Extended Data Fig. 4: Pulse sequence for remote entanglement generation between two ¹⁷¹Yb spin qubits.

a, Energy levels of ¹⁷¹Yb ions at B = 0 with optical and spin transitions indicated. A and E optical transitions have polarization aligned with the cavity and are Purcell enhanced. The \(| {\rm{e}}\rangle \) state referred to in the main text was labelled \(| {0}_{e}\rangle \) in previous work. b, Flow chart showing steps for remote entanglement generation between Ions 1 and 2. c, \(| {\rm{aux}}\rangle \) initialization involves 400 pulses, each 2.5 μs long, applied alternately to the F₁ and F₂ transitions of the two ions, emptying \(| {\rm{aux}}\rangle \) into the qubit manifold via decay on E. d, Initialization into \(| 0\rangle \) is achieved with pairs of consecutively applied π pulses on A and f_e followed by decay on E. The optical path phase difference, ΔΦ, is measured and compensated by a Z rotation, Θ, on Ion 1’s A transition (defined in Methods). A weak superposition is prepared on each qubit, the ions are optically excited and entanglement is heralded via detection of a single photon at stochastic time t₀ in a window of duration τ_h. e, After several periods of dynamical decoupling (inter-pulse separation 2τ_s = 5.8 μs) the spin coherence is rephased for a duration of τ_h − t₀. Optical coherence is rephased for a duration t₀ between two A transition π pulses. A Z rotation is applied to Ion 2’s qubit by angle \(\Delta {\widetilde{\omega }}_{12}{t}_{0}\) where \(\Delta {\widetilde{\omega }}_{12}\) is the A transition driving frequency difference between the two ions. f, Each Ion’s state is read out via repeated excitation on the A transition followed by photodetection. We use four readout periods: the first two determine whether the ions are in \(| 1\rangle \). A qubit π pulse is applied and the final two periods measure \(| 0\rangle \). States are ascribed according to conditions in the table, all other photodetection outcomes are discarded.