Analysis of learnability of a novel hybrid quantum-classical convolutional neural network in image classification

We design a new hybrid quantum-classical convolutional neural network(HQCCNN)model based on parameter quantum circuits.In this model,we use parameterized quantum circuits(PQCs)to redesign the convolutional layer in classical convolutional neural networks,forming a new quantum convolutional layer to achieve unitary transformation of quantum states,enabling the model to more accurately extract hidden information from images.At the same time,we combine the classical fully connected layer with PQCs to form a new hybrid quantum-classical fully connected layer to further improve the accuracy of classification.Finally,we use the MNIST dataset to test the potential of the HQCCNN.The results indicate that the HQCCNN has good performance in solving classification problems.In binary classification tasks,the classification accuracy of numbers 5 and 7 is as high as 99.71%.In multivariate classification,the accuracy rate also reaches 98.51%.Finally,we compare the performance of the HQCCNN with other models and find that the HQCCNN has better classification performance and convergence speed.

Quankum Effects of a Dissipative Mesoscopic Circuit with Mutual Inductance

We study the quantum fluctuations of the charge and current of two L-C dissipative mesoscopic circuit with the mutual inductance in the vacuum state.Our results show that the system state will evolve to a squeezed coherent state under the effect of external source.We find that the squeezing amplitude parameter is relative to the parameters of circuit and the mutual-inductance coefficient in the existence of dissipation.When the circuit has no dissipation or there is complete coupling between two meshes,the squeezing amplitude parameter only depends on the capacitance's ratio.

Quantum state measurement in double quantum dots with a radio-frequency quantum point contact

We study the dynamics of two electron spins in coupled quantum dots （CQDs） monitored by a quantum point contact （QPC） detector. Their quantum state can be measured by embedding the QPC in an LC circuit. We derive the Bloch-type rate equations of the reduced density matrix for CQDs. Special attention is paid to the numerical results for the weak measurement condintion under a strong Coulomb interaction. It is shown that the evolution of QPC current always follows that of electron occupation in the right dot. In addition, we find that the output voltage of the circuit can reflect the evolution of QPC current when the circuit and QPC are approximately equal in frequency. In particular, the wave shape of the output voltage can be improved by adjusting the circuit resonance frequency and bandwidth.

Variational quantum semi-supervised classifier based on label propagation

Label propagation is an essential semi-supervised learning method based on graphs,which has a broad spectrum of applications in pattern recognition and data mining.This paper proposes a quantum semi-supervised classifier based on label propagation.Considering the difficulty of graph construction,we develop a variational quantum label propagation(VQLP)method.In this method,a locally parameterized quantum circuit is created to reduce the parameters required in the optimization.Furthermore,we design a quantum semi-supervised binary classifier based on hybrid Bell and Z bases measurement,which has a shallower circuit depth and is more suitable for implementation on near-term quantum devices.We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set,and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier.This work opens a new path to quantum machine learning based on graphs.

Density Matrix for Mesoscopic Distributed Parameter Circuits

Under the Born-von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix rho(q,q',beta). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T. The higher the temperature is, the stronger quantum noise the circuit exhibits.

一种构建参数化量子线路的区块环拓扑结构

在变分量子算法中,参数化量子线路拓扑结构的选择对算法性能具有重要意义.目前已有的拓扑结构存在一些问题,如全连接拓扑结构所需量子门数量较多,环型拓扑结构的表达能力与纠缠能力略有欠缺.为了解决以上问题,本文提出了一种新型的区块环(Block-Ring,BR)拓扑结构,在保障良好性能的同时减少参数规模(即量子门数量),降低线路复杂度.在BR拓扑中,n个量子比特被等分为多个区块,每个区块包含m个量子比特,区块内部所有量子比特两两连接,区块之间采用环型结构进行连接.为了构造BR拓扑结构的参数化量子线路,设计了一种多层线路生成算法,可自动生成由单量子比特门Rx、Rz和双量子比特门CRx或CRz构成的量子线路.IBM Q模拟实验表明,相较于环型拓扑结构,无论单层、双层以及三层BR拓扑结构的表达能力和纠缠能力均有不同程度的提升;相较于拥有最高表达能力与纠缠能力的全连接拓扑结构,BR拓扑结构呈现接近的性能指标,且线路复杂度显著降低,即参数数量与双量子比特门数量均从O(n^(2))降低为O(mn),线路深度从O(n^(2))降低为O(n/m+m^(2)).

Quantum classifier with parameterized quantum circuit based on the isolated quantum system

It is a critical challenge for quantum machine learning to classify the datasets accurately.This article develops a quantum classifier based on the isolated quantum system(QC-IQS)to classify nonlinear and multidimensional datasets.First,a model of QC-IQS is presented by creating parameterized quantum circuits(PQCs)based on the decomposing of unitary operators with the Hamiltonian in the isolated quantum system.Then,a parameterized quantum classification algorithm(QCA)is designed to calculate the classification results by updating the loss function until it converges.Finally,the experiments on nonlinear random number datasets and Iris datasets are designed to demonstrate that the QC-IQS model can handle and generate accurate classification results on different kinds of datasets.The experimental results reveal that the QC-IQS is adaptive and learnable to handle different types of data.Moreover,QC-IQS compensates the issue that the accuracy of previous quantum classifiers declines when dealing with diverse datasets.It promotes the process of novel data processing with quantum machine learning and has the potential for more comprehensive applications in the future.

基于量子卷积神经网络的图像识别新模型

为了解决卷积神经网络对内存和时间效率要求越来越高的问题,提出一种面向数字图像分类的新模型,该模型为基于强纠缠参数化线路的量子卷积神经网络。首先对经典图像进行预处理和量子比特编码,提取图像的特征信息,并将其制备为量子态作为量子卷积神经网络模型的输入。通过设计模型量子卷积层、量子池化层、量子全连接层结构,高效提炼主要特征信息,最后对模型输出执行Z基测量,根据期望值完成图像分类。实验数据集为MNIST数据,{0,1}分类和{2,7}分类准确率均达到了100%。对比结果表明,采用平均池化下采样的三层网络结构的QCNN模型具有更高的测试精度。

一种量子条件生成对抗网络算法

量子生成对抗网络是量子机器学习算法领域研究热点之一,但其生成过程具有较大的随机性,不太适用于现实场景.为了解决该问题,提出了一种生成过程可控的量子条件生成对抗网络(Quantum Conditional Generative Adversarial Network,QCGAN)算法,其中条件信息采用one-hot形式进行多粒子W态编码,并通过向生成器和判别器输入条件信息达到稳定模型生成过程的目的.性能评估表明,与经典GAN、CGAN相比,本算法可生成离散数据,且将时间复杂度从O(N^(2))降为O(N);与带条件约束的量子生成对抗网络QuGAN相比,QCGAN消耗更少的量子资源.最后,以BAS(3,3)数据集和量子混合态生成为例,选用PennyLane平台进行仿真实验,结果表明QCGAN算法经过训练可有效收敛到Nash均衡点,进而验证了算法的实验可行性.

Simulation of molecular spectroscopy with circuit quantum electrodynamics

Spectroscopy is a crucial laboratory technique for understanding quantum systems through their interactions with the electromagnetic radiation.Particularly,spectroscopy is capable of revealing the physical structure of molecules,leading to the development of the maser—the forerunner of the laser.However,real-world applications of molecular spectroscopy are mostly confined to equilibrium states,due to computational and technological constraints;a potential breakthrough can be achieved by utilizing the emerging technology of quantum simulation.Here we experimentally demonstrate through a toy model,a superconducting quantum simulator capable of generating molecular spectra for both equilibrium and non-equilibrium states,reliably producing the vibronic structure of diatomic molecules.Furthermore,our quantum simulator is applicable not only to molecules with a wide range of electronic-vibronic coupling strength,characterized by the Huang-Rhys parameter,but also to molecular spectra not readily accessible under normal laboratory conditions.These results point to a new direction for predicting and understanding molecular spectroscopy,exploiting the power of quantum simulation.

Towards an efficient variational quantum algorithm for solving linear equations

Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation systems.Initially,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum states.This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver.Subsequently,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive capabilities.Through rigorous numerical analysis,the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm,and it obtained the best score compared to the others.Moreover,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the algorithm.To address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision standards.Finally,EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 220.

基于粒子群优化算法的量子卷积神经网络

针对当前量子卷积神经网络模型中参数化量子电路缺乏自适应目标选择策略的问题,提出了一种基于粒子群优化算法自动优化电路的量子卷积神经网络模型。该模型通过将量子电路编码为粒子,并利用粒子群优化算法对电路进行优化,从而搜索出在图像分类任务上表现优异的电路结构。基于Fashion MNIST和MNIST标准数据集的仿真实验表明,该模型具有较强的学习能力和良好的泛化性能,准确率分别可达94.7%和99.05%。相较于现有量子卷积神经网络模型,平均分类精度最高分别提升了4.14%和1.43%。