= Average Hamiltonian engineering
{title2=$\overline H^{(0)}=T_c^{-1}\sum_j\tau_j P_j^\dagger H_0P_j$}
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.
Back to article page
