I gave this talk at the end of my 2011 Summer Undergraduate Research Fellowship at Caltech as part of the Perpall speaking competition. I advanced to the final round, where I finished in the top seven.
Available via iTunes: search for Caltech, then navigate to SURF Presentations. Alternatively, Caltech SURF graciously uploaded the video here.
A quantum computer built on adiabatic principles has an interesting runtime feature - the time it takes for the computation to execute depends on an energy gap within the system. It is not know whether an adiabatic quantum computer built out of spin 1/2 particles on 1 dimensional ring has energy gaps which close exponentially quickly in the system size. I present a way to investigate this problem numerically.