Minimum-Time Selective Control of Homonuclear Spins

In nuclear magnetic resonance (NMR) quantum computation, the selective control of multiple homonuclear spins is usually slow because their resonance frequencies are very close to each other. To quickly implement the controls against decoherence effects, this brief presents an efficient numerical algorithm for designing minimum-time local transformations in two homonuclear spins. We obtain an accurate minimum-time estimation via geometric analysis on the two-timescale decomposition of the dynamics. Such estimation narrows down the range of search for the minimum-time control with a gradient-type optimization algorithm. Numerical simulations show that this method can remarkably reduce the search efforts, especially when the frequency difference is very small and the control field is high. Its effectiveness is further demonstrated by NMR experiments with two homunuclear carbon spins in a trichloroethylene (C₂H₁Cl₃) sample system.