Extended Data Fig. 2: Generation of remote entanglement and robust memory of the circuit qubits.

a, Entanglement is generated between the network qubits using 200 μs of entanglement attempts interleaved with 2.254 ms of sympathetic recooling using the Sr⁺ ion. This is repeated until the entanglement is successfully heralded by a particular detector click pattern. While attempting to generate entanglement between the network qubits, Knill dynamical decoupling pulses, K_i, are used to preserve the state of the circuit qubits. b, Each entanglement attempt has a total duration of 1168 ns. We perform a 320-ns state-preparation pulse (which has a switching latency of 500 ns), pumping the Sr⁺ ion into the lower ground Zeeman state. An approximately 5-ps pulse excites the Sr⁺ ion to the upper P_1/2 level (lifetime about 7 ns), which rapidly decays to one of the ground Zeeman levels, thereby generating ion–photon entanglement. We collect a photon from each of the modules, interfere them on a beam splitter and perform a projective measurement on the two-photon polarization state. Particular detector click patterns occurring within the detection window herald the successful generation of remote entanglement. We then exit the attempt loop and map the entanglement into the optical network qubits, \({{\mathcal{Q}}}_{{\rm{N}}}\), with an extra π-pulse on the 674-nm transition. c, Difference between the reconstructed process matrices, χ_mem, for the process of storing the state of the circuit qubit in (1) Alice and (2) Bob while generating entanglement on the network qubits and the ideal process matrix, χ_ideal = diag(1, 0, 0, 0). The reconstructed process matrices have fidelities 98.1(4)% and 98.2(5)% for Alice and Bob, respectively. d, Reconstructed density matrix of the remotely entangled network qubits. The state has a fidelity of 96.89(8)% to the |Ψ⁺⟩ Bell state.