  Geometric locality is an important theoretical and practical factor for
quantum low-density parity-check (qLDPC) codes which affects code performance
and ease of physical realization. For device architectures restricted to 2D
local gates, naively implementing the high-rate codes suitable for low-overhead
fault-tolerant quantum computing incurs prohibitive overhead. In this work, we
present an error correction protocol built on a bilayer architecture that aims
to reduce operational overheads when restricted to 2D local gates by measuring
some generators less frequently than others. We investigate the family of
bivariate bicycle qLDPC codes and show that they are well suited for a parallel
syndrome measurement scheme using fast routing with local operations and
classical communication (LOCC). Through circuit-level simulations, we find that
in some parameter regimes bivariate bicycle codes implemented with this
protocol have logical error rates comparable to the surface code while using
fewer physical qubits.
