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PROJECT

# Evaluate Quantum Fourier Transform Using Quantum Machine Learning

In this project, we will evaluate the Quantum Fourier Transform of a statevector through a variational quantum circuit. A gradient-based optimization approach is used with the help of the PennyLane library.

You will learn to:

Plot simulation results in Python.

Optimize a quantum circuit with dedicated packages.

Optimize a quantum circuit using a machine learning approach.

Create and simulate a quantum circuit using PennyLane.

Skills

Quantum Computing

Quantum Machine Learning

Optimization

Prerequisites

Basic understanding of the Python language

Basic knowledge of linear algebra concepts

Basic understanding of quantum computing concepts

Basic understanding of machine learning concepts

Basic understanding of the optimization theory

Technologies

NumPy

PennyLane

Matplotlib

Project Description

Quantum machine learning is a subdomain of quantum computing in which machine learning is integrated with quantum algorithms for data analysis on a quantum computer. Quantum machine learning provides an enhanced, and, in certain cases, improved performance over classical machine learning algorithms.

Quantum Fourier transform is a quantum operator that evaluates the Fourier transform of a state vector. The unitary matrix representation of this operator is as follows:

$\begin{bmatrix} 1 & 1 & \dots & 1\\ 1 & e^{\frac{\iota 2\pi}{N}} & \dots & e^{\frac{\iota2\pi(N-1)}{N}}\\ 1 & e^{\frac{\iota 2\pi. 2}{N}} & \dots & e^{\frac{\iota2\pi. 2(N-1)}{N}}\\ 1 & e^{\frac{\iota 2\pi. 3}{N}} & \dots & e^{\frac{\iota2\pi.3(N-1)}{N}}\\ \vdots & \vdots & \dots & \vdots \\ 1 & e^{\frac{\iota 2\pi.(N-1)}{N}} & \dots & e^{\frac{\iota2\pi.(N-1)(N-1)}{N}}\\ \end{bmatrix}$

Here, $N$ is the number of qubits in the quantum state.

In this project, weâ€™ll train a variational quantum circuitA variational quantum circuit, also called a parameterized quantum circuit, is a circuit with variable parameters. using quantum machine learning. This will provide hands-on experience constructing and training a quantum circuit using a machine learning approach.

1

Construct the Quantum Circuit

Task 3: Create the Quantum Circuit

Task 4: Apply the Inverse QFT Matrix

Task 6: Create the Quantum Node

2

Optimize the Quantum Circuit

Task 7: Create the Cost Function