Preserve measurement classical-bit targets when slicing and recombining circuits

[neuralsorcerer]

What should we add?

Users commonly split a QuantumCircuit at full-width barriers, run or inspect the resulting slices, then recombine those slices. If the circuit includes measurements, each measurement must remain connected to the same classical bit/register after slicing and recombination.

Problem

When slicing circuits that include measurements, the slicing/recombination flow should preserve:

• classical registers,
• classical bits,
• measurement cargs,
• and the mapping from each measured qubit to its original classical bit/register.

If this mapping is dropped or recreated incorrectly, the recombined circuit may no longer be semantically equivalent to the original measured circuit.

Expected behavior

Given a circuit such as:

from qiskit import ClassicalRegister, QuantumCircuit, QuantumRegister
from qiskit_addon_utils.slicing import combine_slices, slice_by_barriers

qreg = QuantumRegister(3, "q")
creg_a = ClassicalRegister(1, "a")
creg_b = ClassicalRegister(2, "b")

qc = QuantumCircuit(qreg, creg_a, creg_b)
qc.h(qreg[0])
qc.measure(qreg[0], creg_b[1])
qc.barrier()
qc.cx(qreg[0], qreg[1])
qc.measure(qreg[1], creg_a[0])
qc.measure(qreg[2], creg_b[0])

slices = slice_by_barriers(qc)
recombined = combine_slices(slices)

The recombined circuit should preserve the same measurement targets:

• q[0] -> b[1]
• q[1] -> a[0]
• q[2] -> b[0]

and should preserve the original classical-register structure.