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.
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Submitted on : Wednesday, November 6, 2019 - 1:44:56 PM
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Nikolas P. Breuckmann, Christophe Vuillot, Earl Campbell, Anirudh Krishna, Barbara M. Terhal. Hyperbolic and semi-hyperbolic surface codes for quantum storage. Quantum Science and Technology, IOP Science, 2017, 2 (3), pp.035007. ⟨10.1088/2058-9565/aa7d3b⟩. ⟨hal-02351423⟩

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