Extended Data Fig. 4. Controlled-Z gate via Rydberg interactions and associated error budget.

a, Rydberg pulse shape that realizes a CZ gate between two optical qubits. We adopt the time-optimal pulse^17,18,46 with a Rydberg Rabi frequency of 5.4 MHz. We optimize the parameters of the phase modulation function and the Rydberg detuning by varying each one in search of the maximal return probability as part of the randomized circuit used to benchmark the fidelity (Fig. 2a). b, Pair-resolved fidelity, inferred from the sequence in Fig. 2a. The blue shaded area represents the array-averaged fidelity 0.9962(3). c, Our error model predicts the infidelity to be 0.00387(5), consistent with the experimental result of 0.0038(3) (blue dashed line and shaded area).