Linear-Optical Quantum Computation with Arbitrary Error-Correcting Codes.

High-rate quantum error-correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of nonlocal, 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 of hyperbolic surface codes and bivariate bicycle codes, promising families of quantum low-density parity-check codes, reveal a threshold comparable to the 2D surface code with substantially better encoding rates.