The proposed general theory of scientific variability for technological evolution explains one of the drivers of technological change for economic progress in human society. Variability is the predisposition of the elements in systems to assume different values over time and space. In biology, the variability is basic to explaining differences and development in organisms. In economics of technical change, the effects of variability within research fields on evolutionary dynamics of related technologies are unknown. In a broad analogy with the principles of biology, suggested theoretical framework here can clarify a basic driver of technological evolution: the variability within research fields can explain the dynamics of scientific development and technological evolution. The study sees whether statistical evidence supports the hypothesis that the rate of growth of scientific and technological fields can be explained by the level of variability within scientific fields. The validation is based on emerging research fields in quantum technologies: quantum imaging, quantum meteorology, quantum sensing, and quantum optics. Statistical evidence seems in general to support the hypothesis stated that the rate of growth can be explained by the level of scientific variability within research fields, measured with the relative entropy (indicating the dispersion of scientific topics in a research field underlying a specific technology). Nonparametric correlation with Spearman’s rho shows a positive coefficient of 0.80 between entropy measures and rates of growth between scientific and technological fields. The linear model of the relation between rate of growth and scientific variability reveals a coefficient of regression equal to 1.63 (R2 = 0.60). The findings here suggest a general law that variability within research fields positively drives scientific development and technological evolution. In particular, a higher variability within research fields can support a high rate of growth in scientific development and technological evolution. The proposed general theory of scientific variability is especially relevant in turbulent environments of technology-based competition to clarify a basic determinant of technological development to design strategies of technological forecasting and management of promising innovations.