RFC: log dialect

[jon-wurtz]

Following #229 .

One option for extracting out the quantum state from a simulator is to have a log dialect. Backing up a bit from what I proposed in #229 , it could be as simple as bloqade.dialects.log_state(label:str="foo"). The results object from the appropriate simulator would be a StochasticWavefunction where each instance is a seed recording bitstring measurements that occurred up to that point, and the wavefunction state of the qpu at that point.

For example, consider doing some sort of Bell state prep:

@bloqade.kernel
def main():
    
    register = bloqade.circuits.line_qubits(2) # This doesn't exactly follow our convention but whatever
    bloqade.circuits.h(register[0])
    bloqade.circuits.cx(register[0], register[1])
    
    bloqade.dialects.log_state(label="A")
    z0 = bloqade.circuits.measure(register[0])
    bloqade.dialects.log_state(label="B")
    z1 = bloqade.circuits.measure(register[1])
    bloqade.dialects.log_state(label="C")
    
    return z0, z1

context = bloqade.executors.statevector()
result = context.log_state(main,repititions=2)
result == StochasticWavefunction:[# First repetition
    {"A":
    BitstringResult: {"data":[],"basis":[]},
    Wavefunction: {"data":[1,0,0,1],"basis":[Qubit(0), Qubit(1)]}},
            {"B":
    BitstringResult: {"data":[0],"basis":[Qubit(0)]},
    Wavefunction: {"data":[1,0],"basis":[Qubit(0)]}},
            {"C":
    BitstringResult: {"data":[0,0],"basis":[Qubit(0),Qubit(1)]},
    Wavefunction: {"data":[],"basis":[]}},
            # Second repetition
    {"A":
    BitstringResult: {"data":[],"basis":[]},
    Wavefunction: {"data":[1,0,0,1],"basis":[Qubit(0), Qubit(1)]}},
            {"B":
    BitstringResult: {"data":[1],"basis":[Qubit(0)]},
    Wavefunction: {"data":[0,1],"basis":[Qubit(0)]}},
            {"C":
    BitstringResult: {"data":[1,1],"basis":[Qubit(0),Qubit(1)]},
    Wavefunction: {"data":[],"basis":[]}},
            # etc.
    ]

Here the dictionaries are a rough representation of the attributes of the appropriate data classes

Other options work too, just being forward-thinking in terms of mid-circuit measurement. debug() could also return the final state, if measurements are not performed. The important thing is to consider the non-physicality of the wavefunction and how this execution differs from what actually happens on hardware-- we cannot directly access or retrieve the wavefunction!!

[jon-wurtz]

Maybe something like MachineState could also include the positions, labels, and moves of atoms, as a way of getting us to atom move animations...