How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon

TL;DR

This paper investigates how the speed of braiding non-Abelian anyons affects error rates, demonstrating that diabatic errors mainly arise from unintended quasiparticle creation and can be mitigated through measurements.

Contribution

It provides a detailed analysis of diabatic errors in anyon braiding, showing that such errors do not compromise quantum information unless they involve creating nontrivial quasiparticles, and suggests measurement-based error control.

Findings

Diabatic corrections decay inversely with braiding time.

Errors from diabatic effects do not affect topological quantum information unless quasiparticles are created.

Measurement of quasiparticles can be used to control and reduce errors.

Abstract

Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as the distance between quasiparticles. However, it is less well-understood how error rates depend on the speed with which non-Abelian quasiparticles are braided. In general, diabatic corrections to the holonomy or Berry's matrix vanish at least inversely with the length of time for the braid, with faster decay occurring as the time-dependence is made smoother. We show that such corrections will not affect quantum information encoded in topological degrees of freedom, unless they involve the creation of topologically nontrivial quasiparticles. Moreover, we show how measurements that detect unintentionally created quasiparticles can be used to control this source of error.