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Chaos An Interdisciplinary Journal of Nonlinear Science

Quantum neural networks for the discovery and implementation of quantum error-correcting codes

A. Chalkiadakis, M. Theocharakis, Georgios D. Barmparis, Giorgos P. Tsironis

Published Nov 1, 2023• 5 citations
Publisher

Abstract

We implement and use quantum neural networks that exploit bit-flip quantum error-correcting codes that correct bit-flip errors in arbitrary logical qubit states. We introduce conjugate layer quantum autoencoders and use them in order to restore states impacted by amplitude damping through the utilization of an approximative four-qubit error-correcting codeword. Our specific implementation avoids barren plateaus of the cost function and improves the training time. Moreover, we propose a strategy that allows one to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified quantum neural networks consistently outperform the standard implementations across all tasks.

DOI
10.1063/5.0157940

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We implement and use quantum neural networks that exploit bit-flip quantum error-correcting codes that correct bit-flip errors in arbitrary logical qubit states. We introduce conjugate layer quantum autoencoders and use them in order to restore states impacted by amplitude damping through the utilization of an approximative four-qubit error-correcting codeword. Our specific implementation avoids barren plateaus of the cost function and improves the training time. Moreover, we propose a strategy that allows one to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified quantum neural networks consistently outperform the standard implementations across all tasks.
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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 highlight that the denoising capabilities of quantum autoencoders are not limited to the protection of specific states but extend to the entire logical codespace. We also show that quantum neural networks can be used to discover new logical encodings that are optimally adapted to the underlying noise. Moreover, we find that, even in the presence of moderate noise in the quantum autoencoders themselves, they may still be successfully used to perform beneficial quantum error correction and thereby extend the lifetime of a logical qubit.
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 highlight that the denoising capabilities of quantum autoencoders are not limited to the protection of specific states but extend to the entire logical codespace. We also show that quantum neural networks can be used to discover new logical encodings that are optimally adapted to the underlying noise. Moreover, we find that, even in the presence of moderate noise in the quantum autoencoders themselves, they may still be successfully used to perform beneficial quantum error correction and thereby extend the lifetime of a logical qubit.
Quantum information hiding, as an extension of classical information hiding techniques into the realm of quantum information, currently focuses on embedding classical bits (0/1) within quantum carriers. This includes methods such as disguising classical secret information as channel noise and embedding it within quantum error correction codes. However, the embedding mechanism for arbitrary quantum states $\alpha |0\rangle + \beta |1\rangle $ is still in the exploratory stage. This paper proposes an innovative framework that leverages the redundant space of quantum error correction codes to construct a nonlinear decoding architecture with quantum neural networks. This approach simultaneously achieves both carrier state error correction and secret state embedding and extraction functions. Specifically, the [5,1,3] stabilizer code is used as the carrier, with secret state embedding achieved through single-qubit substitution, and a quantum autoencoder is designed for steganographic state information decoding. The proposed framework features fully quantum-based input/output systems, overcoming the limitations of traditional variational quantum circuits that rely on probabilistic measurements for output generation. By performing full ground-state measurements at the autoencoder bottleneck layer and optimizing the parallel sub-network architecture, the network achieves efficient convergence and effective extraction of single-copy quantum states. Experimental results show that under the conditions of optimized parameters and data size of 20, the training losses for the carrier and secret states are 0.03 and 0.08, respectively, with test fidelities of 0.92 and 0.93. For a data size of 50, the secret states recovery fidelity exceeds 0.87. KS test analysis indicates that the full ground-state measurement and parallel sub-network are key strategies for achieving network performance. Equivalent error analysis shows that this approach successfully utilizes the potential redundant space of quantum error correction codes, providing new research directions for quantum state information hiding.
Abstract To improve the decoding performance of quantum error-correcting codes in asymmetric noise channels, a neural network-based decoding algorithm for bias-tailored quantum codes is proposed. The algorithm consists of a biased noise model, a neural belief propagation decoder, a convolutional optimization layer, and a multi-objective loss function. The biased noise model simulates asymmetric error generation, providing a training dataset for decoding. The neural network, leveraging dynamic weight learning and a multi-objective loss function, mitigates error degeneracy. Additionally, the convolutional optimization layer enhances early-stage convergence efficiency. Numerical results show that for bias-tailored quantum codes, our decoder performs much better than the belief propagation (BP) with ordered statistics decoding (BP + OSD). Our decoder achieves an order of magnitude improvement in the error suppression compared to higher-order BP + OSD. Furthermore, the decoding threshold of our decoder for surface codes reaches a high threshold of 20%.