  This article introduces a novel approach to perform the simulation of a
single qubit quantum algorithm using laser beams. Leveraging the polarization
states of photonic qubits, and inspired by variational quantum eigensolvers, we
develop a variational quantum algorithm implementing a clustering procedure
following the approach proposed by some of us in SciRep 13, 13284 (2023). A key
aspect of our research involves the utilization of non-orthogonal states within
the photonic domain, harnessing the potential of polarization schemes to
reproduce unitary circuits. By mapping these non-orthogonal states into
polarization states, we achieve an efficient and versatile quantum information
processing unit which serves as a clustering device for a diverse set of
datasets.
