Reconstruct probabilities

[JooNiv]

Description

Version 2.1.0

Reconstructing a probability distribution

• get_experiment_circuits() takes qubits in place of
  observables, and estimate_probabilities() then reconstructs the
  distribution over those qubits by an inverse Walsh-Hadamard transform. Costs
  2**k observables but no extra circuits, since they share one measurement
  setting.
  See the derivation: https://jooniv.github.io/QCut/theory/Probability_reconstruction.html.
• The result is a dict of quasi-probabilities, which can be negative.
  :code:nearest_probabilities() gives the closest true distribution and
  :code:counts() scales it by the shots the experiment ran at, or by one of your own.
• A circuit carrying final measurements can be cut. They are removed on a copy, so the
  circuit passed in is left as it was.
• RawResult.shots and CutExperiment.can_reconstruct_probabilities are
  public, and the types the public functions return are importable from QCut.

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Type of Change

Please check the type(s) of changes made in this PR:

• Bug Fix (non-breaking change that fixes an issue)

• New Feature (non-breaking change that adds functionality)

• Breaking Change (fix or feature that would cause existing functionality to not work as expected)

• Documentation Update (adds or updates documentation)

• Refactor (code restructuring without changing external behaviour)

• Other (please specify):

• For non-breaking changes remember to run toxto test against older qiskit versions.

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Checklist

Please check all relevant boxes to ensure your pull request is ready for review:

• I have tested my changes locally and they work as expected.
  • For changes that should be backwards compatible to older Qiskit versions run tox in addition to pytest tests ran by CI
• I have added/updated relevant documentation (if applicable).
• I have formatted my code using the project’s coding style or linter.
• I have added tests that prove my fix is effective or my feature works (if applicable).
• All new and existing tests pass.
• My code follows the CONTRIBUTING.md guidelines.

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