Efficient optical implementation of the Bernstein-Vazirani algorithm

We implement the Bernstein-Vazirani algorithm on a 15-bit register encoding $2^{15}$ elements using optics. The algorithm provides a polynomial speed up for oracle queries. The apparatus is physically efficient in that its size (i.e., space-time volume) scales linearly with the size (i.e., number of digits) of the register. We demonstrate also that the algorithm may be performed not only without entanglement, but also with a computational basis that does not consist of orthogonal states, and that this coding is the source of the efficiency of the algorithm.