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经历一场革命。最近在图像和语音识别以及大量数据分析和分类方面取得了惊人的发展，对政策制定、经济和社会产生了巨大的影响。与此同时，在技术层面上正在进行一场革命，这场革命涉及我们控制和利用量子物质奇异特性的能力。实验的进展和对如何在应用中利用量子物理学的理论理解的增加导致了量子技术领域的出现，它有望彻底改变计时，传感，通信以及数据存储和处理。该提案的目标是通过开发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桥梁。研究集中在两个架构。第一个是所谓的转子Hopfield神经网络，它代表了一个模型的联想记忆。它基于自旋自由度和自旋之间物理相互作用中存储的信息。第二种架构是由感知器组装的分层网络。在这些前馈神经网络中，信息在相邻层之间传播，并且学习的行为被编码在通过学习策略适当调整的层间耦合中。这两种架构的优点是，它们允许从一个明确定义的经典极限系统地推广到量子域。此外，它们提供了与多粒子系统物理学的直接联系：量子转子Hopfield神经网络是强相互作用的非平衡自旋系统，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，例如存储信息的检索或学习策略的实施，可以从相位和相变的角度来理解和分类。这两种物理架构的动态耦合量子神经元，我们设想是互补的方法，实现量子神经网络的量子算法的形式变分量子电路，或作为波函数ansatzes。拟议的研究不仅将提供如何利用神经网络中的量子效应来增强机器学习的见解。它还将提出在物理平台上实施必要战略的建议，如冷原子气体和捕获离子。所有这一切都是通过图宾根Eberhard Karls大学和Forschungszentrum Jülich之间的新合作以及机器学习，量子信息，量子多体物理学和原子物理学理论专业知识的合并来实现的，目前这两个机构。

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.