Fig. 2: Schematics and implementation of the shelving and two-tone readout technique.
a A π12 and a consecutive π23 pulse are inserted between any experimental sequence U and the final readout pulse comprising two readout tones. This scheme can be implemented in any multi-level quantum processor platform without modifying the hardware design. b Qubit population can be transferred to the desired energy level with consecutive πij pulses. The population in state \(\left\vert j\right\rangle\) decays to \(\left\vert i\right\rangle\) with a rate 1/Tij. c The ground state \(\left\vert 0\right\rangle\) population p0 is plotted as a function of the delay time t after the transmon is initially prepared in \(\left\vert 0\right\rangle\), \(\left\vert 1\right\rangle\), \(\left\vert 2\right\rangle\), or \(\left\vert 3\right\rangle\). The delay time t is counted from the end of the last qubit shelving pulse in the sequence. Points represent experimental data for Qubit 2 while continuous lines show fits of the data according to the solutions of the expanded rate equations including all non-sequential rates34, which are presented in Section III of the Supplementary Note. The inset shows the population at short time scales with the dashed line marking the duration τr = 140 ns of the readout pulse.
