Efficient implementation of coupled logic gates for quantum computation - art. no. 042310

Most natural Hamiltonians do not couple specific pairs of quantum bits and spurious couplings occur along with the intended one. We present an efficie nt scheme that couples any designated pair of spins in heteronuclear spin s ystems. The scheme is based on the existence of Hadamard matrices. For a sy stem of n spins with pairwise coupling, the scheme concatenates cn interval s of system evolution and uses at most cn(2) pulses where c approximate to 1. Our results demonstrate that, in many systems, selective recoupling is p ossible with linear overhead, contrary to common speculation that exponenti al effort is always required.