Make unrealized SingleQubitQPDGate have definition of None rather than raise error

[garrison]

Fixes #417 according to #417 (comment)

Needs

• release note
• test based on Serializing/Deserializing a circuit with QPD gates causes a ValueError #417 (comment)

[garrison]

Removing these lines wasn't essential, but seems more in line with the idea of relying on the base class's Instruction._define to do nothing rather than to raise an error if a definition isn't explicitly provided.

[ibrahim-shehzad]

This makes sense to me, thanks.

[garrison]

Come to think of it, making this change might allow us to avoid having to override the _directive property, as well.

https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/blob/2df09335477469c949cf714f7cf6210cc40ebdf8/circuit_knitting/cutting/qpd/instructions/qpd_gate.py#L210-L213

UPDATE: I tried removing the _directive override, but I got a test failure.

=================================== FAILURES ===================================
___________________ test_transpile_before_realizing_basis_id ___________________

    def test_transpile_before_realizing_basis_id():
        """Test a workflow where a :class:`.SingleQubitQPDGate` is passed through the transpiler."""
        circuit = EfficientSU2(4, entanglement="linear", reps=2).decompose()
        circuit.assign_parameters([0.8] * len(circuit.parameters), inplace=True)
        observables = PauliList(["ZZII"])
        subcircuits, bases, subobservables = partition_problem(
            circuit=circuit, partition_labels="AABB", observables=observables
        )
    
        # Create a fake backend, and modify the target gate set so it thinks a
        # SingleQubitQPDGate is allowed.
        backend = FakeLagosV2()
        target = deepcopy(backend.target)
        sample_qpd_instruction = SingleQubitQPDGate(QPDBasis.from_instruction(CXGate()), 1)
        target.add_instruction(
            sample_qpd_instruction,
            {(i,): None for i in range(target.num_qubits)},
        )
        pass_manager = generate_preset_pass_manager(3, target=target)
    
        # Pass each subcircuit through the pass manager.
>       subcircuits = {
            label: pass_manager.run(subcircuits["A"])
            for label, circuit in subcircuits.items()
        }

test/cutting/test_cutting_workflows.py:54: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 
test/cutting/test_cutting_workflows.py:55: in <dictcomp>
    label: pass_manager.run(subcircuits["A"])
.tox/py/lib/python3.11/site-packages/qiskit/transpiler/passmanager.py:537: in run
    return super().run(circuits, output_name, callback)
.tox/py/lib/python3.11/site-packages/qiskit/transpiler/passmanager.py:231: in run
    return self._run_single_circuit(circuits, output_name, callback)
.tox/py/lib/python3.11/site-packages/qiskit/transpiler/passmanager.py:292: in _run_single_circuit
    result = running_passmanager.run(circuit, output_name=output_name, callback=callback)
.tox/py/lib/python3.11/site-packages/qiskit/transpiler/runningpassmanager.py:125: in run
    dag = self._do_pass(pass_, dag, passset.options)
.tox/py/lib/python3.11/site-packages/qiskit/transpiler/runningpassmanager.py:169: in _do_pass
    dag = self._do_pass(required_pass, dag, options)
.tox/py/lib/python3.11/site-packages/qiskit/transpiler/runningpassmanager.py:173: in _do_pass
    dag = self._run_this_pass(pass_, dag)
.tox/py/lib/python3.11/site-packages/qiskit/transpiler/runningpassmanager.py:227: in _run_this_pass
    pass_.run(FencedDAGCircuit(dag))
.tox/py/lib/python3.11/site-packages/qiskit/transpiler/passes/optimization/commutation_analysis.py:75: in run
    does_commute = self.comm_checker.commute(
.tox/py/lib/python3.11/site-packages/qiskit/circuit/commutation_checker.py:141: in commute
    operator_1 = Operator(op1, input_dims=(2,) * len(qarg1), output_dims=(2,) * len(qarg1))
.tox/py/lib/python3.11/site-packages/qiskit/quantum_info/operators/operator.py:97: in __init__
    self._data = self._init_instruction(data).data
.tox/py/lib/python3.11/site-packages/qiskit/quantum_info/operators/operator.py:632: in _init_instruction
    op._append_instruction(instruction)
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 

self = Operator([[1.+0.j, 0.+0.j],
          [0.+0.j, 1.+0.j]],
         input_dims=(2,), output_dims=(2,))
obj = Instruction(name='qpd_1q', num_qubits=1, num_clbits=0, params=[])
qargs = None

    def _append_instruction(self, obj, qargs=None):
        """Update the current Operator by apply an instruction."""
        from qiskit.circuit.barrier import Barrier
        from .scalar_op import ScalarOp
    
        mat = self._instruction_to_matrix(obj)
        if mat is not None:
            # Perform the composition and inplace update the current state
            # of the operator
            op = self.compose(mat, qargs=qargs)
            self._data = op.data
        elif isinstance(obj, Barrier):
            return
        else:
            # If the instruction doesn't have a matrix defined we use its
            # circuit decomposition definition if it exists, otherwise we
            # cannot compose this gate and raise an error.
            if obj.definition is None:
>               raise QiskitError(f"Cannot apply Operation: {obj.name}")
E               qiskit.exceptions.QiskitError: 'Cannot apply Operation: qpd_1q'

.tox/py/lib/python3.11/site-packages/qiskit/quantum_info/operators/operator.py:676: QiskitError

[coveralls]

Pull Request Test Coverage Report for Build 6709097724

• 2 of 2 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-0.008%) to 92.377%

---

Totals
Change from base Build 6708466730:	-0.008%
Covered Lines:	2957
Relevant Lines:	3201

---

💛 - Coveralls

[ibrahim-shehzad]

This resolution makes sense, thank you.

[caleb-johnson]

LGTM thanks 👍