Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

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We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of n spins with pairwise coupling, the scheme concatenates cn intervals of system evolution and uses at most c n² pulses where c ≈ 1. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.