Completely Quantum Neural Networks

Abstract

Artificial neural networks are at the heart of modern deep learning algorithms. We describe how to embed and train a general neural network in a quantum annealer without introducing any classical element in training. To implement the network on a state-of-the-art quantum annealer, we develop three crucial ingredients: binary encoding the free parameters of the network, polynomial approximation of the activation function, and reduction of binary higher-order polynomials into quadratic ones. Together, these ideas allow encoding the loss function as an Ising model Hamiltonian. The quantum annealer then trains the network by finding the ground state. We implement this for an elementary network and illustrate the advantages of quantum training: its consistency in finding the global minimum of the loss function and the fact that the network training converges in a single annealing step, which leads to short training times while maintaining a high classification performance. Our approach opens a novel avenue for the quantum training of general machine learning models.

12 pages, 6 figures

References in corpus (4)

• Consistency Tests of Classical and Quantum Models for a Quantum Annealer
• Anomaly detection in high-energy physics using a quantum autoencoder
• Bayesian Network Structure Learning Using Quantum Annealing
• Search for heavy particles decaying into a top-quark pair in the fully hadronic final state in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

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• Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations
• Nonnegative/Binary Matrix Factorization for Image Classification using Quantum Annealing
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Jet Discrimination with Quantum Complete Graph Neural Network
• QFitter -- A Quantum Fitting Framework Applied to Effective Field Theories
• 1 Particle - 1 Qubit: Particle Physics Data Encoding for Quantum Machine Learning
• Benchmarking of quantum fidelity kernels for Gaussian process regression
• Ancillary entangling Floquet kicks for accelerating quantum algorithms