On the fault-tolerance threshold for surface codes with general noise

TL;DR

This paper investigates the fault-tolerance threshold of surface codes under general, unstructured noise, revealing that current proof techniques do not establish a nontrivial threshold, challenging assumptions about their robustness.

Contribution

It extends existing proof methods to analyze surface codes with arbitrary noise, finding no guaranteed threshold, and highlights the need for new approaches.

Findings

No nontrivial fault-tolerance threshold established for general noise

Current proof techniques are likely insufficient for such noise models

Surface codes may not be universally robust against all noise types

Abstract

Fault-tolerant quantum computing based on surface codes has emerged as a popular route to large-scale quantum computers capable of accurate computation even in the presence of noise. Its popularity is, in part, because the fault-tolerance or accuracy threshold for surface codes is believed to be less stringent than competing schemes. This threshold is the noise level below which computational accuracy can be increased by increasing physical resources for noise removal, and is an important engineering target for realising quantum devices. The current conclusions about surface code thresholds are, however, drawn largely from studies of probabilistic noise. While a natural assumption, current devices experience noise beyond such a model, raising the question of whether conventional statements about the thresholds apply. Here, we attempt to extend past proof techniques to derive the fault-tolerance threshold for surface codes subjected to general noise with no particular structure. Surprisingly, we found no nontrivial threshold, i.e., there is no guarantee the surface code prescription works for general noise. While this is not a proof that the scheme fails, we argue that current proof techniques are likely unable to provide an answer. A genuinely new idea is needed, to reaffirm the feasibility of surface code quantum computing.