Mapping Qiskit registers via transpilation passes

[andreamari]

Issue Description

We currently have a functions to change the qubit and bit registers in Qiskit circuits (see e.g. this). They are necessary for having consistent names in conversions. However those functions touch very low-level (sometimes private) attributes of the QuantumCircuit class and are therefore subject to bugs, especially when new Qiskit versions are released.

Proposed Solution

In this PR https://github.com/unitaryfund/mitiq/pull/1421 it has been suggested to transform quantum and classical registers with Qiskit transpilation passes. This method is probably more stable.

[1ucian0]

In this PR https://github.com/unitaryfund/mitiq/pull/1421 it has been suggested to transform quantum and classical registers with Qiskit transpilation passes. This method is probably more stable.

I think the same might apply to _add_identity_to_idle, _remove_identity_from_idle, and other circuit transformations. Even the "executor" itself.

[Rahul-Mistri]

Giving this a shot :+1:

Edit:

• Going through the Qiskit transpilation docs