Algoritmos multi-objetivos para la optimización de una secuencia de matrices generadoras en computación cuántica topológica
Laburpena
Quantum Computing is a relatively modern field which simulates quantum computation
conditions. Moreover, it can be used to estimate which quasiparticles would endure better
in a quantum environment. Topological Quantum Computing (TQC) is an approximation
for reducing the quantum decoherence problem1, which is responsible for error appearance
in the representation of information.
This project tackles specific instances of TQC problems using MOEAs (Multi-objective
Optimization Evolutionary Algorithms). A MOEA is a type of algorithm which will optimize
two or more objectives of a problem simultaneously, using a population based
approach.
We have implemented MOEAs that use probabilistic procedures found in EDAs (Estimation
of Distribution Algorithms), since in general, EDAs have found better solutions than
ordinary EAs (Evolutionary Algorithms), even though they are more costly. Both, EDAs
and MOEAs are population-based algorithms.
The objective of this project was to use a multi-objective approach in order to find good
solutions for several instances of a TQC problem. In particular, the objectives considered
in the project were the error approximation and the length of a solution. The tool
we used to solve the instances of the problem was the multi-objective framework PISA.
Because PISA has not too much documentation available, we had to go through a process
of reverse-engineering of the framework to understand its modules and the way they communicate
with each other. Once its functioning was understood, we began working on a
module dedicated to the braid problem. Finally, we submitted this module to an exhaustive
experimentation phase and collected results.