Evaluate Quantum Fourier Transform Using Quantum Machine Learning

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, we’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.