Layer Codes
summary
Claim is that one can saturate 3D locality bounds to get essentially optimal local quantum LDPC codes by concatenating good LDPC codes with stacked surface code layers and using lattice surgery plus the folding trick to turn nonlocal high‑weight checks into local checks of weight ≤6. Construction embeds on an L×L×L grid so n ~ L^3, k ~ O(L), and d ~ O(L^2)/w where w is input check weight, and it provably preserves an energy barrier scaling ∝ L up to constant factors, so the construction works to meet the BPT-type limits.
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chapters (11)
- 0:003D quantum codes intro
- 1:08Motivation for layer codes
- 2:55LDPC and surface codes background
- 9:20BPT bounds in two and three dimensions
- 15:22Concatenating surface and LDPC codes
- 21:05Defects and lattice surgery in 3D
- 27:06Stabilizer construction
- 31:02Code parameters and scaling
- 37:03Energy barrier and thermal robustness
- 40:19Open questions and future work
- 42:46Q&A
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