A scalable and fast artificial neural network syndrome decoder for surface codes

Spiro Gicev1, Lloyd C. L. Hollenberg1, and Muhammad Usman1,2,3

1Center for Quantum Computation and Communication Technology, School of Physics, University of Melbourne, Parkville, 3010, VIC, Australia.
2School of Computing and Information Systems, Melbourne School of Engineering, University of Melbourne, Parkville, 3010, VIC, Australia
3Data61, CSIRO, Clayton, 3168, VIC, Australia

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Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer operators are used to determine appropriate corrections for errors in physical qubits. Decoding algorithms have undergone substantial development, with recent work incorporating machine learning (ML) techniques. Despite promising initial results, the ML-based syndrome decoders are still limited to small scale demonstrations with low latency and are incapable of handling surface codes with boundary conditions and various shapes needed for lattice surgery and braiding. Here, we report the development of an artificial neural network (ANN) based scalable and fast syndrome decoder capable of decoding surface codes of arbitrary shape and size with data qubits suffering from the depolarizing error model. Based on rigorous training over 50 million random quantum error instances, our ANN decoder is shown to work with code distances exceeding 1000 (more than 4 million physical qubits), which is the largest ML-based decoder demonstration to-date. The established ANN decoder demonstrates an execution time in principle independent of code distance, implying that its implementation on dedicated hardware could potentially offer surface code decoding times of O($\mu$sec), commensurate with the experimentally realisable qubit coherence times. With the anticipated scale-up of quantum processors within the next decade, their augmentation with a fast and scalable syndrome decoder such as developed in our work is expected to play a decisive role towards experimental implementation of fault-tolerant quantum information processing.

The accuracy of the current generation of quantum devices suffers from noise or errors. Quantum error correction codes such as surface codes can be deployed to detect and correct errors. A crucial step in the implementation of surface code schemes is decoding, the algorithm that uses error information measured directly from the quantum computer to calculate appropriate corrections. In order to effectively solve the problems caused by noise, decoders need to calculate appropriate corrections at pace with the rapid measurements done on the underlying quantum hardware. This needs to be achieved at surface code distances large enough to sufficiently suppress errors and simultaneously across all active logical qubits. Previous work has primarily looked at graph matching algorithms such as minimum weight perfect matching, with some recent work also investigating the use of neural networks for this task, albeit being limited to small-scale implementations.

Our work proposed and implemented a novel convolutional neural network framework to address the scaling problems encountered when decoding large distance surface codes. The convolutional neural network was given an input comprised of changed parity measurements, as well as the boundary structure of the error correction code. Given the finite window of local observation occurring throughout the convolutional neural network, a mop-up decoder was used to correct any sparse residual errors that may remain. Based on rigorous training over 50 million random quantum error instances, our decoder was shown to work with code distances exceeding 1000 (more than 4 million physical qubits), which was the largest ML-based decoder demonstration to-date.

The use of convolutional neural networks and boundary structure in the input allowed our network to be applied on a wide range of surface code distances and boundary configurations. The local connectivity of the network allows low latency to be retained when decoding larger distance codes and readily facilitates parallelization. Our work addresses a key problem in the use of neural networks for decoding at scales of problems of practical interest and allows further research involving the use of networks with similar structure.

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