数字信号的量子表示与基本运算

doi:10.3969/j.issn.1007-5461.2026.03.012

量子电子学报 ›› 2026, Vol. 43 ›› Issue (3): 456-471.doi: 10.3969/j.issn.1007-5461.2026.03.012

数字信号的量子表示与基本运算

刘显德 *, 李笑

东北石油大学计算机与信息技术学院, 黑龙江大庆 163318

收稿日期:2023-06-29 修回日期:2023-10-11 出版日期:2026-05-28 发布日期:2026-05-28
通讯作者: E-mail: lxddqpi@126.com E-mail:E-mail: lxddqpi@126.com
作者简介:刘显德 ( 1973 - ), 黑龙江大庆人, 教授, 博士, 硕士生导师, 主要从事量子图像处理、量子机器学习方面的研究。E-mail: lxddqpi@126.com
基金资助:
黑龙江省自然科学基金 (LH2022F006)

Quantum representation and basic operations of digital signals

LIU Xiande *, LI Xiao

School of Computer and Information Technology, Northeast Petroleum University, Daqing 163318, China

Received:2023-06-29 Revised:2023-10-11 Published:2026-05-28 Online:2026-05-28
Supported by:

摘要/Abstract

摘要： 为克服数字信号表示的局限性, 本文提出一种一维有限长度数字信号的量子表示方法。该表示借鉴了现有量子音频的灵活表示形式, 利用两组量子比特分别编码信号的振幅与时序信息, 其中振幅采用二进制原码中的(n + 1)位有符号数表示, 包含1个符号位、m个整数位及(n - m)个小数位。进而研究了基于该表示的数字信号基本运算, 包括加法、减法、乘法、除法及循环卷积, 并设计了相应的量子线路以实现上述运算。在此基础上, 通过统计线路中所采用的量子基本门数量, 对线路复杂度进行了分析, 结果表明所提出的量子数字信号处理方案可实现对经典处理方法的加速。同时, 经典计算机上的仿真实验也验证了所设计量子线路的正确性。

关键词: 量子图像处理, 量子信号表示, 量子信号处理, 量子原码乘法, 量子原码除法, 量子循环卷积

Abstract: To address the limitations of digital signal representation, a quantum representation for one-dimensional finite-length digital signals is proposed in this paper. Similar to the existing flexible representation of quantum audio, this representation approach employs two sets of qubits to encode the amplitude and timing information of the signal separately. Specifically, the amplitude is represented by an (n+1)-bit signed number in the binary original code, consisting of one sign bit, m integer bits, and n - m fractional bits. Subsequently, the fundamental operations on this representation, including addition, subtraction, multiplication, division, and circular convolution of two digital signals, are introduced, and corresponding quantum circuits are designed to implement these operations. And then, based on the number of elementary quantum gates employed, the complexity of the circuits is analyzed. The results demonstrate that the proposed quantum digital signal processing scheme achieves acceleration compared to classical processing methods. Meanwhile, simulations conducted on a classical computer confirm the correctness of the designed quantum circuits.

Key words: quantum image processing, quantum signal representation, quantum signal processing; quantum true code multiplication, quantum true code division, quantum circular convolution

中图分类号:

TP391

刘显德 , 李笑 . 数字信号的量子表示与基本运算[J]. 量子电子学报, 2026, 43(3): 456-471.

LIU Xiande , LI Xiao. Quantum representation and basic operations of digital signals[J]. Chinese Journal of Quantum Electronics, 2026, 43(3): 456-471.

参考文献

[1]Sidhu J S, Joshi S K, Gündo?an M, et al.Advances in space quantum communications[J].IET Quantum Communication, 2021, 2(4):182-217 [2]Pirandola S, Andersen U L, Banchi L, et al.Advances in quantum cryptography[J].Advances in optics and photonics, 2020, 12(4):1012-1236 [3]Tebbenjohanns F, Mattana M L, Rossi M, et al.Quantum control of a nanoparticle optically levitated in cryogenic free space[J].Nature, 2021, 595(7867):378-382 [4]Venegas-Andraca S E, Bose S.Storing, processing, and retrieving an image using quantum mechanics[C]//Quantum Information and Computation. SPIE, 2003, 5105: 137-147. [5]Latorre J I.Image compression and entanglement[J]. arXiv preprint quant-ph/0510031, 2005. [6]Le P Q, Dong F, Hirota K.A flexible representation of quantum images for polynomial preparation, image compression, and processing operations[J]. Quantum Information Processing, 2011, 10: 63-84. [7]Sun B, Iliyasu A, Yan F, et al.An RGB multi-channel representation for images on quantum computers[J].J. Adv. Comput. Intell. Intell. Inform, 2013, 17(3):404-417 [8]Sun B, Le P Q, Iliyasu A M, et al.A multi-channel representation for images on quantum computers using the RGBα color space[C]//2011 IEEE 7th International Symposium on Intelligent Signal Processing. IEEE, 2011: 1-6. [9]Zhang Y, Lu K, Gao Y, et al.NEQR: a novel enhanced quantum representation of digital images[J]. Quantum information processing, 2013, 12: 2833-2860. [10]Yan F, Iliyasu A M, Venegas-Andraca S E.A survey of quantum image representations[J]. Quantum Information Processing, 2016, 15: 1-35. [11]Wang B, Xu L, Li J, et al.Quantum-limited localization and resolution in three dimensions[J].Photonics Research, 2021, 9(8):1522-1530 [12]Yuan S, Wen C, Hang B, et al.The dual-threshold quantum image segmentation algorithm and its simulation[J]. Quantum Information Processing, 2020, 19: 1-21. [13]Jiang N, Dong X, Hu H, et al.Quantum image encryption based on Henon mapping[J]. International Journal of Theoretical Physics, 2019, 58: 979-991. [14]Qu Z, Chen S, Wang X.A secure controlled quantum image steganography algorithm[J]. Quantum Information Processing, 2020, 19: 1-25. [15]Hu W W, Zhou R G, Luo J, et al.LSBs-based quantum color images watermarking algorithm in edge region[J].Quantum Information Processing, 2019, 18(1):16- [16]Wang J.QRDA: quantum representation of digital audio[J]. International Journal of Theoretical Physics, 2016, 55: 1622-1641. [17]Yan F, Iliyasu A M, Guo Y, et al.Flexible representation and manipulation of audio signals on quantum computers[J]. Theoretical Computer Science, 2018, 752: 71-85. [18]Chen K, Yan F, Iliyasu A M, et al.Exploring the implementation of steganography protocols on quantum audio signals[J]. International Journal of Theoretical Physics, 2018, 57: 476-494. [19]Li P, Shi T, Zhao Y, et al.Design of threshold segmentation method for quantum image[J].International Journal of Theoretical Physics, 2020, 59(2):514-538 [20]Wang Z, Xu M, Zhang Y.Quantum pulse coupled neural network[J]. Neural Networks, 2022, 152: 105-117. [21]Wan X, Cai J, Yang Q.Remainder Sign Analysis in Fixed-point Division[C]//2010 10th IEEE International Conference on Computer and Information Technology. IEEE, 2010: 2143-2147. [22]Mitra S K.Digital signal processing: a computer-based approach[M]. New York, NY, USA:: McGraw-Hill, 2011: 200–205. [23]Lomont C.Quantum convolution and quantum correlation algorithms are physically impossible[J]. arXiv preprint quant-ph/0309070, 2003. [24]Zhang Y, Lu K, Xu K, et al.Local feature point extraction for quantum images[J]. Quantum Information Processing, 2015, 14: 1573-1588. [25]Wang J, Jiang N, Wang L.Quantum image translation[J].Quantum Information Processing, 2015, 14(5):1589-1604

数字信号的量子表示与基本运算

Quantum representation and basic operations of digital signals

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