  A powerful control method in experimental quantum computing is the use of
spin echoes, employed to select a desired term in the system's internal
Hamiltonian, while refocusing others. Here we address a more general problem,
describing a method to not only turn on and off particular interactions but
also to rescale their strengths so that we can generate any desired effective
internal Hamiltonian. We propose an algorithm based on linear programming for
achieving time-optimal rescaling solutions in fully coupled systems of tens of
qubits, which can be modified to obtain near time-optimal solutions for
rescaling systems with hundreds of qubits.
