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We present methods which allow orders of magnitude increase in the number ofmodes in linear optics experiments by moving from spatial encoding to temporalencoding and using dispersion. This enables significant practical advantagesfor linear quantum optics and Boson Sampling experiments. Passing consecutivelyheralded photons through time-independent dispersion and measuring the outputtime of the photons is equivalent to a Boson Sampling experiment for which noefficient classical algorithm is reported, to our knowledge. Withtime-dependent dispersion, it is possible to implement arbitrarysingle-particle unitaries. Given the relatively simple requirements of theseschemes, they provide a path to realizing much larger linear quantum opticsexperiments including post-classical Boson Sampling machines.

High Dimensional Unitary Transformations and Boson Sampling on Temporal Modes using Dispersive Optics