A route to damage tolerance exceeding $10\%$ in shuttling-equipped quantum processors

Abstract

This is a short study of an approach offering high tolerance to damage (i.e. defects or 'drop outs') in solid state fault-tolerant quantum computing. Our method is primarily aimed at semiconductor electron spin-qubit systems, which have been shown to support fast and high-fidelity shuttling along pre-defined paths. We adapt the recent CAbLECAR method of Chadwick and Chong: stabilisers are performed by ancillas which each follow a bespoke pre-programmed path. We consider the simple surface code but we damage the physical lattice, and rely on route-solving software to find efficient pathways under constraints enforcing stabiliser commutation and hook error avoidance. Solutions are then converted to detector error models for Stim and logical error rates are obtained. We express our results by gauging the logical performance against that of a pristine lattice, using the notion of a reduced equivalent surface-code distance; for reasonable underlying error rates we find that $10\%$ damage leaves roughly half of the pristine equivalent distance ($d_\text{equiv}\approx0.48\,d_\text{pristine}$ in the large-array limit, rising to $\approx0.60$ for our smallest array). This suggests that one can tolerate substantial damage by building oversized arrays. We note that investigating damage tolerance of other qLDPC codes is a straightforward generalisation, and potentially one could adapt to damage emerging at runtime.