Append a controlled Initialize in Qiskit

Question

I would like to create a controlled initialize, I have the following code:

a = QuantumRegister(2,"a")
b = QuantumRegister(2,"b")
circuit = QuantumCircuit(a,b)
circuit.initialize(state)

and I would like to encode state only if qubit a and b are 1. I first tried with isometry but then I discovered there is a new simple method like this:

controlled_gate = StatePreparation(state).control()

the problem is that I can't understand how to append on the circuit and how to set the control qubits.

Answer 1

The way to append gate instances to a QuantumCircuit is with the append method.

circuit.append(controlled_gate, circuit.qubits)

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Here is a full example with explanations:

You mentioned:

I would like to encode state only if qubit a and b are 1

As such, you can create two single-qubit registers $a$ and $b$; and a register for the state to encode:

from qiskit import QuantumCircuit, QuantumRegister

circuit = QuantumCircuit(QuantumRegister(1, "a"),
          QuantumRegister(1, "b"),
          QuantumRegister(2, "state"))

Then, in order to control on two qubits ($a$ and $b$), you need to set control(2).

from qiskit.circuit.library import StatePreparation
import numpy as np

state = [0, 1/np.sqrt(2), -1.j/np.sqrt(2), 0]
controlled_gate = StatePreparation(state).control(2)

Finally, the append. The second parameter describe how to wire the gate, in this case circuit.qubits $= [a, b, state_0, state_1]$:

circuit.append(controlled_gate, circuit.qubits)
circuit.draw()

      a: ──────────────────────■──────────────────────
                               │                      
      b: ──────────────────────■──────────────────────
         ┌─────────────────────┴─────────────────────┐
state_0: ┤0                                          ├
         │  State Preparation(0,0.70711,-0.70711j,0) │
state_1: ┤1                                          ├
         └───────────────────────────────────────────┘