期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 62, 期 6, 页码 3731-3744出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2016.2555700
关键词
Quantum error correction; hyperbolic surfaces; surface code
资金
- EU Program QALGO
We show how to obtain concrete constructions of homological quantum codes based on tilings of 2-D surfaces with constant negative curvature (hyperbolic surfaces). This construction results in 2-D quantum codes whose tradeoff of encoding rate versus protection is more favorable than for the surface code. These surface codes would require variable length connections between qubits, as determined by the hyperbolic geometry. We provide numerical estimates of the value of the noise threshold and logical error probability of these codes against independent X or Z noise, assuming noise-free error correction.
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