Exploring Quantum Neural Networks for the Discovery and Implementation of Quantum Error-Correcting Codes

Entangled states are an important resource for quantum computation, communication, metrology, and the simulation of many-body systems. However, noise limits the experimental preparation of such states. Classical data can be efficiently denoised by autoencoders---neural networks trained in unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger states subject to spin-flip errors and random unitary noise. Various emerge...

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 p...

Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine learning today. In this paper we present quantum algorithms for training and evaluating feedforward neural networks based on the canonical classical feedforward and backpropagation algorithms. Our algorithms rely on an efficient quantum subr...

This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes particles governed by quantum mechanics for computational purposes, leveraging properties like superposition and entanglement for information representation and manipulation. Quantum machine learning applies these principles to enhance class...

Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both clas...

Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good code families. However, the majority of these codes are not suitable for near-term quantum devices. Here we present VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit...

This article gives an overview and a perspective of recent theoretical proposals and their experimental implementations in the field of quantum machine learning. Without an aim to being exhaustive, the article reviews specific high-impact topics such as quantum reinforcement learning, quantum autoencoders, and quantum memristors, and their experimental realizations in the platforms of quantum photonics and superconducting circuits. The field of quantum machine learning could ...

Training quantum neural networks (QNNs) using gradient-based or gradient-free classical optimisation approaches is severely impacted by the presence of barren plateaus in the cost landscapes. In this paper, we devise a framework for leveraging quantum optimisation algorithms to find optimal parameters of QNNs for certain tasks. To achieve this, we coherently encode the cost function of QNNs onto relative phases of a superposition state in the Hilbert space of the network para...

Machine learning with artificial neural networks is revolutionizing science. The most advanced challenges require discovering answers autonomously. This is the domain of reinforcement learning, where control strategies are improved according to a reward function. The power of neural-network-based reinforcement learning has been highlighted by spectacular recent successes, such as playing Go, but its benefits for physics are yet to be demonstrated. Here, we show how a network-...

Belief-propagation (BP) decoders play a vital role in modern coding theory, but they are not suitable to decode quantum error-correcting codes because of a unique quantum feature called error degeneracy. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check (LDPC) codes with a loss function tailored to error degeneracy. Training substantially improves the performance of BP decoders for all families o...