Fig. 3

Experimentally created 12-coherence using MQFC. a Direct observation of the created 12-coherence in one-dimensional NMR spectrum (red), where C₇ is the probe qubit. Simulated spectrum (blue) is also plotted. The experimental result is rescaled by 1.21 times to compensate for the decoherence effect for better visualization. b Spectra of 12-coherence after each odd iteration during the MQFC optimization. Unlike the direct observation, a readout technique is applied to gain a higher resolution. A color scale indicates peak intensities. The height of the peaks is proportional to the value of created 12-coherence. c Comparison between GRAPE (blue) and MQFC (red) optimizations, both in simulation (solid; without decoherence accounted) and experiment (dashed). F _dec is the numerical simulation of decoherence during the 12-coherence creation. Compared to the GRAPE algorithm, MQFC optimization is worse in simulation, but better in experiment. The error bars are plotted by the infidelity of the readout pulse. d Results at iteration 9. The experimental 12-coherence reaches 0.795 using MQFC which approaches the F _dec = 0.824 bound, while GRAPE only leads to 0.703 (i.e., 0.121 lower than F _dec) in experiment