Few-body spin couplings and their implications for universal quantum   computation
  Electron spins in semiconductor quantum dots are promising candidates for the experimental realization of solid-state qubits. We analyze the dynamics of a system of three qubits arranged in a linear geometry and a system of four qubits arranged in a square geometry. Calculations are performed for several quantum dot confining potentials. In the three-qubit case, three-body effects are identified that have an important quantitative influence upon quantum computation. In the four-qubit case, the full Hamiltonian is found to include both three-body and four-body interactions that significantly influence the dynamics in physically relevant parameter regimes. We consider the implications of these results for the encoded universality paradigm applied to the four-electron qubit code; in particular, we consider what is required to circumvent the four-body effects in an encoded system (four spins per encoded qubit) by the appropriate tuning of experimental parameters. 
Ryan Woodworth (1), Ari Mizel (1), Daniel A. Lidar (2) ((1)   Pennsylvania State University, (2) University of Toronto)