基于紧凑型编码与多项式核的量子分类器研究  

Quantum Classifier Based on Compact Encoding and Polynomial Kernel

作　　者：贾瑞虹 杨光 聂敏 刘原华 张美玲 Jia Ruihong;Yang Guang;Nie Min;Liu Yuanhua;Zhang Meiling(School of Communication and Information Engineering&School of Artificial Intelligence,Xi’an University of Posts&Telecommunications,Xi’an 710121,Shaanxi,China)

机构地区：[1]西安邮电大学通信与信息工程学院(人工智能学院),陕西西安710121

出　　处：《激光与光电子学进展》2024年第9期449-457,共9页Laser & Optoelectronics Progress

基　　金：国家自然科学基金(61971348);陕西省自然科学基础研究计划(2021JM-464)。

摘　　要：核方法在机器学习中有广泛的应用。量子计算与核方法结合,可以有效解决经典核方法中当特征空间变大时计算成本随之增加的问题。研究表明,基于核方法构建的最小化量子电路可以可靠地在含噪声的中型量子设备上执行。目前已提出的一些基于量子核方法的分类器在充分映射数据以及电路架构等方面仍存在一定的缺陷。因此,提出了一种基于多项式核函数的紧凑型量子分类器。首先通过引入多项式核函数,提升了非线性数据的分类迭代速率,从而提升了分类效率;在此基础上进一步提出紧凑型振幅编码,将量子态相对应相位的数据标签编码。相比于已有的量子核方法分类器,所提模型的量子电路的编码位数可以从5个量子比特减少到3个量子比特,而且,所提模型将已有方法中的双量子位测量简化为单量子位测量。此外,该模型在测量阶段的量子电路参数达到了最优方差,可以有效节省计算资源开销。实验仿真表明,所提分类器模型中的期望值更接近理论值,且获得了更高的分类精度,同时该模型具有较低的纠缠度,有效降低了整个准备工作的开销。Kernel method has a wide range of applications in machine learning.The combination of quantum computing and kernel method can effectively solve the problem of increasing computational costs in classical kernel method when the feature space becomes larger.Researches show that the minimized quantum circuits based on kernel method can be reliably executed on noisy intermediatescale quantum devices.Some classifiers based on the quantum kernel method that have been proposed so far still have certain defects in terms of fully mapping data and circuit architecture.Therefore,we propose a compact quantum classifier based on polynomial kernel functions.First,a polynomial kernel function is introduced to increase the classification iteration rate of nonlinear data,thereby improve the classification efficiency.On this basis,a compact amplitude encoding is further proposed to encode the data labels corresponding to the quantum state.Compared with the existing quantum kernel method classifier,the number of coding bits of the quantum circuit of the proposed model can be reduced from 5 qubits to 3 qubits,and the twoqubit measurement in the existing method is simplified to a singlequbit measurement in the proposed model.In addition,the model achieves the optimal variance of the quantum circuit parameters in the measurement stage,which can effectively save computing resource overhead.Experimental simulations show that the expected value in the proposed classifier model is closer to the theoretical one,and higher classification accuracy is obtained.At the same time,the model has a low degree of entanglement,which effectively reduces the overhead of the entire preparation work.

关 键 词：量子信息处理 核方法 紧凑型振幅编码 纠缠度 

分 类 号：O413[理学—理论物理]