TY - JOUR VL - 376 IS - 2123 N1 - 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. UR - https://doi.org/10.1098/rsta.2017.0323 SN - 1471-2962 JF - Philosophical Transactions of The Royal Society A - Mathematical, Physical and Engineering Sciences A1 - Conrad, J A1 - Chamberland, C A1 - Breuckmann, NP A1 - Terhal, BM TI - The small stellated dodecahedron code and friends Y1 - 2018/07/13/ AV - public EP - 19 N2 - 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?. ID - discovery10055490 PB - ROYAL SOC KW - Science & Technology KW - Multidisciplinary Sciences KW - Science & Technology - Other Topics KW - quantum error correction KW - fault tolerance KW - homological quantum codes KW - ERROR-CORRECTION KW - QUANTUM ER -