  We present a scalable scheme to design optimized soft pulses and pulse
sequences for coherent control of interacting quantum many-body systems. The
scheme is based on the cluster expansion and the time dependent perturbation
theory implemented numerically. This approach offers a dramatic advantage in
numerical efficiency, and it is also more convenient than the commonly used
Magnus expansion, especially when dealing with higher order terms. We
illustrate the scheme by designing 2nd-order pi-pulses and a 6th-order 8-pulse
refocusing sequence for a chain of qubits with nearest-neighbor couplings. We
also discuss the performance of soft-pulse refocusing sequences in suppressing
decoherence due to low-frequency environment.
