Quantum Error Correction with Quantum Autoencoders

David F. Locher, Lorenzo Cardarelli, and Markus Müller

Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany
Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, D-52425 Jülich, Germany

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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.

Quantum computers are notoriously susceptible to errors and will therefore require quantum error correction to reliably perform extensive calculations. Usually, one combines many noisy physical qubits to compose fewer so-called logical qubits that allow for errors to be detected and corrected. This process, however, requires measurements of additional qubits and feedback operations conditioned on those measurements, which can be a slow and experimentally challenging procedure.
In this paper, we investigate how the process of correcting potential errors on logical qubits can be performed autonomously, i.e., without the need to measure additional qubits. To achieve this, we train and apply quantum autoencoders, which are quantum neural networks that first compress and then decompress the input data. Those quantum autoencoders can learn correction strategies that are optimally suited to combat the noise present in a specific hardware device. The networks correct such errors fully autonomously and may still be beneficial to protect encoded quantum information from decoherence even if they are noisy themselves. Moreover, we show how the proposed scheme can be adapted to discover novel encoding schemes for logical qubits, which are optimally suited to protect encoded quantum information from hardware-specific noise.

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