Quantum brachistochrone for homonuclear multi-spin systems

The control of multiple homonuclear spin systems is a long-standing problem in nuclear magnetic resonance (NMR). In this paper, we introduce the brachistchrone algorithm to local unitary control of such systems, which usually take a long operation time to discriminate because of their small resonant frequency differences. We show that for this particular problem the model can be reduced from 2^N-dimensional to 2N-dimensional for a N-spin system. Numerical simulations demonstrates the effectiveness of the algorithm.