Phase diagram of quantum generalized Potts-Hopfield neural networks

Abstract

We introduce and analyze an open quantum generalization of the q-state Potts-Hopfield neural network, which is an associative memory model based on multi-level classical spins. The dynamics of this many-body system is formulated in terms of a Markovian master equation of Lindblad type, which allows to incorporate both probabilistic classical and coherent quantum processes on an equal footing. By employing a mean field description we investigate how classical fluctuations due to temperature and quantum fluctuations effectuated by coherent spin rotations affect the ability of the network to retrieve stored memory patterns. We construct the corresponding phase diagram, which in the low temperature regime displays pattern retrieval in analogy to the classical Potts-Hopfield neural network. When increasing quantum fluctuations, however, a limit cycle phase emerges, which has no classical counterpart. This shows that quantum effects can qualitatively alter the structure of the stationary state manifold with respect to the classical model, and potentially allow one to encode and retrieve novel types of patterns.

arXiv comment15 pages, 8 figures

References in corpus (39)

• Quantum Machine Learning
• Quantum Mechanics helps in searching for a needle in a haystack
• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantum Convolutional Neural Networks
• Quantum algorithms: an overview
• Efficient Learning for Deep Quantum Neural Networks
• The quest for a Quantum Neural Network
• Quantum Entanglement in Neural Network States
• Continuous-variable quantum neural networks
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Symmetries and many-body excited states with neural-network quantum states
• Tunable-range, photon-mediated atomic interactions in multimode cavity QED
• Quantum simulation of open-system dynamical maps with trapped ions
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Quantum Hopfield neural network
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• Latent Space Purification via Neural Density Operators
• Quantum computing models for artificial neural networks
• Quantum Neuron: an elementary building block for machine learning on quantum computers
• Unitary quantum perceptron as efficient universal approximator
• Sign-changing photon-mediated atom interactions in multimode cavity QED
• Exactness of mean-field equations for open Dicke models with an application to pattern retrieval dynamics
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Neural network representation of tensor network and chiral states
• Enhancing associative memory recall and storage capacity using confocal cavity QED
• Trapped Ion Chain as a Neural Network: Error Resistant Quantum Computation
• Open quantum generalisation of Hopfield neural networks
• Trapped ion chain as a neural network
• Dicke simulators with emergent collective quantum computational abilities
• Method to solve quantum few-body problems with artificial neural networks
• Emergent and broken symmetries of atomic self-organization arising from Gouy phase shifts in multimode cavity QED
• Generalized Transfer Matrix States from Artificial Neural Networks
• Signatures of associative memory behavior in a multi-mode spin-boson model
• Replica Symmetry Breaking in Cold Atoms and Spin Glasses
• Quantum accelerated approach to the thermal state of classical spin systems with applications to pattern-retrieval in the Hopfield neural network
• Quantum Pattern Retrieval by Qubit Networks with Hebb Interactions
• Self-induced glassy phase in multimodal cavity quantum electrodynamics

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