Hyperbolic and semi-hyperbolic surface codes for quantum storage

Journal article (2017)

Authors

Nikolas P. Breuckmann Rheinisch-Westfälische Technische Hochschule
C. Vuillot Rheinisch-Westfälische Technische Hochschule
Earl T. Campbell University of Sheffield
Anirudh Krishna University of Sherbrooke
B.M. Terhal Rheinisch-Westfälische Technische Hochschule
Affiliation
External organisation
Quantum error correction Quantum codes Quantum fault-tolerance
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Published Date

01-09-2017

Language

English

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Abstract

We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3%for the {4, 5}-hyperbolic surface code in a phenomenological noise model (as compared with 2.9% for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the {4, 5}-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.