If the parameter $s$ is varied adiabatically there should be no need to solve the time-dependent Schrodinger equation. The adiabatic theorem implies the instantaneous eigenvalues are always those of the parameterized Hamiltonian, provided its spectrum is separated.

Thus your final statement and hadsed's conclusion are correct: The figure just shows the eigenvalues of the matrix as a function of $s$.

How is the energy/eigenvalue gap plot drawn for adiabatic quantum computation?
In a lot of places I interviewed recently, I have been asked many a times if I have worked with shaders. Even though, I have read and understand the pipeline, the answer to that question has been no. Recently, one of the places asked me if I can send them a sample of 'something' that is "visually polished".

So, I decided to take the plunge and wrote some simple shader in GLSL(with opengl).I now have a basic setup where I can use vbos with glsl shaders.

I have a very short window left to send something to them and I was wondering if someone  with experience, could suggest an idea that is interesting enough to grab someone's attention.

Thanks
