Concatenated cranking representation of the Schrödinger equation and resolution to pulsed quantum operations with spin exchange

We propose a concatenated cranking approach to resolve the dynamics for a class of time-dependent quantum systems with specific algebraic structure. By invoking a series of canonical transformations successively, concatenated representation of the Schroedinger equation is established and evolution of the system is solved in the cranking representation via discarding high-order nonadiabatic terms. The introduced method is then applied to investigate nonadiabatic dynamics and imperfection effects in pulsed gate operations of quantum dot systems regarding the existence of spin-orbit effects. The fidelity loss of the SWAP gate owing to anisotropic exchange and the fidelity retrieval of the Loss-DiVincenzo pulse sequence under nonadiabatic evolution are elaborated by virtue of the proposed method.