Improved phase gate reliability in systems with neutral Ising anyons

TL;DR

This paper demonstrates that neutral Ising anyon systems can implement more reliable phase gates for topological quantum computing, with significantly reduced error rates compared to charged systems, by utilizing the sack geometry and edge tunneling control.

Contribution

It introduces a method to enhance phase gate reliability in neutral Ising anyon systems and proposes a technique to tune edge tunneling rates for better interferometric control.

Findings

Error rate scales as T^3 at low temperatures.

Zero-temperature phase variance remains finite over time.

Neutral systems exhibit lower error rates than charged counterparts.

Abstract

Recent proposals using heterostructures of superconducting and either topologically insulating or semiconducting layers have been put forth as possible platforms for topological quantum computation. These systems are predicted to contain Ising anyons and share the feature of having only neutral edge excitations. In this note, we show that these proposals can be combined with the recently proposed "sack geometry" for implementation of a phase gate in order to conduct robust universal quantum computation. In addition, we propose a general method for adjusting edge tunneling rates in such systems, which is necessary for the control of interferometric devices. The error rate for the phase gate in neutral Ising systems is parametrically smaller than for a similar geometry in which the edge modes carry charge: it goes as $T^3$ rather than $T$ at low temperatures. At zero temperature, the phase variance becomes constant at long times rather than carrying a logarithmic divergence.