Genetic braid optimization: A heuristic approach to compute quasiparticle braids

TL;DR

This paper introduces a genetic algorithm-based heuristic to optimize quasiparticle braids for topologically-protected quantum gates, balancing accuracy and braid length efficiently.

Contribution

It presents a novel genetic algorithm approach for quasiparticle braid optimization, adaptable to various braiding problems and utility preferences.

Findings

Efficiently finds optimal braids balancing accuracy and length.

Quickly produces efficient braids when optimizing for error.

Flexible method applicable to different braiding scenarios.

Abstract

In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well as Leijnse and Flensberg [Phys. Rev. B 86, 104511 (2012)] recently provided schemes for computing quantum gates from quasiparticle braids. Mathematically, the problem of executing a gate becomes that of finding a product of the generators (matrices) in that set that approximates the gate best, up to an error. To date, efficient methods to compute these gates only strive to optimize for accuracy. We explore the possibility of using a generic approach applicable to a variety of braiding problems based on evolutionary (genetic) algorithms. The method efficiently finds optimal braids while allowing the user to optimize for the relative utilities of accuracy and/or length. Furthermore, when optimizing for error only, the method can quickly produce efficient braids.