Extended Data Fig. 1: Atomic-level diagram and pulse sequence.

a, Level diagram showing key levels of ⁸⁷Rb used in our quantum circuits. The clock states, |0⟩ and |1⟩, are the qubit states used in this work. Excitation to the Rydberg state between |1⟩ and |r⟩ is carried out by a two-photon transition driven by 420-nm and 1,013-nm lasers. Single-qubit rotations are realized with an amplitude-modulated 795-nm laser that drives Raman rotations between the m_F = 0 clock states. A DC magnetic field of 8.5 G is applied throughout this work. The Rydberg detuning signs and polarization signs are carefully selected for various optimizations: for suppressing 420-induced differential light shift between |0⟩ and |1⟩, we red-detuned the 6P_3/2 transition; for using dark-state physics (nominally the phase profile corresponds to a certain sign of two-photon detuning), we thereby choose positive two-photon detuning, which—in turn—then suppresses coupling to m_J = − 1/2 by being primarily on the upper side of m_J = +1/2; and, finally, the 1,013-nm light shift is lower (by about 30%) at this single-photon detuning sign, as there is a magic wavelength of about 1 GHz red-detuned of 6P_3/2 for the |1⟩ → 53S_1/2 transition⁹⁸. Two downsides of this detuning choice are that this choice of 420-nm polarization and detuning causes a vector light shift in the hyperfine ground-state manifold that causes the m_F levels to be pushed closer together, as opposed to further apart, which could exacerbate effects arising from 420-induced vector light shifts coupling adjacent m_F states in the ground-state manifold (although negligible here), and the other downside is that the m_J = −1/2 Rydberg pair states are closer detuned to the two-photon excitation and so we require a larger interaction strength to suppress their excitation, although the matrix element to these states is smaller. b, Example pulse sequence, here for making a \(\left|{\Phi }^{+}\right\rangle \) Bell state between two qubits. Traps are pulsed off for a few hundred ns during the Rydberg gate to avoid both antitrapping of the Rydberg state and inhomogeneous light shifts that broaden the transition, and the ground-state atoms are then recaptured for roughly 3 μs between consecutive gate applications.