Perturbation theory for quantum computation with a large number of qubits

We develop a dynamical perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by nonresonant transitions are estimated, We verify our perturbation approach using exact numerical solution for relatively small (N = 10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are reasonably small. Our results can be useful for understanding the mechanisms of errors and for experimental testing of scalable solid-state quantum computers.