Dual-rail quantum code
This is an error-detecting code against one photon loss event; it is often used in photonic quantum devices because of its ease of realization. A single loss event can be detected because, after the loss occurs, the output state \(|00\rangle\) is orthogonal to the codespace. Recovery is not possible, so a successful run of a quantum circuit is conditioned on not losing a photon during the circuit.
For Deutsch''s problem specifically, this code protects against errors resulting in states that have the correct photon number, but in the wrong modes .
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“Dual-rail quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/dual_rail