029) to head (f6885cc).
Report is 10 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2347      +/-   ##
==========================================
+ Coverage   98.22%   98.25%   +0.02%     
==========================================
  Files          87       89       +2     
  Lines        4056     4115      +59     
==========================================
+ Hits         3984     4043      +59     
  Misses         72       72              

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[purva-thakre]

To do: Understand this List comprehension has incompatible type List[Tuple[Any, ...]]; expected List[Tuple[int]]

https://realpython.com/python-type-checking/
https://mypy.readthedocs.io/en/stable/kinds_of_types.html#tuple-types
https://mypy.readthedocs.io/en/stable/builtin_types.html

[cosenal]

1. tuple[int] is the type of a tuple with only one element. If you want the tuple to have an arbitrary number of integer elements, then you want to type it as tuple[int, ...]
2. The Any is because mypy can't infer that the tuple elements generated here are integer. It should go away after fix 1.
3. Instead of built-in types list and tuple, it's recommended to use List and Tuple from the typing module, i.e., from typing import List, Tuple and then List[Tuple[int, ...]]

[purva-thakre]

It would be better to use the default value as None for the parameter num_chunks. Making changes to this currently leads to the circuit getting chunked into 1 layer when I use the default value . Figure this out; make changes.

[purva-thakre]

forgot the return type for this function. mypy caught this as well.

mitiq/lre/multivariate_scaling/layerwise_folding.py:128: error: Function is missing a return type annotation [no-untyped-def]