Reducing the complexity of linear optics quantum circuits - art. no., 052303

Integrated optical elements can simplify the linear optics used to simulate quantum circuits. These linear optical simulations of quantum circuits hav e been developed primarily in terms of the free space optics associated wit h single-photon interferometry. For an L-bit simulation the number of requi red free-space optical elements is proportional to 2(L) if 50/50 beam split ters are used. The implementation (construction and alignment) of these cir cuits with these free-space elements is nontrivial. On the other hand, for the cases presented in this paper in which linear integrated optics (e.g., 2(L)x2(L) fiber couplers) are used, the number of optical devices does not grow exponentially with L. The problem is changed from having an exponentia l growth of the number of devices to having devices with an exponential gro wth in the number of ports. In addition to simplifying the construction, th e association of an NxN fiber coupler with the discrete Fourier transform s uggests alternative formulations for the circuits. Several examples of circ uit reductions are given.