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Decodable Quantum LDPC Codes Beyond the Square Root Distance Barrier Using High Dimensional Expander
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- 1 Intro
- 2 Classical codes
- 3 CSS (Calderbank, Shor, Steane) codes A quantum CSS code is given by two orthogonal subspaces
- 4 CSS codes as 2-complexes A CSS code given by parity check matrices
- 5 Geometric 2-complexes
- 6 Boundaries
- 7 Towards better complexes
- 8 Geometrical approach (II)
- 9 LSV (Lubotzky, Samuels, Vishne) complexes (1) These are explicit bounded degree simplicial complexes, which are highly complicated objects (both locally and globally).
- 10 Link of a vertex
- 11 Decoding LSV complexes (1)
- 12 Balancing distances (1) TA
- 13 LSV 3-complexes
- 14 Final remarks
