 Average Hamiltonian engineering

Fast prescribed pulses change the frame in which the system evolves during successive intervals. To leading order over a short control cycle, the effective Quantum Hamiltonian is the duration-weighted mean of these conjugated generators. The Baker--Campbell--Hausdorff formula supplies commutator corrections. Symmetrizing the cycle can cancel unwanted interactions or retain a desired one. The approximation requires control cycles short compared with the relevant dynamical timescales and a suitable account of finite pulse duration.