  Two recent developments in quantum control, concatenation and optimization of
pulse intervals, are combined to yield a strategy to suppress unwanted
couplings in quantum systems to high order. Longitudinal relaxation and
transverse dephasing can be suppressed so that systems with a small splitting
between their energy levels can be kept isolated from their environment. The
required number of pulses grows exponentially with the desired order but is
only the square root of the number needed if only concatenation is used. An
approximate scheme even brings the number down to polynomial growth. The
approach is expected to be useful for quantum information and for
high-precision nuclear magnetic resonance.
