High-Threshold Code for Modular Hardware with Asymmetric Noise

Abstract

We consider an approach to fault tolerant quantum computing based on a simple error-detecting code operating as the substrate for a conventional surface code. We anticipate that the approach will be efficient when the noise in the hardware is skewed towards one channel (e.g., phase), or alternatively when the hardware is modular in such a fashion that the local error-detect operations have higher fidelity. We employ a customized decoder where information about the likely location of errors, obtained from the error-detection code, is translated into an advanced variant of the minimum-weight perfect-matching algorithm. A threshold gate-level error rate of 1.42% is found for the concatenated code given highly asymmetric noise. This is superior to the standard surface code and remains so as we introduce a significant component of depolarizing noise; specifically, until the latter is 70% the strength of the former. Moreover, given the asymmetric noise case, the threshold rises to 6.24% if we additionally assume that local operations have 20 times higher fidelity than long-range gates. Thus, for systems that are both modular and prone to asymmetric noise our code structure can be very advantageous.