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.

Ising Machines for Diophantine Problems in Physics

“…For this task we shall use the reduction method described in the Appendix of Ref. [35]. This method works by introducing auxilliary spins 1 to represent pairs of spins in the original Hamiltonian of Eq.…”

“…[33] and then more recently in Refs. [15,26,34,35], is completely problem-independent and therefore potentially applicable to any set of Diophantine equations. It can perform the many layers of reduction required to reach a quadratic spin-Hamiltonian representation of the high order problems we will be considering.…”

Qade: Solving Differential Equations on Quantum Annealers

“…Quantum computing provides an immediate solution: the quantum tunnelling mechanism allows to jump between local minima separated by Juan Carlos Criado: juan.c.criado@durham.ac.uk Michael Spannowsky: michael.spannowsky@durham.ac.uk large energy barriers [28]. In this way, the global minimum of non-convex functions can be found reliably [29,43].…”

“…A general method for approximately encoding arbitrary target functions with the compact domain as the Hamiltonian of a quantum annealer has been introduced in Ref. [43]. This can be combined with methods that use a coarse-grained approximation and iteratively improve the precision of the solution, as proposed in Ref.…”

QFitter -- A Quantum Fitting Framework Applied to Effective Field Theories

“…Quantum annealing provides an optimisation framework with the potential to perform better than classical algorithms in minimising non-convex functions [11][12][13][14][15]. The availability of physical quantum annealing devices with thousands of qubits has made it possible to apply this approach to real-world problems in recent years [16][17][18][19][20][21][22][23][24][25][26][27][28].…”