Fusion of deterministically generated photonic graph states.

Entanglement has evolved from an enigmatic concept of quantum physics to a key ingredient of quantum technology. It explains correlations between measurement outcomes that contradict classical physics and has been widely explored with small sets of individual qubits. Multi-partite entangled states build up in gate-based quantum-computing protocols and-from a broader perspective-were proposed as the main resource for measurement-based quantum-information processing1,2. The latter requires the ex-ante generation of a multi-qubit entangled state described by a graph3-6. Small graph states such as Bell or linear cluster states have been produced with photons7-16, but the proposed quantum-computing and quantum-networking applications require fusion of such states into larger and more powerful states in a programmable fashion17-21. Here we achieve this goal by using an optical resonator22 containing two individually addressable atoms23,24. Ring25 and tree26 graph states with up to eight qubits, with the names reflecting the entanglement topology, are efficiently fused from the photonic states emitted by the individual atoms. The fusion process itself uses a cavity-assisted gate between the two atoms. Our technique is, in principle, scalable to even larger numbers of qubits and is the decisive step towards, for instance, a memory-less quantum repeater in a future quantum internet27-29.

Efficient generation of entangled multiphoton graph states from a single atom.

The central technological appeal of quantum science resides in exploiting quantum effects, such as entanglement, for a variety of applications, including computing, communication and sensing1. The overarching challenge in these fields is to address, control and protect systems of many qubits against decoherence2. Against this backdrop, optical photons, naturally robust and easy to manipulate, represent ideal qubit carriers. However, the most successful technique so far for creating photonic entanglement3 is inherently probabilistic and, therefore, subject to severe scalability limitations. Here we report the implementation of a deterministic protocol4-6 for the creation of photonic entanglement with a single memory atom in a cavity7. We interleave controlled single-photon emissions with tailored atomic qubit rotations to efficiently grow Greenberger-Horne-Zeilinger (GHZ) states8 of up to 14 photons and linear cluster states9 of up to 12 photons with a fidelity lower bounded by 76(6)% and 56(4)%, respectively. Thanks to a source-to-detection efficiency of 43.18(7)% per photon, we measure these large states about once every minute, which is orders of magnitude faster than in any previous experiment3,10-13. In the future, this rate could be increased even further, the scheme could be extended to two atoms in a cavity14,15 or several sources could be quantum mechanically coupled16, to generate higher-dimensional cluster states17. Overcoming the limitations encountered by probabilistic schemes for photonic entanglement generation, our results may offer a way towards scalable measurement-based quantum computation18,19 and communication20,21.