Open Access

ARTICLE

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

Artyom M. Grigoryan^1,*, Sos S. Agaian²

1 Department of Electrical and Computer Engineering, The University of Texas at San Antonio, San Antonio, USA
2 Computer Science Department, The College of Staten Island, New York, USA

* Corresponding Author: Artyom M. Grigoryan. Email:

Journal of Quantum Computing 2024, 6, 1-14. https://doi.org/10.32604/jqc.2023.026981

Received 16 October 2023; Accepted 14 December 2023; Issue published 30 January 2024

Abstract

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

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Keywords

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