Efficient qudit encoding for quantum optics

Linear optics are a promising alternative for the realization of quantum computation and quantum communication protocols due to the long coherence time of photons. Linear optics can implement high dimensional computational units called qudits which provide a natural way to compile d-ary algorithms into quantum gates. This work investigates qudits defined by the possible photon number states of a single photon in d > 2 optical modes. We demonstrate how to construct locally optimal non-deterministic many-qudit gates using linear optics and photon number resolving detectors, and explore the use of qudit cluster states in the context of a d-ary optimization problem. We find that the qudit cluster states require less optical modes and are encoded by a fewer number of entangled photons than the qubit cluster states with similar computational capabilities.