Inverse Quantum Fourier Transform in Qiskit 2.0

In the previous article, we explored concrete examples and advantages of the Quantum Fourier Transform.
In this article, we will implement the Inverse Quantum Fourier Transform using Qiskit 2.0 and verify that the original quantum state can be correctly identified.

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Regarding the IBM Quantum Developer Certification Exam

IBM offers a certification exam related to Qiskit, which is introduced in this blog.

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Practice exams

https://www.udemy.com/course/ibm-certified-quantum-computation-qiskit-practice-exams/?referralCode=3B3263DF800E05439AD2

Inverse Quantum Fourier Transform in Qiskit 2.0

In the previous article, we explained that if a 2-qubit quantum state existed in either state $\psi_1 = \frac{1}{2} \left( \ket{00} + i\ket{01} - \ket{10} - i\ket{11} \right)$ or $\psi_2 = \frac{1}{2} \left( \ket{00} - \ket{01} + \ket{10} - \ket{11} \right)$, it is possible to determine which state it is by applying the Inverse Quantum Fourier Transform.
In this article, we will perform the Inverse Quantum Fourier Transform using Qiskit and verify that the original quantum state can be correctly identified.
Firstly, let’s import the necessary functions.

from qiskit import QuantumCircuit
from qiskit.circuit.library import StatePreparation
from qiskit.primitives import StatevectorSampler
from qiskit.circuit.library import QFT

We define Sampler and Quancum Cruicuit.

sampler = StatevectorSampler()
n_qubits = 2
qc = QuantumCircuit(n_qubits, 2)

In this article, we set the target quantum state to $\psi_2$, and append the quantum circuit that generates this state below.

state = [1/2, - 1/2, 1/2, - 1/2]  
prep = StatePreparation(state)
qc.append(prep, [0, 1])

By simply measuring the quantum state at this point, we can only obtain results like the ones below, and it is not possible to determine whether the state was $\psi_1$ or $\psi_2$.

qc.measure([0,1], [0,1])
pub = (qc, None)
job = sampler.run([pub], shots=100)
result=job.result()[0]
print(result.data.c.get_counts())

# Output
{'01': 27, '10': 27, '11': 23, '00': 23}

Let’s implement the Inverse Quantum Fourier Transform.

iqft = QFT(num_qubits=n_qubits, inverse=True, do_swaps=True)
qc.append(iqft, [0, 1])
qc.measure([0,1], [0,1])

The overall circuit is as follows.

As explained in the previous article, if $\ket{01}$ is observed, we know that the original state was $\psi_1$, while if $\ket{10}$ is observed, we know that it was $\psi_2$.

qc.draw('mpl')

Let’s execute the quantum circuit.

pub = (qc, None)
job = sampler.run([pub], shots=100)
result=job.result()[0]
print(result.data.c.get_counts())

As shown below, the result observes state $\ket{10}$, indicating that state $\psi_2$ was originally generated. Similarly, if you generate state $\psi_1$ and then apply the Inverse Quantum Fourier Transform, you will observe state$\ket{01}$. Give it a try when you have a moment.

# Output
{'10': 100}