Hyperbolic and Semi-Hyperbolic Surface Codes for Quantum Storage
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 to 2.9% for the toric code). In this code family parity checks are of weight 4 and 5 while each qubit participates in 4 different parity checks. We introduce a family of semi-hyperbolic codes which 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.
Keywords
Cite
@article{arxiv.1703.00590,
title = {Hyperbolic and Semi-Hyperbolic Surface Codes for Quantum Storage},
author = {Nikolas P. Breuckmann and Christophe Vuillot and Earl Campbell and Anirudh Krishna and Barbara M. Terhal},
journal= {arXiv preprint arXiv:1703.00590},
year = {2017}
}
Comments
28 pages, 21 figures