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The small stellated dodecahedron code and friends

Conrad, J; Chamberland, C; Breuckmann, NP; Terhal, BM; (2018) The small stellated dodecahedron code and friends. Philosophical Transactions of The Royal Society A - Mathematical, Physical and Engineering Sciences , 376 (2123) , Article 20170323. 10.1098/rsta.2017.0323. Green open access

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Abstract

We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for three-dimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity check measurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop fault-tolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuit-based pseudo-threshold. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

Type: Article
Title: The small stellated dodecahedron code and friends
Open access status: An open access version is available from UCL Discovery
DOI: 10.1098/rsta.2017.0323
Publisher version: https://doi.org/10.1098/rsta.2017.0323
Language: English
Additional information: Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Keywords: Science & Technology, Multidisciplinary Sciences, Science & Technology - Other Topics, quantum error correction, fault tolerance, homological quantum codes, ERROR-CORRECTION, QUANTUM
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10055490
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