Improve efficiency of RemoveFinalMeasurement transpiler pass

[mtreinish]

Summary

The RemoveFinalMeasurement was determining which operations were at the
end of a circuit quite inefficiently. It was searching over the entire
DAG to find barrier and measurement instructions and then checking any
that were found if they're children were output nodes. While instead
it'd be much more efficient to chack the parent of each output node for
whether it's a barrier or a measurement. Additionally, the output dag
was being needless rebuilt by modifying the input and then looping over
all nodes in the dag again and copy the node to a new dag. While instead
we can just return the modified input graph. This commit makes those
changes to improve the efficiency of the pass.

Details and comments

Fixes #7038

[mtreinish]

Running this script:

import time
from qiskit.circuit.random import random_circuit
from qiskit.converters import circuit_to_dag

widths = [10, 100, 1000]

for width in widths:
    circuit = random_circuit(width, width, measure=True, seed=42)
    start = time.time()
    circuit.remove_final_measurements()
    stop = time.time()
    print(f"Width {width}: {stop - start}")

Running with this PR:

Width 10: 0.0017766952514648438
Width 100: 0.12475299835205078
Width 1000: 18.337160348892212

Running from main without this PR:

Width 10: 0.002696514129638672
Width 100: 0.7955341339111328
Width 1000: 1058.9532570838928

Now to just fix the test failures fixing the logic and improving the performance in idle_wires() caused fixed in mtreinish@bd96bab

[kdk]

Looks good! QuantumCircuit.remove_final_measurementswould probably also benefit from a similar treatment, but that can be for another issue.

[kdk]

Out of curiosity, we don't usually guard against a malformed DAGCircuit, was there a reason to here?

[mtreinish]

Pylint was yelling at me locally about raising stopiteration without it. This made it happy...

[mtreinish]

This actually will apply to the circuit method too, internally it just uses the transpiler pass: https://github.com/Qiskit/qiskit-terra/blob/main/qiskit/circuit/quantumcircuit.py#L2140-L2181(it's really the only thing using the pass)