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Alex Lubotzky - Quantum error correcting codes...
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Alex Lubotzky (Hebrew University of Jerusalem, Israel)
Title: Quantum error correcting codes and asymptotic properties of 4-dimensional arithmetic hyperbolic manifolds.
Abstract: A family of quantum error correcting codes (QECC) is constructed out of congruence quotients of the 4- dimensional hyperbolic space. The parameters of these codes are expressed by some aymptotic properties of the manifolds and their fundamental groups. By estimating these parameters, we disprove a conjecture of Zémor who predicted that such homological QECC do not exist. All notions will be defined and explained. A joint work with Larry Guth.
Title: Quantum error correcting codes and asymptotic properties of 4-dimensional arithmetic hyperbolic manifolds.
Abstract: A family of quantum error correcting codes (QECC) is constructed out of congruence quotients of the 4- dimensional hyperbolic space. The parameters of these codes are expressed by some aymptotic properties of the manifolds and their fundamental groups. By estimating these parameters, we disprove a conjecture of Zémor who predicted that such homological QECC do not exist. All notions will be defined and explained. A joint work with Larry Guth.
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