Machine-Learning-Assisted Quantum Error Correction

Fault-tolerant and scalable quantum computers rely on the use of QEC codes. QEC codes can be constructed and designed for classes of quantum channels. There are at least two challenges in designing QEC codes. Firstly, most phenomenological-modeling quantum channels are time-dependent. Secondly, state-of-the-art quantum physical systems have abundant sources of noise, making the design of near-optimal QEC codes an extremely demanding and challenging task. One possibility to solve this problem is using two error correction layers. Algebraic QEC codes and QNNs serve as interesting candidates for the first and second layers.

This work proposes a novel use of quantum hardware efficient QEC codes in conjunction with a QNN to detect, correct, and mitigate complex noise sources. We consider that the dominant noise source is known and dealt with via the stabilizer group. The unknown noise is corrected by a QNN reproducing a carefully chosen map that may or not depends on the stabilizer code used. Using the mathematical formulation of QNN and stabilizer codes, we propose a QNN that acts trivially over the code space and adapts to Kraus operators. Numerical simulations considering realistic noise models and chip topologies corroborate the expected improvements. Additionally, we show that the error correction capability is bounded from below by the cost function used to train the QNN. Furthermore, such a lower bound is an improved complexity description over previous literature on approximate QEC assisted by QNN.