QUANTUM DEFORMED NEURAL NETWORKS

Abstract

We develop a new quantum neural network layer designed to run efficiently on a quantum computer but that can be simulated on a classical computer when restricted in the way it entangles input states. We first ask how a classical neural network architecture, both fully connected or convolutional, can be executed on a quantum computer using quantum phase estimation. We then deform the classical layer into a quantum design which entangles activations and weights into quantum superpositions. While the full model would need the exponential speedups delivered by a quantum computer, a restricted class of designs represent interesting new classical network layers that still use quantum features. We show that these quantum deformed neural networks can be trained and executed on normal data such as images, and even classically deliver modest improvements over standard architectures.

1. INTRODUCTION

Quantum mechanics (QM) is the most accurate description for physical phenomena at very small scales, such as the behavior of molecules, atoms and subatomic particles. QM has a huge impact on our every day lives through technologies such as lasers, transistors (and thus microchips), superconductors and MRI. A recent view of QM has formulated it as a (Bayesian) statistical methodology that only describes our subjective view of the (quantum) world, and how we update that view in light of evidence (i.e. measurements) (; t Hooft, 2016; Fuchs & Schack, 2013) . This is in perfect analogy to the classical Bayesian view, a statistical paradigm extensively used in artificial intelligence where we maintain probabilities to represent our beliefs for events in the world. The philosophy of this paper will be to turn this argument on its head. If we can view QM as just another consistent statistical theory that happens to describe nature at small scales, then we can also use this theory to describe classical signals by endowing them with a Hilbert space structure. In some sense, the 'only' difference with Bayesian statistics is that the positive probabilities are replaced with complex 'amplitudes'. This however has the dramatic effect that, unlike in classical statistics, interference between events now becomes a possibility. In this paper we show that this point of view uncovers new architectures and potential speedups for running neural networks on quantum computers. We shall restrict our attention here to binary neural networks. We will introduce a new class of quantum neural networks and interpret them as generalizations of probabilistic binary neural networks, discussing potential speedups by running the models on a quantum computer. Then we will devise classically efficient algorithms to train the networks for a restricted set of quantum circuits. We present results of classical simulations of the quantum neural networks on real world data sizes and related gains in accuracy due to the quantum deformations. Contrary to almost all other works on quantum deep learning, our quantum neural networks can be simulated for practical classical problems, such as images or sound. The quantum nature of our models is there to increase the flexibility of the model-class and add new operators to the toolbox of the deep learning researcher, some of which may only reach their full potential when quantum computing becomes ubiquitous.

