  We analyze the singlet-triplet splitting on a planar array of quantum dots
coupled capacitively to a set of external voltage gates. The system is modelled
using an extended Hubbard Hamiltonian keeping two excess electrons on the
array. The voltage dependence of the low-energy singlet and triplet states is
analyzed using the Feshbach formalism. The formation of a well decoupled
two-level system in the ground state is shown to rely on the fact of having two
particles in the system. Coherent operation of the array is studied with
respect to single quantum bit operations. One quantum gate is implemented via
voltage controls, while for the necessary second quantum gate, a uniform
external magnetic field is introduced. The Aharonov-Bohm phases on the closed
loop tunnel connections in the array are used to effectively suppress the
tunneling, despite a constant tunneling amplitude in the structure. This allows
one to completely stall the qubit in any arbitrary quantum superposition,
providing full control of this interesting quantum system.
