Quantum generalisations and implementations of Hopfield and feed-forward neural networks

人工智能和机器学习领域目前正在见证一场革命。最近在图像和语音识别以及在对大量数据进行分析和分类方面取得了令人惊叹的发展，对政策制定、经济和社会产生了巨大影响。与此同时，在技术层面上正在进行一场革命，这涉及到我们控制和利用量子物质奇异性质的能力。实验的进展和对如何在应用中使用量子物理的理论理解的增加导致了量子技术领域的出现，这一领域有望给计时、传感、通信以及数据存储和处理带来革命性的变化。该提议的目标是通过开发一个量子广义神经网络框架，在机器学习概念和量子技术之间建立一座桥梁。本文的研究集中在两种体系结构上。第一种是所谓的转子Hopfield神经网络，它代表了一种联想记忆模型。它是基于自旋自由度和自旋之间的物理相互作用中存储的信息。第二种体系结构由感知器组装的分层网络给出。在这些前馈神经网络中，信息在相邻层之间传播，学习的行为被编码在层间耦合中，并通过学习策略进行适当的调整。这两种体系结构的优点在于，它们允许从定义明确的经典极限系统地概括到量子领域。此外，它们还提供了与多粒子系统物理的直接联系：量子转子Hopfield神经网络是强相互作用的非平衡自旋系统，而前馈神经网络与开放细胞自动机和驱动耗散量子动力学密切相关。它们的动态和稳态行为，例如检索存储的信息或执行学习策略，都可以从阶段和阶段转变的角度来理解和分类。这两种动态耦合量子神经元的物理结构都是对将量子神经网络实现为变分量子电路形式的量子算法或波函数变换的方法的补充。这项拟议的研究不仅将为如何利用神经网络中的量子效应来增强机器学习提供见解。它还将提出在物理平台上实施必要战略的建议，如冷原子气体和囚禁离子。所有这一切都是通过图宾根的埃伯哈德·卡尔斯大学和Forschungszentum Jülich之间的一项新合作，以及这两个机构目前在机器学习、量子信息、量子多体物理和原子物理方面的理论专业知识的融合而实现的。

The field of artificial intelligence and machine learning is currently witnessing a revolution. Recent breath-taking developments in image and speech recognition as well as in analysing and categorising large amounts of data, have a tremendous impact on policy making, economics and society. At the same time there is an ongoing revolution at the technological level that concerns our ability to control and harness the exotic properties of quantum matter. Experimental progress and an increased theoretical understanding of how to exploit quantum physics in applications have led to the emergence of the field of quantum technologies, which bears a promise to revolutionise time keeping, sensing, communication as well as data storage and processing.The goal of this proposal is to build a bridge between machine learning concepts and quantum technologies by developing a framework of quantum generalised neural networks. The research focusses on two architectures. The first is a so-called rotor Hopfield neural network which represents a model of an associative memory. It is based on spin degrees of freedom and information being stored in the physical interaction between the spins. The second architecture is given by layered networks assembled by perceptrons. In these feed-forward neural networks information is propagated between adjacent layers and learned behaviour is encoded in interlayer couplings which are suitably adjusted via learning strategies. The advantage of both architectures is that they allow a systematic generalisation into the quantum domain from a well-defined classical limit. Moreover, they offer a direct connection to the physics of many-particle systems: quantum rotor Hopfield neural networks are strongly interacting non-equilibrium spin systems, and feed-forward neural networks are closely related to open cellular automata and driven-dissipative quantum dynamics. Both their dynamical and steady-state behaviour, e.g. the retrieval of stored information or the implementation of learning strategies, can be understood and classified from the perspective of phases and phase transitions. Both physical architectures of dynamically coupled quantum neurons, which we envision are complementary to approaches that realise quantum neural networks as quantum algorithms in the form of variational quantum circuits, or as wave function ansatzes. The proposed research will not only deliver insights in how to exploit quantum effects in neural networks to enhance machine learning. It will also yield proposals for implementing the necessary strategies on physical platforms, such as cold atomic gases and trapped ions. All this is achieved through a new collaboration between the Eberhard Karls University of Tübingen and the Forschungszentrum Jülich and the merging of the theoretical expertise on machine learning, quantum information, quantum many-body physics and atomic physics, present at those two institutions.