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We develop in the weak coupling approximation a quasi-non-Markovian masterequation and study the phenomenon of decoherence during the operation of acontrolled-not (CNOT) quantum gate in a quantum computer model formed by alinear chain of three nuclear spins system with second neighbor Isinginteraction between them. We compare with the behavior of the Markoviancounterpart for temperature different from zero (thermalization) and at zerotemperature for low and high dissipation rates. At low dissipation there is avery small difference between Markovian and quasi no-Markovian at anytemperature which is unlikely to be measured, and at high dissipation there isa difference which is likely to be measured at any temperature.

Quasi non-Markovian approach to the study of decoherence of a controlled-not quantum gate in a chain of few nuclear spins quantum computer