A probabilistic evolutionary optimization approach to compute quasiparticle braids

Abstract

Topological quantum computing is an alternative framework for avoiding the quantum decoherence problem in quantum computation. The problem of executing a gate in this framework can be posed as the problem of braiding quasiparticles. Because these are not Abelian, the problem can be reduced to finding an optimal product of braid generators where the optimality is defined in terms of the gate approximation and the braid's length. In this paper we propose the use of different variants of estimation of distribution algorithms to deal with the problem. Furthermore, we investigate how the regularities of the braid optimization problem can be translated into statistical regularities by means of the Boltzmann distribution. We show that our best algorithm is able to produce many solutions that approximates the target gate with an accuracy in the order of $10^{-6}$, and have lengths up to 9 times shorter than those expected from braids of the same accuracy obtained with other methods.

9 pages,7 figures. Accepted at SEAL 2014

References in corpus (6)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Braid Topologies for Quantum Computation
• Topological Quantum Compiling
• Constructing Functional Braids for Low-Leakage Topological Quantum Computing
• Genetic braid optimization: A heuristic approach to compute quasiparticle braids
• Analysis of Evolutionary Algorithms on the One-Dimensional Spin Glass with Power-Law Interactions

Cited by in corpus (2)

• Introduction to topological quantum computation with non-Abelian anyons
• Computing factorized approximations of Pareto-fronts using mNM-landscapes and Boltzmann distributions