Hyperbolic and semi-hyperbolic surface codes for quantum storage
Hyperbolic and semi-hyperbolic surface codes for quantum storage
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DOI：
10.1088/2058-9565/aa7d3b
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发表时间：
2017-09-01
影响因子：
6.7
通讯作者：
Terhal, Barbara M.
中科院分区：
文献类型：
--
作者：
Breuckmann, Nikolas P.;Vuillot, Christophe;Terhal, Barbara M.
我们展示了如何使用双曲表面代码来实现开销高效的量子存储。我们给出了现象学噪声模型中 {4, 5}-双曲表面代码的噪声阈值为 1.3% 的数值证据（相比之下，环面代码为 2.9%）。在此代码系列中，奇偶校验的权重为 4 和 5，而每个量子位参与四种不同的奇偶校验。我们引入了一系列半双曲码，它们在编码率和阈值方面插值在环面码和 {4, 5}-双曲表面码之间。我们展示了这些双曲代码如何在目标逻辑错误概率的量子位开销方面优于环面代码。我们展示了如何使用 Dehn 扭曲和晶格码手术在这种量子存储介质中读取和写入单个量子位。
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.