Stability of topologically-protected quantum computing proposals as seen through spin glasses

TL;DR

This paper reviews how the stability of topologically-protected quantum computing schemes against noise can be analyzed using spin-glass models, highlighting recent results on their error thresholds and robustness.

Contribution

It provides an overview of techniques to estimate error thresholds in topological quantum computing and summarizes recent findings on their noise stability.

Findings

Error thresholds can be mapped to phase transitions in spin-glass models.

Different topological schemes show varying robustness to specific error sources.

Recent results indicate certain models have higher stability against noise.

Abstract

Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for small proof-of-principle devices. Topologically-protected quantum computing aims at solving this problem by encoding quantum bits and gates in topological properties of the hardware medium that are immune to noise that does not impact the entire system at once. There are different approaches to achieve topological stability or active error correction, ranging from quasiparticle braidings to spin models and topological color codes. The stability of these proposals against noise can be quantified by their error threshold. This figure of merit can be computed by mapping the problem onto complex statistical-mechanical spin-glass models with local disorder on nontrival lattices that can have many-body interactions and are sometimes described by lattice gauge theories. The error threshold for a given source of error then represents the point in the temperature-disorder phase diagram where a stable symmetry-broken phase vanishes. An overview of the techniques used to estimate the error thresholds is given, as well as a summary of recent results on the stability of different topologically-protected quantum computing schemes to different error sources.