Extended Data Fig. 2: Single-qubit Raman addressing.

a, 5S_1/2 hyperfine level diagram illustrating the two possible implementations of local single-qubit gates: resonant X(θ) (purple) and off-resonant Z(θ) (turquoise) rotations with two-photon Rabi frequencies Ω_Raman. In this work, we use the Z rotation scheme and are blue-detuned by 2 MHz from the two-photon resonance. Owing to Clebsch–Gordan coefficients, \({\widetilde{\Omega }}_{{\rm{Raman}}}^{Z}=-\sqrt{3}{\Omega }_{{\rm{Raman}}}^{Z}\). b, Schematic showing the conversion of local Z(π/2) into local X(±π/2) gates, in which the pulses before (after) the central Y(π) have positive (negative) sign, while leaving non-addressed qubit states unchanged. The Gaussian-smoothed local pulses have duration 2.5 μs for π/4 pulses and 5 μs for π/2 pulses and are performed on single rows at a time with a 3-μs gap between subsequent gates to allow the RF tones in the AODs to be changed (including this, duration is 5–8 μs per row). In this way, arbitrary patterns of qubits, such as the example drawn, can be addressed. c, Calibration procedure used to homogenize the Rabi frequency over a 220 μm × 35 μm array. The position calibration is illustrated for 80 sites: approximate X(π/2) gates are locally performed and the horizontal/vertical position of all tones is scanned in parallel such that a Gaussian fit returns the optimal alignment. After this, powers are iteratively calibrated until the fitted scale factors for the individual RF tones converge to unity. d, Single-qubit randomized benchmarking of local Z(π/2) gates. The local gates are interleaved with random global single-qubit Clifford gates and the final operation C_f is chosen to return to the initial state. Each data point is the average of 100 random sets of Clifford gates and fitting an exponential decay to the return probability quantifies the fidelity \({\mathcal{F}}\) per local gate. Note that we apply all 51 global Clifford gates for each data point, such that errors from the global Clifford gates (as well as SPAM errors) do not contribute to the fitted value.