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IEEE International Conference on Acoustics Speech and Signal Processing

Signal Analysis-Synthesis Using the Quantum Fourier Transform

Aradhita Sharma, Glen S. Uehara, Vivek Narayanaswamy, Leslie Miller, Andreas Spanias

Published May 5, 2023• 13 citations
Publisher

Abstract

This paper presents the development of Quantum Fourier transform (QFT) education tools in the object-oriented Java-DSP (J-DSP) simulation environment. More specifically, QFT and Inverse QFT (IQFT) user-friendly J-DSP functions are developed to expose undergraduate students to quantum computing. These functions provide opportunities to examine QFT resolution, precision (qubits), and the effects of quantum measurement noise. In our study, we also describe a laboratory exercise on QFT-based speech analysis-synthesis which has been deployed in our senior-level DSP class and in our NSF workforce development programs. The software and the laboratory exercise are evaluated using formative and summative assessments.

DOI
10.1109/icassp49357.2023.10096524

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This paper presents the development of Quantum Fourier transform (QFT) education tools in the object-oriented Java-DSP (J-DSP) simulation environment. More specifically, QFT and Inverse QFT (IQFT) user-friendly J-DSP functions are developed to expose undergraduate students to quantum computing. These functions provide opportunities to examine QFT resolution, precision (qubits), and the effects of quantum measurement noise. In our study, we also describe a laboratory exercise on QFT-based speech analysis-synthesis which has been deployed in our senior-level DSP class and in our NSF workforce development programs. The software and the laboratory exercise are evaluated using formative and summative assessments.
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This paper introduces a hybrid two-dimensional Quantum Fourier Transform (2D hybrid QFT) method for image analysis and synthesis. The QFT and Inverse QFT (IQFT) functions enable analysis-synthesis implementation using frequency spectrum-based selection approaches for compression. We study the resolution and precision of the QFT by comparing its outputs against classical two-dimensional Fast Fourier Transform (FFT) techniques using pixel-level Signal to Noise Ratio (SNR) as a metric. Formative and summative assessments have been deployed as a laboratory exercise in two National Science Foundation (NSF) workforce development programs. Preliminary evaluation results are presented in this paper.
This Innovative Practice Work in Progress Paper describes the development and assessment of a web-based simulation lab exercise introducing basic quantum computing concepts in a sophomore signals and systems course. Specifically, students make the connection between quantum computing and signals and systems theory through a comparative study of using Quantum Fourier Transforms and Fast Fourier Transforms for a speech analysis-synthesis application. In addition, quantum noise models are introduced and simulated to show their effect on computation performance. Statistics from pre/post quizzes show that there is significant knowledge improvement by completing the lab exercise.
Fourier Transform (FT) is an important signal processing technique that translates time-domain signals to frequency-domain forms. It is widely used in several applications, including 5G networks, image processing, & spectrum analysis. In 5G networks, efficient frequency analysis is critical for noise reduction, channel optimisation, and signal dependability.This study explores the implementation of Classical Fourier Transform, Fast Fourier Transform, and Quantum Fourier Transform using Python (NumPy, Pandas, Matplotlib) and Qiskit. The FFT significantly improves processing speed, making it suitable for real-time applications. On the other hand, QFT leverages quantum superposition and entanglement, offering promising advancements for future high-speed communication and secure data transmission. Additionally, the signal is successfully reconstructed using both the Inverse Fast Fourier Transform (IFFT) and the Inverse Quantum Fourier Transform (IQFT). While IFFT efficiently restores the original signal with minimal numerical artifacts, IQFT ensures exact reconstruction without errors. The study also includes execution on IBM Quantum’s real hardware, showcasing the practical feasibility of quantum-based signal processing.
Quantum Fourier transform (QFT) plays a key role in many quantum algorithms, but the existing circuits of QFT are incomplete and lacking the proof of correctness. Furthermore, it is difficult to apply QFT to the concrete field of information processing. Thus, this chapter firstly investigates quantum vision representation (QVR) and develops a model of QVR (MQVR). Then, four complete circuits of QFT and inverse QFT (IQFT) are designed. Meanwhile, this chapter proves the correctness of the four complete circuits using formula derivation. Next, 2D QFT and 3D QFT based on QVR are proposed. Experimental results with simulation show the proposed QFTs are valid and useful in processing quantum images and videos. In conclusion, this chapter develops a complete framework of QFT based on QVR and provides a feasible scheme for QFT to be applied in quantum vision information processing.
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