Quantum Convolutional Neural Networks

TL;DR

This paper introduces a quantum convolutional neural network (QCNN) model that is efficient, scalable, and applicable to quantum state recognition and error correction, demonstrating promising results for near-term quantum devices.

Contribution

The paper presents the first QCNN architecture combining entanglement renormalization and error correction, with only logarithmic parameters, enabling efficient training and broad applications.

Findings

QCNN accurately recognizes topological phases

QCNN reproduces phase diagrams from small training sets

QCNN-based error correction outperforms existing codes

Abstract

We introduce and analyze a novel quantum machine learning model motivated by convolutional neural networks. Our quantum convolutional neural network (QCNN) makes use of only $O(\log(N))$ variational parameters for input sizes of $N$ qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices. The QCNN architecture combines the multi-scale entanglement renormalization ansatz and quantum error correction. We explicitly illustrate its potential with two examples. First, QCNN is used to accurately recognize quantum states associated with 1D symmetry-protected topological phases. We numerically demonstrate that a QCNN trained on a small set of exactly solvable points can reproduce the phase diagram over the entire parameter regime and also provide an exact, analytical QCNN solution. As a second application, we utilize QCNNs to devise a quantum error correction scheme optimized for a given error model. We provide a generic framework to simultaneously optimize both encoding and decoding procedures and find that the resultant scheme significantly outperforms known quantum codes of comparable complexity. Finally, potential experimental realization and generalizations of QCNNs are discussed.