Aharonov-Bohm phase as quantum gate in two-electron charge qubits

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.