I'm trying to do Quantum PCA but I came across a problem. I now have a quantum state, say $\frac{|00\rangle+|01\rangle+|11\rangle}{\sqrt{3}}$ and I want to know how to prepare it from two $|0\rangle$ qubits. I mean, I wonder how can I calculate the parameters ($\theta, \phi, \lambda$) of unitary gates? I really do appreicate it if you can help me!

  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    May 18, 2022 at 16:51
  • $\begingroup$ U3 gates are single qubit gates. For the state that you are trying to create, you need two qubit gates (as shown by @Andrés Ruiz) in addition to single qubit gates. If you want to create a single unitary gate you can use a single 4x4 matrix, but that will have more than just 3 parameters. $\endgroup$ May 18, 2022 at 21:40

1 Answer 1


You can initialize the state of a quantum circuit using the initialize method of the QuantumCircuit class. Here is the documentation:


One you have initialize your state, you can see the angles and gates inside the initialization gate using the decompose method. Its documentation can be found in the next page:


A small code that initialize your state $\frac{|00\rangle+|01\rangle+|11\rangle}{\sqrt{3}}$ and decompose the circuit so you can see the basic 2 and 1 qubit gates with their angles is posted below:

import numpy as np

from qiskit.circuit import QuantumCircuit
from qiskit.circuit import QuantumRegister

psi_0 = [1, 1, 0, 1]

psi_0 = psi_0/np.linalg.norm(psi_0)

nbqbits = 2

qr = QuantumRegister(nbqbits)
qc = QuantumCircuit(qr)


d_c = qc.decompose().decompose().decompose().decompose()


You should obtain the next image:

enter image description here

If you want to know about how they implement the initialize method, I think they used this article:



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