Use Isometry to implement Initialize instruction

[EgrettaThula]

What is the expected enhancement?

As per documentation, Isometry instruction can be used for state preparation.
On the other hand, Initialize instruction does its work by first resetting the qubits to |0⟩ followed by an state preparing unitary.
That means circ.initialize is equivalent to circ.reset + circ.iso.

However, I noticed that using Isometry almost always results in a circuit with much less number of CNOTs.

n = 4
psi = random_statevector(2 ** n)

# Using initialize
qr1 = QuantumRegister(n)
qc1 = QuantumCircuit(qr1)
qc1.initialize(psi, qr1)
tr_qc1 = transpile(qc1, basis_gates = ['u', 'cx'], optimization_level = 3)
print('Initialize:', tr_qc1.count_ops())

# Using reset + iso
qr2 = QuantumRegister(n)
qc2 = QuantumCircuit(qr2)
qc2.reset(qr2)
qc2.iso(psi, qr2, [])
tr_qc2 = transpile(qc2, basis_gates = ['u', 'cx'], optimization_level = 3)
print('Isometry:', tr_qc2.count_ops())

The result is something like that:

Initialize: OrderedDict([('u', 26), ('cx', 22)])
Isometry: OrderedDict([('u', 15), ('cx', 11)])

So, I suggest to use Isometry to implement Initialize instruction. This should lead to a better end result with less code to maintain.

[Cryoris]

Isometry and Initialize use two different algorithms to construct the circuits. Rather than replace one with the other I think it would be better to keep synthesis part of Initialize (i.e. without the initial resets) in some class in Qiskit but have QuantumCircuit.initialize use the more efficient isometry instead.

[ShellyGarion]

close in favor of #12081.
the separation of initialize to reset + state preparation was done in #7666