Fixed issue 4526 by adding InitializeGate

[incud]

Summary

Fixes #4526

Details and comments

Initialize is implemented as an Instruction object instead of Gate because it uses reset instruction which is not unitary. This fix modifies Initialize passing an additional named parameter reset to its constructor whose default value is True. You can expect the behavior of Initialize to be the same if you don't specify the reset parameter.

However, instantiating Initialize with reset=False lets us define the InitializeGate gate. We can now create the controlled version of Initialize using InitializeGate(desired_vector).control(how_many_controlled_qubits).

Here an example usage:

from qiskit import * 
from qiskit.extensions.quantum_initializer.initializer import InitializeGate
import math

circuit = QuantumCircuit(2)
circuit.x(0)
wanted_state = [1 / math.sqrt(2), 1 / math.sqrt(2)]
circuit.append(InitializeGate(wanted_state).control(1), [0, 1])

result = execute(circuit, backend=Aer.get_backend('statevector_simulator'), shots=1).result()
print(result.get_statevector())

The introduction of InitializeGate and its controlled version may help with the implementation of quantum distance-based classifier like the one you find in [Schuld, Fingerhuth, Petruccione, 2018].

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[ajavadia]

State preparation should really not be a unitary operation. Which part of the paper you link to above has this?

The reset could be removed by the transpiler if it occurs in the beginning of the circuit, but the reset is required to reliably prepare a state.

cc'ing @Cryoris too as he opened the initial issue.

[incud]

@ajavadia thank you for your feedback

I've implemented the circuit performing controlled-initialize and twice-controlled-initialize in order to extend the circuit presented in the linked paper. In particular, when the author initializes its single-qubit data with the controlled version of RY (sometimes controlled X when the data is $|1\rangle$) I used my own controlled-initialize to initialize my multiple-qubits data.

[Cryoris]

After discussing with @ajavadia I think it would make sense to move the state-preparation logic into a Gate and have Initialize be only resets plus this state-preparation gate. I don't like the name InitializeGate though, this name only makes sense to us because we have a very specific definition of the term Gate and it will be weird for outside users to have this alongside Initialize. We can decide on naming later though.

[incud]

@Cryoris Thank you for your comment.

There is anything I can do to improve the code?

[Cryoris]

Yes, could you put all the logic inside InitializeGate and have Initialize just be a layer of resets and then a call to InitializeGate? So schematically

class InitializeGate(Gate):
    def _define(self):
         # all the logic of `Initialize` in here

class Initialize(Instruction):
    def _define(self):
        # resets and then InitializeGate

Once that is done, we can think of a better name than InitializeGate 😄

[Cryoris]

I think the approach looks good. @ajavadia do you have an idea on the naming?

[Cryoris]

I think this comment can be removed, it applies to InitializeGate since the decomposition is computed there.

[incud]

The comment is now removed

[incud]

@Cryoris Thank you for your comment. I've merged the fix

[prakharb10]

Following #7666, now that we have a StatePreparation class, I believe that solves the issue this PR was intended for?

[jakelishman]

Yeah, this is obsolete as of #7666, thanks.

For the future: the motivating example for including the unitary component of initialisation as a separate instruction was so users could define their own mappings $\lvert\psi\rangle\to\lvert\phi\rangle$ more easily by using the state-prep unitary $\mathcal U_\chi\lvert0\rangle\coloneqq \lvert\chi\rangle$ as $\mathcal U_\phi\mkern2mu\mathcal U_\psi^\dagger$. So Initialize is now an Instruction that uses a StatePreparation Gate interally, where the "state preperation" operation is just defined to map $\lvert0\rangle\to\lvert\psi\rangle$.