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Hyperbolic and semi-hyperbolic surface codes for quantum storage
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DOI：10.1088/2058-9565/aa7d3b.png)
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摘要
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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.
Keyword:
quantum fault-tolerance
quantum error correction
quantum codes
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