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arXiv · 2504.20649

Short-time quantum Fourier transform processing

Sreeraj Rajindran Nair·Benjamin Southwell·Christopher Ferrie
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Abstract

Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based processing schemes. Whilst quantum analogs to some digital signal processing algorithms have been discovered, including the quantum Fourier transform (QFT), there has been no development of short-time processing techniques in the quantum domain. In this manuscript, we introduce the short-time QFT (STQFT) processing technique to bridge this gap in research. We develop a novel overlap-add reconstruction technique in the quantum domain using a permutation gate to combine subsequent windows. With this in mind, we discuss convolution under our novel STQFT processing scheme. We demonstrate filtering in the quantum Fourier domain with a filter stored in a quantum register as well as in a block encoded unitary gate. Throughout the paper, we elaborate upon implementation details such as applying DC offsets to input signals, skipping input data frames whenever necessary, the use of overlap-save as a reconstruction technique and mitigating time-varying scaling due to normalization of the windowed input data and filters.

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Sreeraj Rajindran Nair, Benjamin Southwell, Christopher Ferrie. 2025-04-29. Short-time quantum Fourier transform processing. https://doi.org/10.1109/icassp49660.2025.10890646

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