Quantum Algorithms for Deep Convolutional Neural Networks

TL;DR

This paper introduces a quantum algorithm for deep convolutional neural networks that mimics classical CNNs, enabling potential speedups and new capabilities in image recognition tasks.

Contribution

It proposes a quantum CNN model that incorporates non-linearities and pooling, along with a novel quantum tomography algorithm and applications of probabilistic sampling.

Findings

Numerical simulations show effective classification of MNIST dataset.

The QCNN model reproduces classical CNN features with potential quantum speedup.

Introduces a new quantum tomography method with $$-norm guarantees.

Abstract

Quantum computing is a new computational paradigm that promises applications in several fields, including machine learning. In the last decade, deep learning, and in particular Convolutional neural networks (CNN), have become essential for applications in signal processing and image recognition. Quantum deep learning, however remains a challenging problem, as it is difficult to implement non linearities with quantum unitaries. In this paper we propose a quantum algorithm for applying and training deep convolutional neural networks with a potential speedup. The quantum CNN (QCNN) is a shallow circuit, reproducing completely the classical CNN, by allowing non linearities and pooling operations. The QCNN is particularly interesting for deep networks and could allow new frontiers in image recognition, by using more or larger convolution kernels, larger or deeper inputs. We introduce a new quantum tomography algorithm with $\ell_{\infty}$ norm guarantees, and new applications of probabilistic sampling in the context of information processing. We also present numerical simulations for the classification of the MNIST dataset to provide practical evidence for the efficiency of the QCNN.