Decoding quantum color codes with MaxSAT

Lucas Berent; Lukas Burgholzer; Peter-Jan H.S. Derks; Jens Eisert; Robert Wille

doi:10.22331/q-2024-10-23-1506

Decoding quantum color codes with MaxSAT

Lucas Berent¹, Lukas Burgholzer², Peter-Jan H.S. Derks³, Jens Eisert^3,4, and Robert Wille^1,5

¹Technical University of Munich, Germany
²Johannes Kepler University Linz, Austria
³Freie Universität Berlin, Germany
⁴Helmholtz-Zentrum Berlin für Materialien und Energie, Germany
⁵Software Competence Center Hagenberg GmbH (SCCH), Austria

Published:	2024-10-23, volume 8, page 1506
Eprint:	arXiv:2303.14237v3
Doi:	https://doi.org/10.22331/q-2024-10-23-1506
Citation:	Quantum 8, 1506 (2024).

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Abstract

In classical computing, error-correcting codes are well established and are ubiquitous both in theory and practical applications. For quantum computing, error-correction is essential as well, but harder to realize, coming along with substantial resource overheads and being concomitant with needs for substantial classical computing. Quantum error-correcting codes play a central role on the avenue towards fault-tolerant quantum computation beyond presumed near-term applications. Among those, color codes constitute a particularly important class of quantum codes that have gained interest in recent years due to favourable properties over other codes. As in classical computing, $decoding$ is the problem of inferring an operation to restore an uncorrupted state from a corrupted one and is central in the development of fault-tolerant quantum devices. In this work, we show how the decoding problem for color codes can be reduced to a slight variation of the well-known $\texttt{LightsOut}$ puzzle. We propose a novel decoder for quantum color codes using a formulation as a MaxSAT problem based on this analogy. Furthermore, we optimize the MaxSAT construction and show numerically that the decoding performance of the proposed decoder achieves state-of-the-art decoding performance on color codes. The implementation of the decoder as well as tools to automatically conduct numerical experiments are publicly available as part of the $\textit{Munich Quantum Toolkit}$ (MQT) on GitHub.

Featured image: Illustrative comparison of the decoding accuracy and runtime of color code decoders.

Munich Quantum Toolkit (MQT) on GitHub.

Popular summary

Qubits are inherently fragile, and it is difficult to control qubits precisely. Therefore, when using qubits to compute, the amount of errors grows over time. This leads to incorrect computation outcomes. To prevent this issue, specific measurements can be performed to check for errors. Decoding is the process of inferring how to correct errors given such measurement outcomes. In this work, we propose a decoding procedure based on a reduction of the decoding problem to the well-known LightsOut puzzle. We design a satisfiability formulation and propose to solve the decoding problem using SAT solving. We focus on the highly non-trivial problem of decoding color codes, but our approach is more generally applicable. We numerically investigate the decoding performance on color codes under data qubit and phenomenological noise.

► BibTeX data

@article{Berent2024decodingquantum,
  doi = {10.22331/q-2024-10-23-1506},
  url = {https://doi.org/10.22331/q-2024-10-23-1506},
  title = {Decoding quantum color codes with {M}ax{SAT}},
  author = {Berent, Lucas and Burgholzer, Lukas and Derks, Peter-Jan H.S. and Eisert, Jens and Wille, Robert},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1506},
  month = oct,
  year = {2024}
}

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