Add SProd.terms() method

[Qottmann]

Missed to add SProd.terms(), SProd.ops and SProd.coeffs, fixing this here

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[PietropaoloFrisoni]

Great. Thank you for adding this!

[dime10]

@Qottmann could you elaborate what the intention here is? Is it that SProd should recursively determine what the terms and coeffs are? Only one level deep or several? Only for specific observables or all?

I believe previously it always returned a single coeff (the scalar) and a single observable (whether compound or not), but happy to be corrected here.

[Qottmann]

In Prod and Sum the terms() method flattens out the operator to its coefficients and "pure" and simplified ops (i.e. products are executed). The request was for that to be consistens also with SProd such that you always receive a flattened down list of coeffs and ops.

E.g. if you have some operator op = qml.sum(*[qml.s_prod(0.5, X(i)) for i in range(3)]). The terms are [0.5, 0.5, 0.5] and [X(i) for i in range(3)]. Consider that you then later decide to renormalize it by multiplying with a scalar op = 2 * op, but now the terms would just yield [2], [<original_op]`. The motivation was for this to be consistent.

Frankly its not super urgent and probably a matter of taste what one prefers.

more context here on slack

[dime10]

Thanks @Qottmann! The change is not a problem for us as long as we're aware of the new behaviour, so feel free to re-merge this whenever convenient :)

[dime10]

Was this added back or is that not planed anymore?

[albi3ro]

@dime10 Still definitely wanted, but I guess is got backlogged. Probably too late for the next release, but we should definitely look into making this change together in tandem.

[dime10]

Just checking in on this again 😅

[albi3ro]

@astralcai is now looking into this again with #5885 . But not going into the release since we know it's going to break things for catalyst.