Enhanced Fault-tolerance in Photonic Quantum Computing: Comparing the Honeycomb Floquet Code and the Surface Code in Tailored Architecture

Fault-tolerant quantum computing is crucial for realizing large-scale quantum computation, and the interplay between hardware architecture and quantum error-correcting codes is a key consideration. We present a comparative study of two quantum error-correcting codes - the surface code and the honeycomb Floquet code - implemented on the spin-optical quantum computing architecture, either with controlled-Z operations or with direct parity measurements. This allows for a direct comparison of the codes using consistent noise models. Notably, we achieve a loss threshold of 6.3% with the honeycomb Floquet code implemented on our tailored architecture, almost twice as high as the loss threshold obtained with the surface code on the previous architecture, all the while requiring less physical qubits. This finding is particularly significant given that photon loss is the primary source of errors in photon-mediated quantum computing. Moreover, we benchmark the general performances of the two codes in a multi-error setting by computing the volume of the fault-tolerant region, and show that the fault-tolerant region of the honeycomb code is over twice as large as that of the surface code.