  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.
