Simulating a surface code based on dual-rail cavity qubits

Erasure qubits based on dual-rail cavity qubits are a relatively new concept [Teoh et al. PNAS 2023]. In these qubits, the dominant error - photon loss out of the dual-rail code space may be detected and converted to erasures, simplifying the task of quantum error correction. In this talk, we simulate the surface code with dual-rail cavity qubits as our physical qubits. Designing gates at the hardware-level such that they exhibit highly structured noise is essential to achieving good surface code performance. We show that with reasonable current hardware parameters, surface codes based on dual-rail cavity qubits are already expected to be far-below the relevant thresholds. An error correction gain \Lambda = \epsilon_{d}/\epsilon_{d+2} > 20 is expected, leading to low logical error rates even at modest code distances.