3-Qubit Circular Quantum Convolution Computation using Fourier Transform with Illustrative Examples

TL;DR

This paper introduces a quantum method for computing 1-D circular convolution of 3-qubit signals using Fourier transforms, with practical examples and quantum circuit schemes for filters.

Contribution

It presents a novel quantum convolution technique leveraging Fourier transforms with minimal quantum resources, applicable to linear systems and filters.

Findings

Quantum convolution method demonstrated with illustrative examples

Quantum schemes for ideal filters provided

Efficient use of Fourier transform with one additional qubit

Abstract

In this work, we describe examples for calculating the 1-D circular convolution of signals represented by 3-qubit superpositions. The case is considered, when the discrete Fourier transform of one of the signals is known and calculated in advance and only the QFT of another signal is calculated. The frequency characteristics of many linear time-invariant systems and filters are well known. Therefore, the considered method of convolution can be used for these systems in quantum computation. The ideal low pass and high pass filters are considered and quantum schemes for convolution are presented. The method of the Fourier transform is used with one addition qubit to prepare the quantum superposition for the inverse quantum Fourier transform.