Recursive quantum circuits for generating sequency ordering Walsh-Hadamard transform

In the field of information processing, Walsh-Hadamard transforms (WHTs) are exten-sively 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. & COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a recursive circuit for quantum version of Walsh-Hadamard transform (QWHT) based on sequence ordering, which effectively processes discrete signals, images, and videos. Quantum circuits are designed to implement both QWHT and its inverse transform for a more intuitive representation. Simulation results on the IBM platform demonstrate the algorithm's effectiveness. Comparative analysis shows that the proposed sequency ordering QWHT approach outperforms the equivalent quantum version of the conventional WHT algorithm. Based on complexity analysis, our methods are exponentially faster than traditional WHTs.