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How to initialise a qubit in the state $frac{1}{sqrt2}(|0rangle+|1rangle)$ in qiskit?

Quantum Computing Asked by Shivam on January 30, 2021

In qiskit, how can I initialise a qubit in a complex state, specifically in the state:
$$left|qright> = frac{1}{sqrt2} left|0right> + i frac{1}{sqrt2} left|1right>$$

2 Answers

You can generate a general quantum state $|psirangle$ in Qiskit by using their Custom package.

from qiskit.aqua.components.initial_states import Custom 
import math 
state_vector = [1, 1j]
Psi = Custom(1,state_vector = state_vector).construct_circuit()
Psi.draw()

Running the above code in Qiskit would give you something like below:

enter image description here


But also notice that your state $|qrangle = dfrac{1}{sqrt{2}}big( |0rangle + i | 1rangle big) $ is actually resulting from

$$ dfrac{Z + Y}{sqrt{2}} |0rangle = |qrangle $$

where $Z$ and $Y$ are the Pauli matrices and $|0rangle = begin{bmatrix} 1 0 end{bmatrix} $.

Answered by KAJ226 on January 30, 2021

You can use initialize function. Here is a code constructing your one qubit state:

from qiskit import ClassicalRegister, QuantumRegister, QuantumCircuit, Aer, execute
import math as m

quantumState = [
    1 / m.sqrt(2) * complex(1, 0),
    1 / m.sqrt(2) * complex(0, 1)]

q = QuantumRegister(1, name = 'q')
c = ClassicalRegister(1, name = 'c')

circuit = QuantumCircuit(q,c)

circuit.initialize(quantumState, [q[0]])

You can prepare multiqubit states as well, for example for $|psirangle = frac{1}{2}(|00rangle + |01rangle+|10rangle+|11rangle)$:

from qiskit import ClassicalRegister, QuantumRegister, QuantumCircuit, Aer, execute
import math as m

quantumState = [0.5,0.5,0.5,0.5]

q = QuantumRegister(2, name = 'q')
c = ClassicalRegister(2, name = 'c')

circuit = QuantumCircuit(q,c)

circuit.initialize(quantumState, [q[0],q[1]])

Answered by Martin Vesely on January 30, 2021

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