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Double-dot exchange-only qubit represents a promising compromise between highspeed and simple fabrication in solid-state implementations. A couple ofinteracting double-dot exchange-only qubits, each composed by three electronsdistributed in a double quantum dot, is exploited to realize controlled-NOT(CNOT) operations. The effective Hamiltonian model of the composite system isexpressed by only exchange interactions between pairs of spins. Consequently,the evolution operator has a simple form and represents the starting point forthe research of sequences of operations that realize CNOT gates. Two differentgeometrical configurations of the pair are considered, and a numerical mixedsimplex and genetic algorithm is used. We compare the nonphysical case in whichall the interactions are controllable from the external and the realisticcondition in which intra-dot interactions are fixed by the geometry of thesystem. In the latter case, we find the CNOT sequences for both the geometricalconfigurations and we considered a qubit system where electrons areelectrostatically confined in two quantum dots in a silicon nanowire. Theeffects of the geometrical sizes of the nanowire and of the gates on thefundamental parameters controlling the qubit are studied by exploiting aspin-density-functional theory-based simulator. Consequently, CNOT gateperformances are evaluated.

Effective Hamiltonian for two interacting double-dot exchange-only qubits and their controlled-NOT operations