Rework virtual gate propagation for MCMs

[joshuasn]

Description

With the release of 0.20.0, some circuits with MCMs that were previously buildable are no longer

from qiskit.circuit import QuantumCircuit
from samplomatic import build, Twirl
from samplomatic.transpiler import generate_boxing_pass_manager

circuit = QuantumCircuit(2, 1)
# Add mid-circuit measurement
circuit.measure(0, 0)
# Continue with more gates after measurement
circuit.cx(0, 1)

pm = generate_boxing_pass_manager(
    enable_gates=False,
    enable_measures=True,
    twirling_strategy="all",
    measure_annotations="change_basis"
)
boxed_circuit = pm.run(circuit)

build(boxed_circuit)

due to how measure propagates are handled.

The PreSamplex of the boxed circuit in 0.19.0 has its propagate CX node attached to both collectors:

When calling finalize, the CX nodes get removed, and the resulting samplex produces the correct samples. However, this mechanism also allows the boxed circuit with

with boxed_circuit.box([Twirl(dressing="right")]):
     boxed_circuit.noop(0, 1)

appended to be buildable. The samples generated by this samplex are incorrect as Paulis travelling leftward end up ignoring the presence of a measurement. This circuit is (correctly) not buildable in 0.20.0.

Acceptance criteria

The first boxed circuit in the description is buildable, the appended boxed circuit is not, the following rules are implemented:

Rightward propagation

Optional danglers stay optional when being propagated so that fragments like

circuit = QuantumCircuit(1, 1)
with circuit.box([Twirl()]):
    circuit.measure(0, 0)
circuit.h(0)

are buildable.

Consider allowing implicit identities as well so that fragments like

circuit = QuantumCircuit(2, 1)
with circuit.box([Twirl()]):
    circuit.measure(0, 0)
circuit.cx(0, 1)

are buildable.

Leftward propagation

If a node doesn't find predecessor nodes with all its subsystems, cease propagation on those subsystems but don't error. The error will be raised by PreSamplex.add_emit_twirl when attempting to emit gates, otherwise the nodes get pruned in finalize. Fragments like the following

with circuit.box([ChangeBasis()]):
    circuit.measure(0, 0)
    circuit.noop(1)
circuit.cx(0, 1)

should be buildable.