Extended Data Fig. 5: iToffoli gate characterizations.
a, Schematic of the iToffoli gate implementation. The iToffoli gate can be realized by a combination of an exchange pulse and a microwave pulse. The exchange pulse duration (tdc1 + tMW + tdc2), microwave pulse duration (tMW) and timing (tdc1 − tdc2) are fine-tuned to obtain a correct phase evolution. b, Quantum circuit used to measure the phase accumulation during the iToffoli gate operation. The iToffoli gate is interleaved between two π/2 pulses to realize Ramsey-type phase detection. Only when \({{\rm{Q}}}_{1}{{\rm{Q}}}_{3}=| \downarrow \downarrow \rangle \) does a spin flip occur, which is detected as a π phase shift for a correct iToffoli gate. For the other ancilla qubit configurations, the phase accumulation should be zero. c, Example phase measurement result before the iToffoli gate phase calibration. The resonance frequency and microwave amplitude are calibrated. d, Phase measurement after the calibration of both conditional and unconditional phases. In the calibration procedure, we optimize the duration of the exchange pulse and the timing of the microwave pulse (see Methods). We obtain correct phase evolution for all ancilla qubit configurations. The phase offsets are (1.03 ± 0.01)π, (0.04 ± 0.01)π, (0.03 ± 0.01)π and (0.05 ± 0.01)π for \({{\rm{Q}}}_{1}{{\rm{Q}}}_{3}=| \downarrow \downarrow \rangle ,\;| \uparrow \downarrow \rangle ,\;| \downarrow \uparrow \rangle \;{\rm{and}}\;| \uparrow \uparrow \rangle \), respectively. The errors are 1σ from the mean. e, Experimental process matrix (χ matrix) of the iToffoli gate obtained by three-qubit quantum process tomography (see Methods). The labels represent three-qubit Pauli operators. We obtain a gate fidelity of 0.67 from the data. f, Ideal process matrix of iToffoli gate. g, Simulated process matrix of iToffoli gate under quasi-static single-qubit phase noise. Here we assume \({T}_{2}^{* }\) = 1.2, 1.2 and 1.3 μs for Q1, Q2 and Q3, respectively (ergodic \({T}_{2}^{* }\) measured for long integration time). The effect of charge-noise-induced exchange fluctuation (noise in ZZ term) is not taken into account. The simulation reproduces some features in the experimental data. The gate fidelity estimated from the simulation is 0.69, which agrees well with the experimental result.
