Twisted Product Constructions for LDPC Quantum Codes

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Three product constructions use twists in fiber bundles, lifted products over group algebras, and balanced products with symmetry reduction to build LDPC CSS codes whose distances break the old √N barrier. Random twisted bundles (Hastings, Ha, O’Donnell) give distance ~N^{3/5} up to polylogs; Panteleev–Kalachev reach almost linear distance up to logarithms; an unconditional lifted-product variant avoids randomness. Balanced-product codes use LPS expander Cayley graphs and Sipser–Spielman local blocks to yield explicit families (example: 546 qubits, 6 logical, distances 13 and 18, check weights 4–8).

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" chapters (18)

1. 0:00Introduction
2. 0:33Quantum Codes
3. 5:43Quantum Code History
4. 8:11Product Constructions
5. 8:45Topology
6. 11:06Twists
7. 16:32Polylog Factor
8. 16:56Lifting Products
9. 18:25Lifted Products
10. 23:14Dimension Balancing
11. 24:21Balanced Product
12. 25:31Expanders
13. 26:45Calligraphs
14. 27:57Local Block Codes
15. 32:29Balance Product
16. 36:06Expander Codes
17. 40:24conjecture
18. 41:09Questions