`PlacementPass` on `SquareGrid` architecture causes RunTime Error when running on AerBackend

[IlanIwumbwe]

Benny and I found this by running a randomly generated circuit through the compiler.

Recreate with:

subcirc_4 = Circuit(2, "subcirc_4")

a = SquareGrid(subcirc_4.n_qubits, 1)
NaivePlacementPass(a).apply(subcirc_4)

no_pass_circ = backend.get_compiled_circuit(subcirc_4, optimisation_level=0)
counts_no_pass = backend.run_circuit(no_pass_circ, 1000).get_counts()

Results in:

[q[0], q[1]]
[gridNode[0, 0, 0], gridNode[1, 0, 0]]
NotImplementedError: Qiskit registers must use a single index

This is because routing on square grid creates indices with 3 dimensions, which won't work and throw a NotImplementedError as shown here.

This also limits users from using the feature where you can define qubit indices more than one dimension.

subcirc_4 = Circuit(2, "subcirc_4")
subcirc_4.add_qubit(Qubit("qw", [0, 1]))
print(subcirc_4.qubits)

no_pass_circ = backend.get_compiled_circuit(subcirc_4, optimisation_level=0)
counts_no_pass = backend.run_circuit(no_pass_circ, 1000).get_counts()

Although this isn't really a RunTime error, this limitation isn't stated in documentation as far as we can tell.