One area of study is the theory of dilute magnetic semiconductors (DMS). Topics include calculations of thermodynamic, electronic and magneto-optical properties of magnetic quantum dots. We also model Angle Resolved Photoemission spectra of bulk GaMnAs.
Another topic is computational band-gap engineering of phononic crystals. The phononic crystal is based on a semiconducting material and will host spin qubits.
Additionally, our group conducts research into the use of superconducting qubits for the purposes of quantum computing. This focuses primarily on their function in quantum adiabatic computation. This research is conducted by Dr. Andre Petukhov and Jacob Boschee in conjunction with D-Wave Systems Inc. and Google.
From the computational point of view, we use e.g. Mathematica (finite-difference approach to the 3D Schrodinger equation), COMSOL (finite-element method for phononic crystal simulation), and codes developed in the group (tight-binding).