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Table of Contents
1 Introduction
2 Quantum Annealing and the Ising Model Encoding
3 Encoding a quantum neural network
3.1 Neural networks and classical training
3.2 Training a NN in a quantum annealer
3.3 An example encoding
Summary
Artificial neural networks are at the heart of modern deep learning algorithms. This paper describes how to embed and train a general neural network in a quantum annealer without introducing any classical element in training. The authors develop crucial ingredients including binary encoding of free parameters, polynomial approximation of activation functions, and reduction of higher-order polynomials into quadratic ones. These innovations enable encoding the loss function as an Ising model Hamiltonian, allowing the quantum annealer to train the network by finding the ground state. The paper demonstrates quantum training advantages such as consistency in finding the global minimum of the loss function and quick convergence in a single annealing step, leading to shorter training times while maintaining high classification performance. The approach presents a new pathway for quantum training of machine learning models.