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  • Dominic J. Williamson

    (University of Sydney)

  • Nouédyn Baspin

    (University of Sydney)

Abstract

Quantum computers require memories that are capable of storing quantum information reliably for long periods of time. The surface code is a two-dimensional quantum memory with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet optimal code was not previously known. Here we present a family of three dimensional topological codes with optimal scaling code parameters and a polynomial energy barrier. Our codes are based on a construction that takes in a stabilizer code and outputs a three-dimensional topological code with related code parameters. The output codes are topological defect networks formed by layers of surface code joined along one-dimensional junctions, with a maximum stabilizer check weight of six. When the input is a family of good quantum low-density parity-check codes the output codes have optimal scaling. Our results uncover strongly-correlated states of quantum matter that are capable of storing quantum information with the strongest possible protection from errors that is achievable in three dimensions.

Suggested Citation

  • Dominic J. Williamson & Nouédyn Baspin, 2024. "Layer codes," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-53881-3
    DOI: 10.1038/s41467-024-53881-3
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    1. Sebastian Krinner & Nathan Lacroix & Ants Remm & Agustin Paolo & Elie Genois & Catherine Leroux & Christoph Hellings & Stefania Lazar & Francois Swiadek & Johannes Herrmann & Graham J. Norris & Christ, 2022. "Realizing repeated quantum error correction in a distance-three surface code," Nature, Nature, vol. 605(7911), pages 669-674, May.
    2. Lukas Postler & Sascha Heuβen & Ivan Pogorelov & Manuel Rispler & Thomas Feldker & Michael Meth & Christian D. Marciniak & Roman Stricker & Martin Ringbauer & Rainer Blatt & Philipp Schindler & Markus, 2022. "Demonstration of fault-tolerant universal quantum gate operations," Nature, Nature, vol. 605(7911), pages 675-680, May.
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