ar X iv : 1 31 0 . 55 55 v 1 [ m at h . D G ] 2 1 O ct 2 01 3 QUANTUM ERROR CORRECTING CODES AND 4 - DIMENSIONAL ARITHMETIC HYPERBOLIC MANIFOLDS
نویسنده
چکیده
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. Their rate is evaluated via Euler characteristic arguments and their distance using Z2-systolic geometry. This construction answers a queston of Zémor [Z], who asked whether homological codes with such parameters could exist at all.
منابع مشابه
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
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. Their rate is evaluated via Euler characteristic arguments and their distance using Z2-systolic geometry. This construction answers a queston of Zémor [Z], who asked whether homological codes with such parameters could exist ...
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(28, 12, 11) [117]. (31, 10, 3) [34]. (36, 16, 12) [117]. (49, 9, 6) [142]. (64, 2, 12) [236]. (Ck ⊕G,k, 1) [251]. (G, k, 1) [251]. (m,n) [151]. (m− 1)/pm [167]. (p, p, p, p) [139]. (q, 6, 1) [342]. (v, {2, 4}, 1) [245]. (v, k, λ) [109]. −1 [26]. 0 [102, 205]. {0, 1, 2} [101]. 1 [205]. 15 [102]. 2 [14, 36, 55, 61, 68, 86, 117, 142, 143, 223, 265, 266, 271, 296, 324]. 25 [302]. 27 [93, 120]. 28 ...
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تاریخ انتشار 2013