Self-consistent non-Markovian theory of a quantum state evolution for quantum information processing

It is shown that the operator sum representation for non-Markovian dynamics and the Lindblad master equation in Markovian limit can be derived from a formal solution to quantum Liouville equation for a qubit system in the presence of decoherence processes self-consistently. Our formulation is the first principle theory based on projection-operator formalism to obtain an exact reduced density operator in time-convolutionless form starting from the quantum Liouville equation for a noisy quantum computer. The advantage of our approach is that it is general enough to describe a realistic quantum computer in the presence of decoherence provided details of the Hamiltonians are known.