Quantum neural network

Medical image classification via quantum neural networks

Machine Learning provides powerful tools for a variety of applications, including disease diagnosis through medical image classification. In recent years, quantum machine learning techniques have been put forward as a way to potentially enhance performance in machine learning applications, both through quantum algorithms for linear algebra and quantum neural networks. In this work, we study two different quantum neural network techniques for medical image classification: first by employing quantum circuits in training of classical neural networks, and second, by designing and training quantum …

用于量子多体模拟的量子增强神经网络

Quantum-enhanced neural networks for quantum many-body simulations

针对神经量子态在优化、可扩展性和表达性上的局限，提出结合参数化量子电路与神经网络的量子-神经混合框架，在自旋系统和量子化学问题中实现了比纯NQS更低的相对能量，展现了量子多体模拟潜力。

受量子启发的权重约束神经网络：与标准神经网络相比，变量数量减少100倍

Quantum-Inspired Weight-Constrained Neural Network: Reducing Variable Numbers by 100x Compared to Standard Neural Networks

受量子启发的权重约束神经网络通过减少变量数量提升效率，增强对抗鲁棒性，适用于工业应用。

The quest for a Quantum Neural Network

With the overwhelming success in the field of quantum information in the last decades, the "quest" for a Quantum Neural Network (QNN) model began in order to combine quantum computing with the striking properties of neural computing. This article presents a systematic approach to QNN research, which so far consists of a conglomeration of ideas and proposals. It outlines the challenge of combining the nonlinear, dissipative dynamics of neural computing and the linear, unitary dynamics of quantum computing. It establishes requirements for a meaningful QNN and reviews existing literature against …

A Quantum Convolutional Neural Network for Image Classification

Artificial neural networks have achieved great success in many fields ranging from image recognition to video understanding. However, its high requirements for computing and memory resources have limited further development on processing big data with high dimensions. In recent years, advances in quantum computing show that building neural networks on quantum processors is a potential solution to this problem. In this paper, we propose a novel neural network model named Quantum Convolutional Neural Network (QCNN), aiming at utilizing the computing power of quantum systems to accelerate classic…

Neural-network quantum state tomography

We revisit the application of neural networks techniques to quantum state tomography. We confirm that the positivity constraint can be successfully implemented with trained networks that convert outputs from standard feed-forward neural networks to valid descriptions of quantum states. Any standard neural-network architecture can be adapted with our method. Our results open possibilities to use state-of-the-art deep-learning methods for quantum state reconstruction under various types of noise.

Quantum Methods for Neural Networks and Application to Medical Image Classification

Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum orthogonal neural network, which is based on a quantum pyramidal circuit as the building block for implementing orthogonal matrix multiplication. We provide an efficient way for training such orthogonal neural networks; novel algorithms are detailed for both classical and quantum hardware, where both are proven to scale asymptotically better than previously known t…

Quantum neural networks driven by information reservoir

This study concerns with the dynamics of a quantum neural network unit in order to examine the suitability of simple neural computing tasks. More specifically, we examine the dynamics of an interacting spin model chosen as a candidate of a quantum perceptron for closed and open quantum systems. We adopt a collisional model enables examining both Markovian and non-Markovian dynamics of the proposed quantum system. We show that our quantum neural network (QNN) unit has a stable output quantum state in contact with an environment carrying information content. By the performed numerical simulation…

Building quantum neural networks based on swap test

Artificial neural network, consisting of many neurons in different layers, is an important method to simulate humain brain. Usually, one neuron has two operations: one is linear, the other is nonlinear. The linear operation is inner product and the nonlinear operation is represented by an activation function. In this work, we introduce a kind of quantum neuron whose inputs and outputs are quantum states. The inner product and activation operator of the quantum neurons can be realized by quantum circuits. Based on the quantum neuron, we propose a model of quantum neural network in which the wei…

基于量子图态的量子图神经网络统一基础框架

A unifying primary framework for quantum graph neural networks from quantum graph states

该研究提出基于量子图态的量子图神经网络统一框架，证明图态可作为参数化量子电路表征神经网络，也可作为底层结构在量子计算机上构建图神经网络，为量子图神经网络的理解与实现提供统一基础。

Quantum Graph Neural Networks

We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable to be executed on distributed quantum systems over a quantum network. Along with this general class of ansatze, we introduce further specialized architectures, namely, Quantum Graph Recurrent Neural Networks (QGRNN) and Quantum Graph Convolutional Neural Networks (QGCNN). We provide four example applications of QGNNs: learning Hamiltonian dynamics of quantum systems, learning how to create …

量子神经网络用于量子神经计算

Quantum Neural Network for Quantum Neural Computing

提出一种利用单量子比特操作和测量的量子神经网络模型，克服状态空间指数增长问题，在数字识别等任务中展现强非线性分类能力和噪声鲁棒性，推动量子神经计算机发展。

Nonlinear Quantum Neuron: A Fundamental Building Block for Quantum Neural Networks

Quantum computing enables quantum neural networks (QNNs) to have great potentials to surpass artificial neural networks (ANNs). The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various models related to QNNs have been developed, they are facing the challenge of merging the nonlinear, dissipative dynamics of neural computing into the linear, unitary quantum system. In this paper, we establish different quantum circuits to approximate nonlinear functions and then propose a generalizable framework to realize any nonlinear quantum neuron. We …

Learning Quantum Processes with Memory -- Quantum Recurrent Neural Networks

Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent neural networks, based on dissipative quantum neural networks, capable of learning general causal quantum automata. A quantum training algorithm is proposed and classical simulations for the case of product outputs with the fidelity as cost function are carried out. We thereby demonstrate the potential of these algorithms to learn complex quantum processes with …

Neural network representation of tensor network and chiral states

We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasi-local neural network representation for a chiral $p$-wave superc…

Quantum enhanced cross-validation for near-optimal neural networks architecture selection

This paper proposes a quantum-classical algorithm to evaluate and select classical artificial neural networks architectures. The proposed algorithm is based on a probabilistic quantum memory and the possibility to train artificial neural networks in superposition. We obtain an exponential quantum speedup in the evaluation of neural networks. We also verify experimentally through a reduced experimental analysis that the proposed algorithm can be used to select near-optimal neural networks.

QDCNN: Quantum Dilated Convolutional Neural Network

In recent years, with rapid progress in the development of quantum technologies, quantum machine learning has attracted a lot of interest. In particular, a family of hybrid quantum-classical neural networks, consisting of classical and quantum elements, has been massively explored for the purpose of improving the performance of classical neural networks. In this paper, we propose a novel hybrid quantum-classical algorithm called quantum dilated convolutional neural networks (QDCNNs). Our method extends the concept of dilated convolution, which has been widely applied in modern deep learning al…

基于变分量子线路的量子神经网络可解释性研究

On the explainability of quantum neural networks based on variational quantum circuits

本文证明基于变分量子线路的量子神经网络可表示为岭函数的线性组合，从而将其可解释性研究转化为岭函数线性组合的逼近问题。

Development of Quantum Circuits for Perceptron Neural Network Training, Based on the Principles of Grover's Algorithm

This paper highlights a practical research of the possibility of forming quantum circuits for training neural networks. The demonstrated quantum circuits were based on the principles of Grover's Search Algorithm. The perceptron was chosen as the architecture for the example neural network. The multilayer perceptron is a popular neural network architecture due to its scalability and applicability for solving a wide range of problems.

Quantum perceptron over a field and neural network architecture selection in a quantum computer

In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neura…

Exploration of Quantum Neural Architecture by Mixing Quantum Neuron Designs

With the constant increase of the number of quantum bits (qubits) in the actual quantum computers, implementing and accelerating the prevalent deep learning on quantum computers are becoming possible. Along with this trend, there emerge quantum neural architectures based on different designs of quantum neurons. A fundamental question in quantum deep learning arises: what is the best quantum neural architecture? Inspired by the design of neural architectures for classical computing which typically employs multiple types of neurons, this paper makes the very first attempt to mix quantum neuron d…

Nonparametric Regression Quantum Neural Networks

In two pervious papers \cite{dndiep3}, \cite{dndiep4}, the first author constructed the least square quantum neural networks (LS-QNN), and ploynomial interpolation quantum neural networks ( PI-QNN), parametrico-stattistical QNN like: leanr regrassion quantum neural networks (LR-QNN), polynomial regression quantum neural networks (PR-QNN), chi-squared quantum neural netowrks ($χ^2$-QNN). We observed that the method works also in the cases by using nonparametric statistics. In this paper we analyze and implement the nonparametric tests on QNN such as: linear nonparametric regression quantum neur…

Quantum Deformed Neural Networks

We develop a new quantum neural network layer designed to run efficiently on a quantum computer but that can be simulated on a classical computer when restricted in the way it entangles input states. We first ask how a classical neural network architecture, both fully connected or convolutional, can be executed on a quantum computer using quantum phase estimation. We then deform the classical layer into a quantum design which entangles activations and weights into quantum superpositions. While the full model would need the exponential speedups delivered by a quantum computer, a restricted clas…

Quantum Neural Networks: Concepts, Applications, and Challenges

Quantum deep learning is a research field for the use of quantum computing techniques for training deep neural networks. The research topics and directions of deep learning and quantum computing have been separated for long time, however by discovering that quantum circuits can act like artificial neural networks, quantum deep learning research is widely adopted. This paper explains the backgrounds and basic principles of quantum deep learning and also introduces major achievements. After that, this paper discusses the challenges of quantum deep learning research in multiple perspectives. Last…

Quantum Neural Networks -- Computational Field Theory and Dynamics

To address Quantum Artificial Neural Networks as quantum dynamical computing systems, a formalization of quantum artificial neural networks as dynamical systems is developed, expanding the concept of unitary map to the neural computation setting and introducing a quantum computing field theory on the network. The formalism is illustrated in a simulation of a quantum recurrent neural network and the resulting field dynamics is researched upon, showing emergent neural waves with excitation and relaxation cycles at the level of the quantum neural activity field, as well as edge of chaos signature…

Statistical Tests and Confidential Intervals as Thresholds for Quantum Neural Networks

Some basic quantum neural networks were analyzed and constructed in the recent work of the author \cite{dndiep3}, published in International Journal of Theoretical Physics (2020). In particular the Least Quare Problem (LSP) and the Linear Regression Problem (LRP) was discussed. In this second paper we continue to analyze and construct the least square quantum neural network (LS-QNN), the polynomial interpolation quantum neural network (PI-QNN), the polynomial regression quantum neural network (PR-QNN) and chi-squared quantum neural network ($χ^2$-QNN). We use the corresponding solution or test…

使用含时神经量子态的量子动力学

Quantum Dynamics with Time-Dependent Neural Quantum States

本研究通过求解量子谐振子并模拟相干态与呼吸模动力学，验证了含时神经量子态捕捉连续介质量子动力学的有效性，结果与解析解高度一致。

Are classical neural networks quantum?

Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual classical neural networks have some actual hidden quantum properties that make them such suitable tools for a highly coupled quantum problem. I discuss here what makes a system quantum and to what extent we can interpret a neural network as having quantum remnants.

Deep Neural Networks as the Semi-classical Limit of Quantum Neural Networks

Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spinnetworks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theories (TQFT); (2) Deep Neural Networks (DNN) are a subcase of QNN, in the sense that they emerge as the semiclassical limit of QNN; (3) A number of Machine Learning (ML) key-concepts can be rephrased by using the terminology of TQFT. Our framework provides as well a working hypothesis for understanding the generalization behavior of DNN, relating it to the topological f…

On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension

In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the ground state of short-range Hamiltonians. We show that when mapping a neural network, the resulting tensor network is highly constrained and thus the neural network states do in general not deliver the naive expected drastic improvement against the state-of-the-art tensor network methods. We explicitly show this result in two paradigmatic examples, the 1D ferro…

Quantum Codes from Neural Networks

We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we initiate the study of neural network states in quantum information-processing tasks. We demonstra…