Transpilation does not take place if an instruction with {None: None} properties is added to the target

[hay-k]

Environment

• Qiskit Terra version: 0.22.0
• Python version: 3.9.12
• Operating system: Windows 10

What is happening?

Tranpilation return a not-properly-routed circuit.

How can we reproduce the issue?

The documentation of qiskit.transpiler.Target.add_instruction says If there are no constraints on the instruction (as in a noisless/ideal simulation) this can be set to {None, None} which will indicate it runs on all qubits (or all available permutations of qubits for multi-qubit gates)..

So, let's create a target and add a single-qubit instruction to it by specifying {None: None} as its properties

from qiskit import QuantumCircuit
from qiskit.circuit import Parameter
from qiskit.circuit.library import CXGate, RXGate
from qiskit.compiler import transpile
from qiskit.transpiler import Target

n_qubits = 3
target = Target()
target.add_instruction(CXGate(), {(i, i+1): None for i in range(n_qubits - 1)})
target.add_instruction(RXGate(Parameter('theta')), {None: None})

assert target.build_coupling_map() is None

qc = QuantumCircuit(3)
qc.cx(0, 1)
qc.cx(1, 2)
qc.cx(2, 0)

qc_transpiled = transpile(qc, target=target, optimization_level=2, layout_method='trivial')
print(qc_transpiled.draw())

This code prints the following circuit

               ┌───┐
q_0: ──■───────┤ X ├
     ┌─┴─┐     └─┬─┘
q_1: ┤ X ├──■────┼──
     └───┘┌─┴─┐  │  
q_2: ─────┤ X ├──■──
          └───┘    

which is clearly not routed against the target.

The root cause seems to be, that in this scenario the transpiler target fails to generate the coupling map. Note how the assert line in the above code snippet passes, meaning that the coupling map is None.

What should happen?

Transpiler target should have a properly defined coupling map and transpilation should work correctly

Any suggestions?

No response