Add kwargs for equal functions

[kenya-sk]

Before submitting

Please complete the following checklist when submitting a PR:

• All new features must include a unit test.
  If you've fixed a bug or added code that should be tested, add a test to the
  test directory!

• All new functions and code must be clearly commented and documented.
  If you do make documentation changes, make sure that the docs build and
  render correctly by running make docs.

• Ensure that the test suite passes, by running make test.

• Add a new entry to the doc/releases/changelog-dev.md file, summarizing the
  change, and including a link back to the PR.

• The PennyLane source code conforms to
  PEP8 standards.
  We check all of our code against Pylint.
  To lint modified files, simply pip install pylint, and then
  run pylint pennylane/path/to/file.py.

When all the above are checked, delete everything above the dashed
line and fill in the pull request template.

---

Context:
The kwargs (check_interface, check_trainability, atol and rtol) were not available for _equal_pow, _equal_adjoint, _equal_exp and _equal_sprod, which are overrides of qml.equal. Therefore, comparisons that allowed for interfacing and numerical errors were not possible.

Description of the Change:
Changed to allow kwargs to be used in override of qml.equal.

Benefits:
The following interfaces and comparisons with tolerance for numerical errors are possible.

>>> op1 = qml.RX(1.2, wires=0)
>>> op2 = qml.RX(1.2 + 1e-4, wires=0)
>>> qml.equal(op1 **2, op2 ** 2, atol=1e-3)
True
>>> qml.equal(op1 **2, op2 ** 2, atol=1e-6)
False
>>> qml.equal(qml.adjoint(op1), qml.adjoint(op2), atol=1e-3)
True
>>> qml.equal(qml.adjoint(op1), qml.adjoint(op2), atol=1e-6)
False
>>> op3 = qml.exp( qml.s_prod(2j, qml.X(0)))
>>> op4 = qml.exp(qml.s_prod(qml.numpy.array(2j), qml.X(0)))
>>> qml.equal(op3, op4, check_interface=True)
False
>>> qml.equal(op3, op4, check_interface=False)
True

Possible Drawbacks:

Related GitHub Issues:
#5408

[albi3ro]

Thanks for opening this PR @kenya-sk ! Looking great 🎉

I looked into the jax failure in test_jit_simplification. This is a simple by-product of the fact we are now actually checking the ML framework of the coefficient, and correctly stating that jax.numpy.array(2.0) is not equal to 2.0. A simple update to the relevant test should do the job.

This kind of failure is exactly why we are now in the process of adding an assert_equal function to explain these things.

Now other comments from my side. I'll check back later.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.67%. Comparing base (f960c0e) to head (1bf4644).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5668      +/-   ##
==========================================
- Coverage   99.68%   99.67%   -0.01%     
==========================================
  Files         414      414              
  Lines       38819    38550     -269     
==========================================
- Hits        38695    38425     -270     
- Misses        124      125       +1     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[albi3ro]

Looks perfect 🎉 I'm happy to approve.

[dwierichs]

Hi @kenya-sk, thanks for this upgrade! 🎉
I had a few very small comments/suggestions, some of which are optional.
And a question to briefly check in on with @albi3ro.

[kenya-sk]

@dwierichs @albi3ro
Thanks insight full comment!
I will prepare the PR again reflecting your comments.

[kenya-sk]

@dwierichs @albi3ro
I have reflected your comments in the code!
I have skipped the handling of numerical errors in _equal_pow that need to be discussed in the internals. If implementation is needed, please let me know so that I can address it immediately.

Also, since _equal_exp and others execute the equal method again by passing kwargs to nested base operators (return qml.equal(op1.base, op2.base, **kwargs)), the test code was created by separating the evaluation of Exp and Base Operator.

[dwierichs]

Thank you @kenya-sk for this thorough work! 💯