[Feature] Implement a State result type

[Doomsk]

To allow the handling of:

• State vectors
• Density matrices useful for [Feature] Computing partial trace outputs for statevectors and density matrices qadence#367
• Samples ?

Unfinished prototype here

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@Roland-djee cloning the same issue from qadence-core in here. Both places should be involved in this endeavor.

[RolandMacDoland]

@Doomsk is this still relevant ? Or will it be handled by the runtime ?

[Doomsk]

@Doomsk is this still relevant ? Or will it be handled by the runtime ?

@Roland-djee the state result type should be included in the RuntimeInterface. However, it's up to each backend to implement/provide it correctly. Thus, on the RuntimeInterfaceApi we refer generically to a TypeVar that expects the
backend's side RuntimeInterface implementation to define which those results are.

[RolandMacDoland]

@Doomsk is this still relevant ? Or will it be handled by the runtime ?

@Roland-djee the state result type should be included in the RuntimeInterface. However, it's up to each backend to implement/provide it correctly. Thus, on the RuntimeInterfaceApi we refer generically to a TypeVar that expects the backend's side RuntimeInterface implementation to define which those results are.

I guess my question was more: is the RuntimeInterfaceAPI already drafted somewhere ?

[Doomsk]

@Doomsk is this still relevant ? Or will it be handled by the runtime ?

@Roland-djee the state result type should be included in the RuntimeInterface. However, it's up to each backend to implement/provide it correctly. Thus, on the RuntimeInterfaceApi we refer generically to a TypeVar that expects the backend's side RuntimeInterface implementation to define which those results are.

I guess my question was more: is the RuntimeInterfaceAPI already drafted somewhere ?

yes! you can find it on this branch (which is in this PR)
working examples are found on the tests folder, for pyq and pulser. Note that pyq has the old version of Dominik's implementation (for the sake of comparison and benchmarking; will be removed before merging) as well

[Doomsk]

@Roland-djee the same issue from core is also here to keep track on the results

[RolandMacDoland]

@Roland-djee the same issue from core is also here to keep track on the results

Indeed, will close the other, thanks.