Decomposing large unitaries into multimode devices of arbitrary size

Decomposing complex unitary evolution into a series of constituent components is a cornerstone of practical quantum information processing. While the decompostion of an ntimes n unitary into a series of 2times2 subunitaries is well established (i.e. beamsplitters and phase shifters in linear optics), we show how this decomposition can be generalised into a series of mtimes m multimode devices, where m>2. If the cost associated with building each mtimes m multimode device is less than constructing with frac{m(m-1)}{2} individual 2times 2 devices, we show that the decomposition of large unitaries into mtimes m submatrices is is more resource efficient and exhibits a higher tolerance to errors, than its 2times 2 counterpart. This allows larger-scale unitaries to be constructed with lower errors, which is necessary for various tasks, not least Boson sampling, the quantum Fourier transform and quantum simulations.