Bounds on qLDPC Code Parameters
summary
Provides geometry‑oblivious bounds on qLDPC parameters by analyzing the connectivity graph of qubits and using the separation profile plus an expansion lemma and the union lemma to build large correctable regions. Claims a tightened separator‑based tradeoff between k and d (previous separator proofs gave k ≲ n/d or k ≲ n/d^2 in earlier constructions; the new partitioning reduces that gap) but still does not recover the Bravyi‑Poulin‑Terhal (BPT) bound. Also shows good codes must contain many expanding subgraphs of size ≈ d whose total size scales with k.
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chapters (14)
- 0:00Introduction
- 1:06Stabilizer codes
- 2:35Low-dimensional code bounds
- 3:41Quantum code connectivity
- 7:12Correctable regions
- 10:50Partitioning correctable regions
- 11:32Bounds via separators
- 12:56Improving bounds with expansion
- 15:24General partitioning
- 17:32Graph expansion role
- 20:44Tighter bounds via expansion
- 22:08Obstructions from expansion
- 22:50Embedding into architectures
- 24:17Summary
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