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 processing^1,2. The latter requires the ex-ante generation of a multi-qubit entangled state described by a graph^3,4,5,6. Small graph states such as Bell or linear cluster states have been produced with photons^{7,8,9,10,11,12,13,14,15,16}, but the proposed quantum-computing and quantum-networking applications require fusion of such states into larger and more powerful states in a programmable fashion^{17,18,19,20,21}. Here we achieve this goal by using an optical resonator²² containing two individually addressable atoms^23,24. 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 internet^27,28,29.

纠缠已经从量子物理学的一个神秘概念发展成为量子技术的关键要素。它解释了与经典物理学相矛盾的测量结果之间的相关性，并已通过小组单独量子位进行了广泛探索。基于门的量子计算协议中建立的多部分纠缠态，从更广泛的角度来看，被提议作为基于测量的量子信息处理的主要资源^1,2。后者需要事前生成图^3,4,5,6描述的多量子位纠缠态。小图态（例如贝尔态或线性簇态）已经用光子^{7,8,9,10,11,12,13,14,15,16}产生，但提出的量子计算和量子网络应用需要融合这些以可编程方式将状态转换为更大、更强大的状态^{17,18,19,20,21}。这里，我们通过使用包含两个单独可寻址原子^23，24的光学谐振器²²来实现该目标。环²⁵和树²⁶图形状态具有多达 8 个量子位，其名称反映了纠缠拓扑，可以从各个原子发射的光子态有效地融合。聚变过程本身在两个原子之间使用空腔辅助门。原则上，我们的技术可以扩展到更多数量的量子位，并且是迈向未来量子互联网中无记忆量子中继器等的决定性一步^27,28,29。