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

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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.