Extended Data Fig. 2: Single-qubit rotations.
All measurements are performed with all qubits initialized to spin-down and the exchange couplings turned off. a, Rabi oscillation measurement sequence. tp is the duration of the microwave pulse. b–d, Rabi oscillation measurement results. The microwave amplitude is adjusted so that the Rabi frequency is 4 MHz. e, Schematic sequence of the randomized benchmarking measurement. We prepare 16 randomly generated Clifford gate sequences and average the outcomes to obtain the sequence fidelities. f–h, Randomized benchmarking results. The implementation is the same as in, for example, refs. 7,24. We perform two sets of benchmarking measurements, one designed to obtain an ideal spin-up outcome and the other designed to obtain an ideal spin-down outcome, wherein both cases the measurement is projected at a spin-up state. The sequence fidelity F(m) is then defined as \(F(m)={F}_{\uparrow }(m)-{F}_{\downarrow }(m)\), in which \({F}_{\uparrow }(m)\) (\({F}_{\downarrow }(m)\)) is the measured sequence fidelity for the spin-up (spin-down) final state. Each dataset is fit by an exponential decay F(m) = Vpm to extract the depolarizing parameter p and visibility V. The primitive gate fidelity shown in each figure is obtained as \(1-(1-p)/(2\times 1.875)\), in which the factor 1.875 is the average number of primitive gates per Clifford gate. The errors are 1σ from the mean.
