A 775-nm, 1.6 ps–pulsed Ti:sapphire laser was focused into a 22-mm periodically poled potassium titanyl phosphate (ppKTP) crystal in a Sagnac-type interferometer (16, 27), where it generated pairs of 1550-nm single photons through collinear type-II parametric down-conversion. The 80-MHz repetition rate of the pump laser was quadrupled through temporal multiplexing (28) to suppress higher-order emissions (see fig. S1). We thereby achieved a signal-to-noise ratio (i.e., photon pairs versus higher-order contributions) of 140 ± 10 in each photon source, generating ∼8000 photon pairs mW−1 s−1 with a typical heralding efficiency η=(cc/s1s2) of ∼50%, where cc is the number of coincidence counts, and s1 and s2 are the numbers of singles in the first and second output, respectively. Single photons passed through 3-nm band-pass filters to guarantee high spectral purity and were detected with superconducting nanowire single-photon detectors (SNSPDs) with a detection efficiency of ∼80%. Detector clicks were time-tagged using a field-programmable gate array and processed to detect coincidences within a temporal window of 1 ns.

To benchmark the three required two-qubit states, we performed maximum-likelihood quantum state tomography directly at each source. From the reconstructed density matrices, we computed the fidelity, concurrence, and purity quoted in the main text. Further transmission of the photon pairs to the fusion gates slightly degrades the fidelities of the three entangled pairs to F0=98.790.03+0.03%, FA=98.700.03+0.03%, and FB=98.590.03+0.03% for sources S0, SA, and SB, respectively (see Fig. 2). This indicates that the optical circuit preserves the excellent quality of the initial states.

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