Is it possible to create a controlled initialize instruction in Qiskit?

Question

I know it's possible to create custom controlled gates from a circuit, for example,

qc_gate = QuantumCircuit(2)
qc_gate.x(0)
qc_gate.x(1)

gate = qc_gate.to_gate().control(2)

However, since initialization is not considered a gate operation, one cannot do

qc_gate = QuantumCircuit(2)
qc_gate.initialize[a,b]

gate = qc_gate.to_gate().control(2)

but instead, one can do

qc_gate = QuantumCircuit(2)
qc_gate.initialize[a,b]

gate = qc_gate.to_instruction()

This, however, does not allow for control qubits. Is there any way to get around this, to create a quantum instruction that is applied in terms of a set of control qubits?

Answer 1

You can use QuantumCircuit.isometry instead of QuantumCircuit.initialize for state preparation. Like Initialize, Isometry is not a gate so you can't call control() method. But it doesn't use resets internally. So you can use it as follows:

state = [0.5, 0.5, 0.5, 0.5]

qc_iso = QuantumCircuit(2)
qc_iso.isometry(state, [0, 1], [])
controlled_gate = UnitaryGate(Operator(qc_iso)).control()

---

Update

Qiskit 0.35 introduced a new class StatePreparation. This class allows us to prepare a state in the same fashion as Initialize without the reset being automatically applied. So, creating a controlled initialization is now as simple as:

controlled_gate = StatePreparation(state).control()

Answer 2

As far as I know, you cannot do that, but depending on what you want to do, there is a way around.

Using the $\texttt{transpile}$ function, you can turn an instruction in the beginning of your circuit into a unitary. Here's an example:

>>> qc_gate = QuantumCircuit(2)
>>> qc_gate.initialize([0,1,0,0])
>>> qc=transpile(qc_gate,basis_gates=["u1","u2","u3","cx"],optimization_level=1)
>>> print(qc_gate)
     ┌──────────────────────┐
q_0: ┤0                     ├
     │  Initialize(0,1,0,0) │
q_1: ┤1                     ├
     └──────────────────────┘
>>> print(qc)
     ┌─────────┐┌───┐┌─────────┐┌───┐
q_0: ┤ U2(0,0) ├┤ X ├┤ U2(0,0) ├┤ X ├
     └─────────┘└─┬─┘└─────────┘└─┬─┘
q_1: ─────────────■───────────────■──
                                     

and you can then use $\texttt{qc.to_instruction().control(2)}$