Neural network decoder for quantum error correcting codes

Yoni Choukroun, Lior Wolf

Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across redundant physical qubits, such that errors can be detected and corrected. In this work, we efficiently train novel end-to-end deep quantum error decoders. We resolve the quantum measurement collapse by augmenting syndrome decoding to predict an initial estimate of the system noise, which is then refined iteratively through a deep neural network. The logical error rates calculated over finite fields are directly optimized via a differentiable objective, enabling efficient decoding under the constraints imposed by the code. Finally, our architecture is extended to support faulty syndrome measurement, by efficient decoding of repeated syndrome sampling. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy, outperforming for small distance topological codes, the existing end-to-end neural and classical decoders, which are often computationally prohibitive.

Y.S. Balashov, S.N. Panychev, Marina Horoshaylova

Luca Menti

Nishad Maskara, Aleksander Kubica, Tomas Jochym-O’Connor

Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes, developing good and efficient decoders still remains a challenge. In our paper, we systematically study a very versatile class of decoders based on feedforward neural networks. To demonstrate adaptability, we apply neural decoders to the triangular color and toric codes under various noise models with realistic features, such as spatially correlated errors. We report that neural decoders provide a significant improvement over leading efficient decoders in terms of the error-correction threshold. In particular, the neural decoder threshold for the two-dimensional color code is very close to the toric code threshold. Using neural networks simplifies the design of decoders and does not require prior knowledge of the underlying noise.

Evgenii Egorov, Roberto Bondesan, Max Welling

Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the system size. Neural network decoders are an appealing solution since they can learn from data an efficient approximation to such a mapping and can automatically adapt to the noise distribution. In this work, we introduce a data efficient neural decoder that exploits the symmetries of the problem. We characterize the symmetries of the optimal decoder for the toric code and propose a novel equivariant architecture that achieves state of the art accuracy compared to previous neural decoders.

Davide Pastorello