The first iteration of Grover's algorithm using classical light with orbital angular momentum

We present an experimental realization of the first iteration in Grover's quantum algorithm using classical light and linear optical elements. The algorithm serves to find an entry marked by an oracle in an unstructured database. In our scheme, the quantum states encoding the database are represented by helical modes generated by means of a Spatial Light Modulator, while the marking corresponds to a phase shift of the hidden mode. The optical implementation of Grover's algorithm then selectively amplifies the intensity of the marked mode such that it can be revealed by a modal decomposition. The core of the algorithm - a geometrical reflection of the point representing all database entries - is implemented in a single step independent of the size of the database. Moreover, we demonstrate experimentally that one iteration of the algorithm is enough to identify the marked entry, as a consequence of using classical states of light.