Recursive quantum circuits for generating sequency ordering Walsh–Hadamard transform

Xiao Chen, Xi Li, Chengzhuo Xu and Zhihao Liu

Physica A: Statistical Mechanics and its Applications, 2023, vol. 621, issue C

Abstract: In the field of information processing, Walsh–Hadamard transforms (WHTs) are extensively employed. However, there exists a dearth of WHT algorithms based on sequence ordering that can be employed for quantum information processing. This paper presents a pioneering attempt to address this issue by proposing a recursive circuit for quantum version of WHT (QWHT) based on sequence ordering, which can effectively process discrete signals, images, and videos. To provide a more intuitive representation of the sequency ordering QWHT, we design quantum circuits to implement both the QWHT and its inverse transform. Furthermore, simulation results on the IBM platform demonstrate the effectiveness of the algorithm. Meanwhile, comparative analysis reveals that the proposed sequency ordering QWHT approach is superior to the equivalent quantum version of the conventional WHT algorithm. Based on the complexity analysis, our methods are exponentially faster than traditional WHTs.

Keywords: Quantum Walsh–Hadamard transformation; Quantum circuit; Sequence ordering (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:621:y:2023:i:c:s0378437123002534

DOI: 10.1016/j.physa.2023.128698

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