Bilayer LOCC 2D Implementation Boundary

Claim/Theorem

Berthusen, Devulapalli, Schoute, Childs, Gullans, Gorshkov, and Gottesman present a bilayer architecture for implementing certain qLDPC codes in 2D using local operations and classical communication (LOCC), together with a protocol that measures some generators less frequently than others. For bivariate-bicycle codes, they report competitive logical performance relative to the surface code in some regimes. This identifies a concrete boundary of Conjecture 3: 2D realizations can improve substantially once one allows bilayer layouts, LOCC-assisted fast routing, and nonuniform measurement schedules.

Dependencies

• [[thin-planar-connectivity-escape.md]]

Conflicts/Gaps

• This is not a static single-layer SWAP-only implementation, so it does not refute the current lower-bound program.
• The code family is bivariate-bicycle rather than the expander-style Tanner family used in the current theorem candidate.
• The protocol deliberately measures some generators less frequently, so it is not the same operational target as one full coherent syndrome-extraction round for all checks.

Sources

• 10.1103/PRXQuantum.6.010306