Figure 6

Experimental results (dots) for high-order time-correlation functions \({ {\mathcal M} }_{xx}^{n}\) and \({ {\mathcal M} }_{xy}^{n}\) (\(n=\mathrm{2,}\,\mathrm{3,}\,\mathrm{...,}\,10\)). \(n\) controlled quantum gates \({U}_{\alpha }^{0}\), \({U}_{\beta }^{1}\), …, \({U}_{\gamma }^{n-1}\) are sequentially applied with a time interval \({\rm{\Delta }}t=0.3\) ms. Refocusing pulses are used to decouple the interaction between the nuclei of ¹³C and ¹H, during the time intervals \(\Delta t\) between gates. For this experiment, we use the GRAPE pulsed technique to implement the quantum circuit. Using hard pulses like in the previous experiments would result in poor quality of the measured data due to the high number of pulses required and the cumulative effect of their imperfections.