Extended Data Fig. 2: Tunable CPHASE gates and automated calibration procedures.

a, Example entangling gate phase profiles for different entangling phases, with detuning included as a linear phase term. As the entangling phase becomes larger, the gate becomes longer. An entangling phase of θ = 1 is equivalent to the CZ gate profile. b, Theoretical parameters for different entangling phase gates, where the gate has a constant amplitude profile and a phase profile given by the cosine function \(A\cos (\omega t+\varphi )\)¹². We optimize these gates experimentally with parameter scans in the vicinity of theoretical values¹². c, Circuit used to benchmark and calibrate the entangling phase gates, adapted from the approach in ref. ⁷². One atom is prepared in \(| 0\rangle \) and the other in \({| +\rangle }_{y}=(| 0\rangle +i| 1\rangle )/\sqrt{2}\) with a local Raman gate. Then a series of CPHASE gates are applied to the atom pair, which effectively rotates the phase of the initial \({| +\rangle }_{y}\) state. A precalculated final Z(ϕ) gate ensures that both atoms return to \(| 0\rangle \) in the absence of errors. Errors, for example coming from a miscalibrated entangling phase or qubit loss/leakage during the gate, will reduce the probability of finding both atoms in \(| 0\rangle \) at the end of the circuit (the return probability). d, Data used to extract the entangling phase in Fig. 1d, shown for two different CPHASE gates. For different numbers of gates applied, we scan the Z(ϕ) gate before the final local π/2 pulse in order to extract the amount of phase accumulated. The trend shows how much phase has been accumulated over the 10 gates, and the reduction in the peak return probability is a result of gate errors. Note that for a smaller number of gates, we use the same Raman pulse sequence as for the 10 gate sequence and only reduce the number of CPHASE gates. e, Comparison of return probability after 20 CPHASE gates with this benchmarking method for different entangling phases, with the point θ = 1 being the CZ gate. We attribute the non-monotonic behavior to varying levels of calibration between the gates. These values can be compared to a return probability after 0 gates of 0.952(3) owing to errors from components separate from the CPHASE gates. We note that this calibration sequence is not a proper measure of fidelity, and we rather use this measurement to compare the different CPHASE gates to each other. The CZ gate was benchmarked right after taking this data with a fidelity of 99.4% in the global RB sequence utilized in ref. ¹² (the slightly lower fidelity than our typical 99.5% operation can be attributed to the increased scattering from the closer intermediate-state detuning used here). f, Example calculated Rydberg beam profile and the effect of adding two separate peak-correction holograms. The local peak corrections are added to the base holograms with variable weights on the Rydberg beam SLMs, in addition to correcting for more global Zernike aberrations. g, Example automatic calibration routine showing the homogenization of our Rydberg beam across an array. (top) The peak-to-peak variations in row intensity across the array during calibration, as measured by the differential light shift on the hyperfine qubit. (bottom) Example of how the defocus and one of the peak corrections change during this automated calibration procedure. h, Examples of the measured light shift across the rows of our atom array for the two Rydberg beams, comparing the uniformity before and after the automated calibration procedure. We also ensure that the columns are uniform, although they are naturally more homogeneous due to the beam geometry.