Extended Data Fig. 7: Comparison to digital quantum devices executing random circuits.

a, Numerical simulations of a one-dimensional digital quantum device implementing a random unitary circuit (RUC). Two different digital gate implementations are tested: a configuration based on the gate-set used in ref. ⁵ (bottom), and a configuration where each cycle is composed of parallel two-qubit SU(4) gates (top)⁴. Cross markers indicate when the half-chain entanglement entropy saturates. b, Due to the Rydberg blockade mechanism, as well as symmetries of the Rydberg Hamiltonian (Supplementary Information), an equal number of atoms in the Rydberg simulator, N, and qubits in the RUC, N_RUC, will not saturate to the same half-chain entanglement entropy. However, we can still find an equivalence by plotting the saturated entanglement entropy for the RUC (blue crosses for the SU(4) gate-set, open red squares for gate-set from ref. ⁵) and for the Rydberg simulator (grey markers) as a function of their respective system sizes. We fit the results for the Rydberg simulator (black line), and plot the analytic prediction for the RUC⁵⁴ (purple line), from which we can write an equivalent N_RUC as a function of N, in the sense of maximum achievable entanglement entropy (Methods). c, For a given N (and equivalent N_RUC), we plot the SPAM-corrected, two-qubit cycle fidelity for an equivalently-sized RUC to match the evolution fidelity of our Rydberg simulator at the time/depth when entanglement saturates. Red lines, markers and crosses are for the gate-set of ref. ⁵, while blue are for the SU(4) gate-set. Shaded regions come from the error on fitting the various N-dependent parameters which enter this calculation (Methods).