Quantum clustering methods based in tunable external potentials or configurable phase singularities

Abstract

[ES] El objetivo es estudiar métodos de agrupamiento cuántico o de aprenidzaje automático basados en la ecuación de Schrödinger con un potencial externo controlable y proponer métodos basados en condiciones iniciales multisingulares configurables que se propagan mediante la ecuación de Schrödinger en ausencia de potencial externo. Un segundo objetivo es extender este segundo método a sistemas ópticos, donde la ecuación relevante es la ecuación paraxial, haciendo el sistema mucho mas accesible a experimentos actuales que los análogos sistemas cuánticos.

[EN] The aim of the present Master Thesis is to study quantum clustering and quantum machine learning methods based on the control of the external potential in a system described by a Schrodinger equation and to propose new quantum clustering methods based in configurable initial conditions with the form of a multisingular Gaussian beam. Since the paraxial wave equation for the optical field is analog to the Schrodinger equation in quantum systems, a second goal is to study these methods in optical systems. This would eventually permit one to realize such methods in optical systems, which are more accessible than quantum systems.