数字信号的量子补码浮点表示及运算研究  

Study on Quantum Complement Floating Point Representation and Operations of Digital Signals

作　　者：王兵[1] 周冰琪 李盼池[1] 肖红[1] WANG Bing;ZHOU Bingqi;LI Panchi;XIAO Hong(School of Computer&Information Technology,Northeast Petroleum University,Daqing,Heilongjiang 163318,China)

机构地区：[1]东北石油大学计算机与信息技术学院,黑龙江大庆163318

出　　处：《信号处理》2024年第12期2165-2177,共13页Journal of Signal Processing

基　　金：黑龙江省自然科学基金(LH2022F006)。

摘　　要：为了提高量子数字信号表示的灵活性,本文提出了一种新的基于补码浮点表示的一维有限长度量子数字信号表示模型(Complement Floating-point Representation of Digital Signals,CFRDS)。该模型使用两组量子比特序列分别表示位置信息与幅值信息。其中,位置信息采用有符号定点整数补码形式表示,保证了信号位置的精确性和负数处理能力;幅值信息则采用浮点数形式表示,浮点数的阶码和尾数均采用补码形式,能够更灵活地应对不同幅值的信号,确保在极端数值条件下依然保持高精度,同时,这种表示方法也简化了数学运算,能够处理更广泛的信号类型。该模型不仅在信号幅值的表示范围与精度上取得了显著提升,还在数学运算的便捷性方面展现了优越性,使得各种信号处理算法更加高效和可靠,适用于更加复杂的信号处理算法,提高了信号处理的效率。本文提出了CFRDS模型,设计了该模型的量子制备线路与基于该模型的量子数字信号基本运算线路,包括两个量子数字信号的序列加法、序列乘法以及自相关函数序列运算,并深入分析了线路复杂度,最后通过计算机仿真实验验证了所提出方案的可行性和有效性。A novel one-dimensional finite-length quantum digital signal representation model,Complement Floating-point Representation of Digital Signals(CFRDS),based on two’s complement floating-point representation is proposed in this paper to enhance the flexibility of quantum digital signal representation.The model uses two sets of qubit se‐quences to represent position information and amplitude information independently.Position information is represented using signed fixed-point integers in two’s complement form,ensuring the accuracy of signal positions and the ability to handle negative values.Amplitude information is represented using floating-point numbers,with both the exponent and mantissa in two’s complement form,enabling the model to flexibly handle signals of varying amplitudes while main‐taining high precision under extreme numerical conditions.This representation method also simplifies mathematical op‐erations,enabling the processing of a broader range of signal types.The model greatly improves the range and precision of signal amplitude representation and demonstrates superior convenience in mathematical operations,making various signal processing algorithms more efficient and reliable.This enhancement makes the model suitable for more complex signal processing tasks,improving the overall signal processing efficiency.This paper presents the CFRDS model and designs the quantum preparation circuits and basic quantum digital signal operation circuits based on this model.These include sequence addition,sequence multiplication,and autocorrelation function sequence operations of two quantum digital signals.The complexity of these circuits is analyzed in depth,and the feasibility and effectiveness of the pro‐posed scheme are validated in computer simulations.

关 键 词：量子数字信号 补码浮点表示 量子浮点数加法 量子浮点数乘法 量子自相关函数 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]