Construction of quantum states by special superpositions of coherent states

TL;DR

This paper develops a numerical method using genetic algorithms to optimally approximate specific harmonic oscillator quantum states with superpositions of coherent states arranged on geometric patterns, achieving superior accuracy over previous methods.

Contribution

It introduces a novel optimization approach for constructing quantum states from superpositions of coherent states on ellipses or lattices, improving approximation quality.

Findings

Optimized superpositions outperform existing approximations.

Genetic algorithms effectively find optimal parameters.

Approximations are experimentally feasible.

Abstract

We consider the optimal approximation of certain quantum states of a harmonic oscillator with the superposition of a finite number of coherent states in phase space placed either on an ellipse or on a certain lattice. These scenarios are currently experimentally feasible. The parameters of the ellipse and the lattice and the coefficients of the constituent coherent states are optimized numerically, via a genetic algorithm, in order to obtain the best approximation. It is found that for certain quantum states the obtained approximation is better than the ones known from the literature thus far.