We propose a computational design framework to design the architecture of a white lighting system having multiple pixelated patterns of electric-field-driven quantum dot light-emitting diodes. The quantum dot of the white lighting system has been optimised by a system-level combinatorial colour optimisation process with the Nelder-Mead algorithm used for machine learning. The layout of quantum dot patterns is designed precisely using rigorous device-level charge transport simulation with an electric-field dependent charge injection model. A theoretical maximum of 97% colour rendering index has been achieved with red, green, cyan, and blue quantum dot light-emitting diodes as primary colours. The white lighting system has been fabricated using the transfer printing technique to validate the computational design framework. It exhibits excellent lighting performance of 92% colour rendering index and wide colour temperature variation from 1612 K to 8903 K with only the four pixelated quantum dots as primary.