  Spins of electrons in CMOS quantum dots combine exquisite quantum properties
and scalable fabrication. In the age of quantum technology, however, the
metrics that crowned Si/SiO2 as the microelectronics standard need to be
reassessed with respect to their impact upon qubit performance. We chart the
spin qubit variability due to the unavoidable atomic-scale roughness of the
Si/SiO$_2$ interface, compiling experiments in 12 devices, and developing
theoretical tools to analyse these results. Atomistic tight binding and path
integral Monte Carlo methods are adapted for describing fluctuations in devices
with millions of atoms by directly analysing their wavefunctions and electron
paths instead of their energy spectra. We correlate the effect of roughness
with the variability in qubit position, deformation, valley splitting, valley
phase, spin-orbit coupling and exchange coupling. These variabilities are found
to be bounded and lie within the tolerances for scalable architectures for
quantum computing as long as robust control methods are incorporated.
