On the Fault-Tolerance Threshold for Surface Codes with General Noise

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 realizing quantum devices. The current conclusions about surface code thresholds are, however, drawn largely from studies of probabilistic noise. While probabilistic noise is a natural assumption, current devices experience noise beyond such a model, raising the question of whether conventional statements about the thresholds apply. This work attempts to extend past proof techniques to derive the fault-tolerance threshold for surface codes subjected to general noise with no particular structure. Surprisingly, no nontrivial threshold is found, i.e., there is no guarantee the surface code prescription works for general noise. While this is not a proof that the scheme fails, it appears 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.