fix expand_matrix for qudit matrices

[albi3ro]

Context:

We were incorrectly manipulating qutrit matrices.

Description of the Change:

Allow expand_matrix to work on higher qudit matrices.

Benefits:

Possible Drawbacks:

Related GitHub Issues:

[sc-75501] Fixes #6368

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.40%. Comparing base (e0f614c) to head (0b4a7ee).
Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #6398   +/-   ##
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  Coverage   99.40%   99.40%           
=======================================
  Files         447      447           
  Lines       42400    42405    +5     
=======================================
+ Hits        42146    42151    +5     
  Misses        254      254           

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[glassnotes]

@albi3ro and team, thank you so much for making this improvement!! 🎉 🙏 This will be super helpful for our qutrit researchers @jackyruth and @Gabriel-Bottrill 🚀

[mudit2812]

Looks great! Should qml.matrix and Operator.matrix be updated accordingly?

Also, I don't mean to be frustrating but I wanted to get your thoughts on adding a test for qudit_dim > 3 and/or more wires. I guess at least for the former suggestion it might be unnecessary since we don't have any operations for higher qudit dimensions, but the latter might make sense.

[albi3ro]

Looks great! Should qml.matrix and Operator.matrix be updated accordingly?

Also, I don't mean to be frustrating but I wanted to get your thoughts on adding a test for qudit_dim > 3 and/or more wires. I guess at least for the former suggestion it might be unnecessary since we don't have any operations for higher qudit dimensions, but the latter might make sense.

What do we need to update in qml.matrix or Operator.matrix? Just adding a few more tests?

I'd like to test with more wires, but then we start to run into the challenge with figuring out what the "correct" answer should be 🤔

[mudit2812]

What do we need to update in qml.matrix or Operator.matrix? Just adding a few more tests?

Oh, never mind. The fact that expand_matrix automatically computes the qudit dimension slipped my mind. Though tests aren't a bad idea, but I'd say not necessary either.

I'd like to test with more wires, but then we start to run into the challenge with figuring out what the "correct" answer should be 🤔

Regarding this point, we can either:

• Use some elbow grease and manually figure out how the matrix should permute. Not ideal, and most likely not worth the labour.
• Use a mildly less accurate heuristic to assert correctness. For example, we can generate a random matrix and a random state vector and assert that the state vector after applying the matrix is correct regardless of the wire order. This would also allow us to parametrize over arbitrary wire orders and input matrix dimensions to make the test more robust.

[dwierichs]

Looks good to me, just two tiny comments.
Nice! 🚀

[JerryChen97]

Thank you so much! These days I've been wanting this implemented but didn't get a chance to add; now finally we don't need multiple copies of expansion for any other arbitrary spins in the future😊!!