Add type annotations to the PauliSum class

[rht]

Description

Continuation of the effort to type-annotate paulis.py

Checklist

• The above description motivates these changes.
• There is a unit test that covers these changes.
• All new and existing tests pass locally and on Semaphore.
• Parameters have type hints with PEP 484 syntax.
• Functions and classes have useful sphinx-style docstrings.
• (New Feature) The docs have been updated accordingly.
• (Bugfix) The associated issue is referenced above using
  auto-close keywords.
• The changelog is updated,
  including author and PR number (@username, gh-xxx).

[rht]

Here comes the conflict between Number and Union[int, float, complex] again:
E.g. pyquil/paulis.py:1028: error: Unsupported operand types for * ("float" and "PauliTerm") at

pyquil/pyquil/paulis.py

Line 1025 in 7b8cc72

param_prog = exponential_map(coeff * first_pauli_term)

. This is because __rmul__'s argument is typed to be Number instead of Union[int, float, complex].

[appleby]

This looks basically good to me. I think the only open question is whether we want to stick with Number for now or switch to Union[int, float, ...] everywhere.

[karalekas]

Sorry for all the back and forth, but this is what I think we should do (let's punt on the Number problem). If you make these two changes I'm happy to move forward 👍

[karalekas]

instead of importing this, let's define PauliCoefficientDesignator = Union[int, float, complex] and use that in place of ExpressionValueDesignator

[karalekas]

let's remove PauliT and replace all of its uses with Union[PauliDesignator, PauliCoefficientDesignator]

[rht]

@karalekas added the final change in the 3rd commit that will be squashed later.

[appleby]

Two small changes. Otherwise lgtm.

[rht]

@appleby addressed in commit "Third-round-of-review".

[appleby]

looks good to me. thanks @rht!

[rht]

I will squash after an approval from @karalekas.

[karalekas]

LGTM! I can squash as part of the merge 👍