Implementing Quantum Fourier Transform With Qiskit

Introduction

The Quantum Fourier Transform (QFT) is an important function in Quantum Computing. It is a key component in many quantum algorithms, such as Shor's factoring algorithm and quantum phase estimation. The Quantum Fourier Transform on a quantum state is quite similar to the classical Fourier Transform.

Background

The Fourier Transform is an essential tool in classical computing as it enables the frequency domain examination of a value sequence. Similarly, the Quantum Fourier Transform serves the same function but for quantum bits (qubits).

In this blog post, we will implement the Quantum Fourier Transform using Qiskit, which is an open-source quantum computing framework for leveraging today's quantum computers.

Implementation using Qiskit

The key to understanding the quantum Fourier transform is understanding that it translates amplitude information into phase information. The first step is to install Qiskit, which you can do with pip:

pip install qiskit

Then we can move on to create our Quantum Fourier Transform function using Qiskit:

from qiskit import QuantumCircuit

def qft_rotations(circuit, n):
    if n == 0:
        return circuit
    n -= 1
    circuit.h(n)
    for qubit in range(n):
        circuit.cp(pi/2**(n-qubit), qubit, n)
    # At the end of our function, we call the same function again on
    # the next qubits (we reduced n by one earlier in the function)
    qft_rotations(circuit, n)

This function creates the necessary rotations for each qubit depending on their positions. The controlled phase rotations and the Hadamard gate implemented before them are fundamental to the Fourier Transform. The function then calls itself reducing the value of 'n' until 'n' is 0 essentially creating the necessary gate for each qubit in a recursive manner.

The Quantum Fourier Transform, at its core, is just a bunch of gates applied to each qubit--each gate is determined by the position of the qubit. After all the qubits are processed, we reverse their order by adding a swap gate at the end of our circuit:

def swap_registers(circuit, n):
    for qubit in range(n//2):
        circuit.swap(qubit, n-qubit-1)
    return circuit


def qft(circuit, n):
    """QFT on the first n qubits in circuit"""
    qft_rotations(circuit, n)
    swap_registers(circuit, n)
    return circuit

Conclusion

Quantum Fourier Transform is a key component in quantum algorithms. The code snippets provided should work perfectly as it uses Qiskit, the widely accepted library for quantum computing.

Remember to experiment with the code to understand the underlying process better. The nature of quantum computing ensures there is always something fascinating to learn, which is precisely why it's such a captivating field. So, don't stop exploring!