How to import circuit libraries into qiskit

Question

Im trying to put the QFT circuit in my qiskit circuit but im having trouble:

import numpy as np
# Importing standard Qiskit libraries
from qiskit import QuantumCircuit, transpile, Aer, IBMQ
from qiskit.tools.jupyter import *
from qiskit.visualization import *
from ibm_quantum_widgets import *
from math import sqrt
from qiskit.quantum_info import DensityMatrix
from qiskit.circuit.library import QFT

# Loading your IBM Q account(s)
provider = IBMQ.load_account()

qc = QuantumCircuit(1,1)

init = [sqrt(3/4),-sqrt(1/4)]
qc.initialize(init,0)
qc.h(0)
qc.x(0)
qc.h(0)
qc.QFT(0)

display(qc.draw())


s0 = DensityMatrix(qc)
sim = Aer.get_backend('unitary_simulator')
job = transpile(qc,sim)
state = sim.run(job).result().get_unitary()
print(qc.qasm())

Answer 1

The way you imported the packages, including the QFT circuit is correct. You just didn't execute it correctly.

When you call QFT, it creates a circuit that perform QFT on its own. To add this circuit to your original circuit, you can just use +. Also the to perform a QFT on 1 qubit, you should use QFT(1) instead of QFT(0).

So your circuit without QFT is:

qc = QuantumCircuit(1,1)

init = [sqrt(3/4),-sqrt(1/4)]
qc.initialize(init,0)
qc.h(0)
qc.x(0)
qc.h(0)
display(qc.draw())
     ┌──────────────────────────┐┌───┐┌───┐┌───┐
q_0: ┤ initialize(0.86603,-0.5) ├┤ H ├┤ X ├┤ H ├
     └──────────────────────────┘└───┘└───┘└───┘
c: 1/═══════════════════════════════════════════
                                                

Now to add on the 1-qubit QFT operation which is just the Hadamard gate, you can do it as:

qc = QuantumCircuit(1,1)
init = [sqrt(3/4),-sqrt(1/4)]
qc.initialize(init,0)
qc.h(0)
qc.x(0)
qc.h(0)
qc = qc + QFT(1)
display( qc.draw() )

     ┌──────────────────────────┐┌───┐┌───┐┌───┐┌───┐
q_0: ┤ initialize(0.86603,-0.5) ├┤ H ├┤ X ├┤ H ├┤ H ├
     └──────────────────────────┘└───┘└───┘└───┘└───┘
c: 1/════════════════════════════════════════════════
                                                     

As you can see, the Hadamard gate is now added to the circuit.