Implementing the Deutsch algorithm with polarization and transverse spatial modes

Abstract

In this paper we implement a simple quantum algorithm using polarization and transverse spatial modes of the electromagnetic field as qubits. The transverse spatial modes used are the Laguerre–Gaussian and Hermite–Gaussian beams of order N = 1. With these two qubits carried by the same photon, we have implemented the Deutsch algorithm using a simple linear optical setup.