YPowGate has no dimension

[95-martin-orion]

Follow-up to #4782: we added a dimension property for X and Z, but Y remains locked to qubits. This seems like an oversight - can we finish out the pauli trio by adding dimensions to YPowGate?

[95-martin-orion]

CC @daxfohl

[95-martin-orion]

When this is implemented we'll also need to update its docstring, as seen in #5648.

[daxfohl]

X and Z have standard generalizations to higher dimensions https://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices#Construction:_The_clock_and_shift_matrices

I wasn't able to find a standard for Y. Probably the relation Y**k = X**0.5 * Z**k * X**-0.5 (or something like that) holds in higher dimensions? If so, we could define Y in higher dimensions via decomposition. (Unless someone with more linear algebra background than me can figure out the actual eigencomponents).

[dabacon]

Yeah I don't think there is a canonical definition of a higher order Y operator. Consider for exampleX Z and X**(-1)Z. In d=2 these are the same, but in d>2 they are different. So which one are we to chose?

[daxfohl]

(Except in other contexts where Y is the canonical higher order operator https://en.m.wikipedia.org/wiki/Fixed-point_combinator#Fixed-point_combinators_in_lambda_calculus) :)