[discussion] Move the borders between QVM and QPU

There are typically three stages in quantum programming

1. Write and debug using wavefunction-based methods
2. Run the program as if it were running on a real device, perhaps with a noise model
3. Run the program on a device.

The current distinction between QVMConnection and QPUConnection groups (1,2) and makes (3) separate. This causes some API warts: the difference between the two run_and_measures, and the different behavior on the QVMConnection between run+MEASURE and run_and_measure.

I propose we make (1) separate and group (2,3). The quil paper specifies

The QAM may be implemented either classically or on quantum hardware. A classical implementation is called a Quantum Virtual Machine (QVM). We describe one such implementation in Section V-F. An implementation on quantum hardware is called a Quantum Processing Unit (QPU).

(h/t @tarballs-are-good ) so (2) should be named with the QVM moniker, (3) should continue to be named with the QPU moniker, and (1) should be re-named to not mention a QVM but rather stress the wavefunction simulation aspect.

[marcusps]

Is this just a discussion about naming conventions and constructor function signatures, or can we also debate the different behaviors of run when using QVM vs QPU?

I personally would want a strict behavioral equivalence between the QVM and the QPU, and just struggled with the fact that the QVM wanted MEASURE instructions in order to make the run meaningful, which was quite frustrating (and not well documented).

@mpharrigan @tarballs-are-good

[mpharrigan]

Example of what this might look like:

program = Program([H(0)])

# (1)
simulator = WavefunctionSimulator()
wfn = simulator.wavefunction(program)
i = np.argmax(wfn.probabilities())
# ...

# (2)
qvm = QAM(device='qvm', noise=0.05)
prog_with_measures = measure_all(program)
bitstrings = qvm.run(prog_with_measures)
qvm_expectation = np.mean(function_that_operates_on_bitstrings(bitstrings))
# ...

# (3)
qpu = QAM(device='acorn')
bitstrings = qpu.run(prog_with_measures)
qpu_expectation = np.mean(function_that_operates_on_bitstrings(bitstrings))
# ...