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

This work investigates the application of quantum machine learning techniques for classical and quantum communication across different qubit channel models. By employing parameterized quantum circuits and a flexible channel noise model, we develop a machine learning framework to generate quantum channel codes and evaluate their effectiveness. We explore classical, entanglement-assisted, and quantum communication scenarios within our framework. Applying it to various quantum c...

Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we demonstrate how quantum neural networks, in the form of quantum autoencoders, can be trained to learn optimal strategies for active detection and correction of errors, including spatially correlated computational errors as well as qubit losses. We ...

Quantum noise is currently limiting efficient quantum information processing and computation. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using classical feedforward neural networks. By framing reconstruction as a regression problem, we show how such an approach can be used to recover with fidelities exceeding 99% the noiseless density matrices of quantum states of up to three qubits ...

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implement...

This paper presents a comprehensive study on the possible hybrid quantum-classical autoencoder architectures for end-to-end radio communication against noisy channel conditions using standard encoded radio signals. The hybrid scenarios include single-sided, i.e., quantum encoder (transmitter) or quantum decoder (receiver), as well as fully quantum channel autoencoder (transmitter-receiver) systems. We provide detailed formulas for each scenario and validate our model through ...

Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and correct corresponding errors. However, most of the research on quantum error correction is theoretical or has been evaluated for specific hardware models only. Moreover, the development of corresponding codes and the evaluation of whether th...

We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In...

According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a large-scale quantum computing using PMs, especially with neural networks which have the innate capability for probabilistic information processing. Restricting ourselves to a particular model, we construct and numerically examine the performance o...

While the ability to build quantum computers is improving dramatically, developing quantum algorithms is limited and relies on human insight and ingenuity. Although a number of quantum programming languages have been developed, it is challenging for software developers who are not familiar with quantum computing to learn and use these languages. It is, therefore, necessary to develop tools to support developing new quantum algorithms and programs automatically. This paper pro...

We implement a Quantum Autoencoder (QAE) as a quantum circuit capable of correcting Greenberger-Horne-Zeilinger (GHZ) states subject to various noisy quantum channels : the bit-flip channel and the more general quantum depolarizing channel. The QAE shows particularly interesting results, as it enables to perform an almost perfect reconstruction of noisy states, but can also, more surprisingly, act as a generative model to create noise-free GHZ states. Finally, we detail a use...