  High-rate quantum error correcting codes mitigate the imposing scale of
fault-tolerant quantum computers but require the efficient generation of
non-local many-body entanglement. We provide a linear-optical architecture with
these properties, compatible with arbitrary codes and Gottesman-Kitaev-Preskill
qubits on generic lattices, and featuring a natural way to leverage physical
noise bias. Simulations involving hyperbolic surface codes, promising quantum
low-density parity-check codes, reveal a threshold comparable to the 2D surface
code at about a ten-fold improvement in encoding rate.
