A probabilistic evolutionary optimization approach to compute quasiparticle braids

TL;DR

This paper introduces a probabilistic evolutionary optimization method using estimation of distribution algorithms to efficiently compute quasiparticle braids for topological quantum computing, achieving high accuracy and shorter braid lengths.

Contribution

It presents a novel application of estimation of distribution algorithms to optimize quasiparticle braids, leveraging statistical regularities for improved performance.

Findings

Achieved gate approximation accuracy of around 10^{-6}

Produced solutions with braid lengths up to 9 times shorter

Demonstrated the effectiveness of probabilistic algorithms in braid optimization

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.