We present methods which allow orders of magnitude increase in the number of modes in linear optics experiments by moving from spatial encoding to temporal encoding and using dispersion. This enables significant practical advantages for linear quantum optics and Boson Sampling experiments... Passing consecutively heralded photons through time-independent dispersion and measuring the output time of the photons is equivalent to a Boson Sampling experiment for which no efficient classical algorithm is reported, to our knowledge. With time-dependent dispersion, it is possible to implement arbitrary single-particle unitaries. Given the relatively simple requirements of these schemes, they provide a path to realizing much larger linear quantum optics experiments including post-classical Boson Sampling machines. (read more)