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arXiv · 1310.5555

Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds

Larry Guth·Alexander Lubotzky
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Abstract

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance $n^ε$. Their rate is evaluated via Euler characteristic arguments and their distance using $\mathbb{Z}_2$-systolic geometry. This construction answers a queston of Zémor, who asked whether homological codes with such parameters could exist at all.

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Larry Guth, Alexander Lubotzky. 2013-10-21. Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds. https://doi.org/10.1063/1.4891487

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