You are asking for a QM explanation at the level of photons and the atomic lattice structure (in your case the wall) of the object.
Now when you see an object having a certain color, it comes basically from two sources:
reflection of photons from the object, this can be:
-specular reflection, that is mirror like, it is elastic scattering, like in the case of metals (except gold for example), and is caused because metals atoms in the lattice structure interact with incoming photon mostly by elastic scattering, and the photons keep their energy levels, thus the metal does not have its own color, it just reflects
-diffuse reflection, that is with a wall in your case, the photons get absorbed and re-emitted but they do not keep their energy level and angle (this is why it is not mirror like). In this case the wall's atoms in the lattice structure have a certain QM intrinsic property, and that causes a certain wavelength of photons to be absorbed and re-emitted, thus the wall will have a certain color. Though, if you shine blue light on a white wall, you get a blue looking wall. In your case, when you shine white light on a blue wall, white light (and yes, the Sunlight is white, and not yellow) is made up of all different wavelength photons, and the wall's QM lattice structure is so, that blue wavelength photons get re-emitted.
- Objects can have color even without incoming light. The Sun emits photons for example, though it does not need incoming light to do so. This is photon emission in the case of the Sun, and other objects, like heated up metals, can emit photons, even if no photon is incoming. And this is just visible light. Every hot object (that is not in thermal equilibrium with its environment) emits non-visible light, always. This is how the object tries to come to thermal equilibrium with its environment, emitting energy, thus cooling (until it reaches thermal equilibrium with its environment).