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This is my code using qiskit below. I am not familiar with Unitarygate, so I tried to creat a cnot-gate.

from qiskit import QuantumCircuit
from qiskit.extensions import UnitaryGate
import numpy as np

matrix1 = [[1, 0, 0, 0],
          [0, 1, 0, 0],
          [0, 0, 0, 1],
          [0, 0, 1, 0]]
gatecx = UnitaryGate(matrix1)
matrix2 = [[0,1],
          [1,0]]
gatex = UnitaryGate(matrix2)
matrix3 = [[1/np.sqrt(2),1/np.sqrt(2)],
           [1/np.sqrt(2),-1/np.sqrt(2)]]
gateh = UnitaryGate(matrix3)


circuit = QuantumCircuit(2,2)
circuit.append(gatex,[0])
circuit.append(gatecx,[0,1])
circuit.draw('mpl',scale=0.6)

I apply a x-gate to qubit0 first, then apply a cx-gate. enter image description here

After running this code, qubit1 haven't be flipped. The result have shown that qubit0 is target-q and qubit1 is control-q. That is beyond comprehension!! enter image description here

What make me confused is why qubit0 isn't control-qubit in code circuit.append(gatecx,[0,1])?

Then I swapped the position of 0 and 1, circuit.append(gatecx,[1,0]), qubit1 was flipped. Is the first position a control qubit? enter image description here

Telore
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1 Answers1

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This is because Qiskit uses little endian bit ordering. See the details here.

So, in your code should define matrix1 as follows:

matrix1 = [
    [1, 0, 0, 0],
    [0, 0, 0, 1],
    [0, 0, 1, 0],
    [0, 1, 0, 0]
]

You may also use the fact that Qiskit saves matrix representation in the gate to define matrix1

from qiskit.circuit.library import CXGate

matrix1 = CXGate().to_matrix()
Egretta.Thula
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  • Thanks for your answer. After reading the link above and the docs of qiskit, I found that to be the case. Although I think that's a little counter-intuitive... – Telore Mar 19 '23 at 08:21