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Digest - IEEE Antennas and Propagation Society. International Symposium

On the Use of Quantum Fourier Transform for Array Antenna Analysis

Paolo Rocca, Luca Tosi, Nicola Anselmi, Andrea Massa

Published Jul 10, 2022• 2 citations
Publisher

Abstract

The analysis of the power pattern of linear phased arrays (PAs) is addressed by exploiting advantages offered by the Quantum Computing (QC) framework. The proposed approach is described in its mathematical formulation and the parallel between the classical Discrete Fourier Transform (DFT) and the Quantum Fourier Transform (QFT) algorithm is discussed in the context of the power pattern analysis. The proposed QFT-based method is validated by means of proof-of-concept results, in order to show the peculiarity of the quantum method in terms of accuracy and computational cost.

DOI
10.1109/ap-s/usnc-ursi47032.2022.9886119

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The analysis of the power pattern of linear phased arrays (PAs) is addressed by exploiting advantages offered by the Quantum Computing (QC) framework. The proposed approach is described in its mathematical formulation and the parallel between the classical Discrete Fourier Transform (DFT) and the Quantum Fourier Transform (QFT) algorithm is discussed in the context of the power pattern analysis. The proposed QFT-based method is validated by means of proof-of-concept results, in order to show the peculiarity of the quantum method in terms of accuracy and computational cost.
A study on the analysis of the power-pattern of phased-array antennas (PAs) based on the quantum Fourier transform (QFT) is presented. The computation of the power pattern given the set of complex excitations of the PA elements is addressed within the quantum computing (QC) framework by means of a customized procedure that exploits the quantum mechanics principles and theory. A representative set of numerical results, yielded with a quantum computer emulator, is reported and discussed to validate the proposed method also pointing out its features in comparison with the classical approach based on the discrete Fourier transform (DFT).
Thinning antenna arrays through quantum Fourier transform (QFT) is proposed. Given the lattice of the candidate locations for the array elements, the problem of selecting which antenna location has to be either occupied or not by an array element is formulated in the quantum computing (QC) framework and then addressed with an ad-hoc design method based on a suitable implementation of the QFT algorithm. Representative numerical results are presented and discussed to point out the features and the advantages of the proposed QC-based thinning technique.
Thinning antenna arrays through quantum Fourier transform (QFT) is proposed. Given the lattice of the candidate locations for the array elements, the problem of selecting which antenna location has to be either occupied or not by an array element is formulated in the quantum computing (QC) framework and then addressed with an ad-hoc design method based on a suitable implementation of the QFT algorithm. Representative numerical results are presented and discussed to point out the features and the advantages of the proposed QC-based thinning technique.
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank-1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix-2 QFT decomposition to a radix-d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view.
This survey presents a comprehensive analysis of the quantum Fourier transform (QFT), a fundamental tool in quantum computing, in comparison to its classical counterpart, the fast Fourier transform (FFT). The study begins with an introduction to the classical Fourier transform, which is widely used in different disciplines such as signal and image processing. The article introduces the QFT as a quantum version of the Fourier transform, detailing how it leverages quantum parallelism and superposition to reduce the time complexity of the operation, and highlighting its crucial role in quantum algorithms like Shor’s algorithm for integer factorization. The analysis also addresses the mathematical foundations of the QFT, its implementation in quantum circuits, and the key advantages and challenges associated with its use, such as measurement precision and quantum decoherence. Finally, it concludes with an exploration of the current and potential applications of QFT in quantum computing.