PhD thesis: Homological Quantum Codes Beyond the Toric Code

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PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries.

• In the first part we will consider closed surfaces with constant negative curvature.
• We show how such surfaces can be constructed and enumerate all quantum codes derived from them which have less than 10.000 physical qubits.
• For codes that are extremal in a certain sense we perform numerical simulations to determine the value of their threshold.