We investigate the morphology of epitaxial Si layers grown on clean and on hydrogen terminated Si(001) to explore the growth strategy for the fabrication of a Si-based quantum computer. We use molecular beam epitaxy to deposit 5monolayers of silicon at a temperature of 250°C and scanning tunnelling microscopy to image the surface at room temperature after growth and after various rapid annealing steps in the temperature range of 350–600°C. The epitaxial layer grown on the hydrogenated surface shows a significantly higher surface roughness due to a lower mobility of silicon surface atoms in the presence of hydrogen. Annealing at temperatures ≥550°C reduces the roughness of both epitaxial layers to the value of a clean silicon surface. However, the missing dimer defect density of the epitaxial layer grown on the hydrogenated surface remains higher by a factor of two compared to the layer grown on clean Si(001). Our results suggest a quantum computer growth strategy in which the hydrogen resist layer is desorbed before the epitaxial silicon layer is grown at low temperature to encapsulate phosphorus quantum bits.