Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying these requirements. We then introduce the construction of local neural network (NN) decoders using three-dimensional convolutions. These local decoders are adapted to circuit-level noise and can be applied to surface code volumes of arbitrary size. Their application removes errors arising from a certain number of faults, which serves to substantially reduce the syndrome density. Remaining errors can then be corrected by a global decoder, such as Blossom or union find, with their implementation significantly accelerated due to the reduced syndrome density. However, in the circuit-level setting, the corrections applied by the local decoder introduce many vertical pairs of highlighted vertices. To obtain a low syndrome density in the presence of vertical pairs, we consider a strategy of performing a syndrome collapse which removes many vertical pairs and reduces the size of the decoding graph used by the global decoder. We also consider a strategy of performing a vertical cleanup, which consists of removing all local vertical pairs prior to implementing the global decoder. By applying our local NN decoder and the vertical cleanup strategy to a d = 17 surface code volume, we show a 10⁶× speedup of the minimum-weight perfect matching decoder. Lastly, we estimate the cost of implementing our local decoders on field programmable gate arrays.
Published October 2023
| Published
Journal Article
Open
Techniques for combining fast local decoders with global decoders under circuit-level noise
Abstract
Copyright and License
© 2023 The Author(s). Published by IOP Publishing Ltd. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Acknowledgement
C C would like to thank Aleksander Kubica, Nicola Pancotti, Connor Hann, Arne Grimsmo and Oskar Painter for useful discussions.
Data Availability
The data cannot be made publicly available upon publication due to legal restrictions preventing unrestricted public distribution. The data that support the findings of this study are available upon reasonable request from the authors.
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Additional details
- Caltech groups
- Institute for Quantum Information and Matter, AWS Center for Quantum Computing