More efficient synthesis of StatePreparation and Initialize based on Isometry

[ShellyGarion]

What should we add?

The current code for StatePreparation and Initialize is based on [1], but there is a more efficient code in [2] which is currently implemented in Isometry.

Therefore, it would be better to replace the internal implementation of StatePreparation and Initialize by the one implemented in Isometry.

References
[1] Shende, Bullock, Markov. Synthesis of Quantum Logic Circuits (2004) https://arxiv.org/abs/quant-ph/0406176v5
[2] Iten et al., Quantum circuits for isometries (2016). Phys. Rev. A 93, 032318

For example,

for n_qubits in [5, 7, 10, 12, 15]:

    state = np.random.rand(2 ** n_qubits) + np.random.rand(2 ** n_qubits) * 1j
    state = state/np.linalg.norm(state)

    # State preparation
    qc = QuantumCircuit(n_qubits)
    qc.append(StatePreparation(state), range(n_qubits))

    transpiled = transpile(qc, basis_gates=['u', 'cx'], optimization_level=0)
    cx_sp = transpiled.count_ops()['cx']

    # Isometry
    reg_iso = QuantumRegister(n_qubits)
    circuit_iso = QuantumCircuit(reg_iso)
    isom = Isometry(state, 0, 0)

    qc = QuantumCircuit(n_qubits)
    qc.append(isom, range(n_qubits))

    transpiled = transpile(qc, basis_gates=['u', 'cx'], optimization_level=0)
    cx_isom = transpiled.count_ops()['cx']

    print ("num qubits=", n_qubits, "cx count StatePreparation=", cx_sp, "cx count Isometry=", cx_isom)

gives:

num qubits= 5 cx count StatePreparation= 52 cx count Isometry= 26 
num qubits= 7 cx count StatePreparation= 240 cx count Isometry= 120 
num qubits= 10 cx count StatePreparation= 2026 cx count Isometry= 1013 
num qubits= 12 cx count StatePreparation= 8166 cx count Isometry= 4083 
num qubits= 15 cx count StatePreparation= 65504 cx count Isometry= 32752