Add "mitiq.raw.execute"?

[rmlarose]

Without an observable, the canonical way to compute "raw results" (i.e., results without error mitigation) is execute(circuit).

However, with an observable, the interface is different:

• Without error mitigation: Either Executor.evaluate(circuit, observable) or observable.expectation(circuit, executor).
• With error mitigation: execute_with_xxx(circuit, executor, observable).

Should we (i) support a common interface? and (ii) do this by adding a "raw" module which does not do any error mitigation but exists solely for the purpose of having a common interface?

Pros

It would be really useful for documentation and examples. For example:

import cirq

from mitiq import Executor, Observable, PauliString, zne, raw
from mitiq.interface import mitiq_cirq

circuit = cirq.Circuit(cirq.H.on(cirq.LineQubit(0)) for _ in range(10))
executor = Executor(mitiq_cirq.compute_density_matrix)
observable = Observable(PauliString("Z"))
print(f"Problem: ⟨𝜓| {observable} |𝜓⟩ where |𝜓⟩ is given by", circuit, sep="\n\n")

# Without error mitigation.
raw_result = raw.execute(circuit, executor, observable)
print("\nRaw result:", raw_result)
print("Executed circuits:", *executor.executed_circuits, sep="\n")

# With error mitigation.
zne_result = zne.execute_with_zne(circuit, executor, observable)
print("\nZNE result:", zne_result)
print("Executed circuits:", *executor.executed_circuits[1:], sep="\n")

Problem: ⟨𝜓| Z(0) |𝜓⟩ where |𝜓⟩ is given by

0: ───H───H───H───H───H───H───H───H───H───H───

Raw result: 0.95
Executed circuits:
0: ───H───H───H───H───H───H───H───H───H───H───

ZNE result: 0.99
Executed circuits:
0: ───H───H───H───H───H───H───H───H───H───H───
0: ───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───
0: ───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───H───

Cons

It doesn't really have a use beyond documentation. One may misinterpret mitiq.raw to do error mitigation.

[rmlarose]

From Mitiq meeting: Should it be a module or just a function?

[github-actions]

This issue had no activity for 2 months, and will be closed in one week unless there is new activity. Cheers!