Phase factors of periodically driven two-level systems

Using a specially developed perturbative solution for periodically driven quantum systems, we show how to obtain phase factors for both a single qubit and for two interacting qubits. The method is easily implemented by numerical routines. Comparing to more traditional methods, it presents the advantage of being stable for long-time periods, therefore allowing the computation of phase factors with arbitrary precision. We furthermore explore the possibility of implementing a quantum phase gate using the perturbative solution. Our method allows the numerical computation of phase factors with arbitrary precision provided, of course, sufficient computational resources are at disposal. (paper)