ensure error is raised for invalid parameters in `partial_trace`

[aman-coder03]

currently, partial_trace does not explicitly validate:
that input_mat is square.
that np.prod(dim) equals the matrix dimension.
that sys indices are within valid subsystem bounds.

in some cases, invalid inputs lead to NumPy IndexError or unintended behavior rather than a clear ValueError.
i propose adding explicit validation checks along with corresponding unit tests for invalid inputs.

[vprusso]

Sounds good, @aman-coder03 . If you add these checks, make sure to add corresponding tests to keep the coverage of these extra checks up!

[aman-coder03]

thanks for the feedback! @vprusso
i will add validation checks and tests.

[aman-coder03]

@vprusso i have opened a PR, please have a look!!

[purva-thakre]

See #1324 (comment)

It might be worth closing this until we agree on a plan.

[vprusso]

See #1324 (comment)

It might be worth closing this until we agree on a plan.

Perhaps we can keep it open, but turn it into a discussion thread? @purva-thakre