Abstract 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 resonator22containing two individually addressable atoms23,24. Ring25and tree26graph 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.
Abstract 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 resonator22containing two individually addressable atoms23,24. Ring25and tree26graph 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.
Entanglement in multiphoton graph states is an important resource with various applications, such as measurement-based quantum computing and memory-less quantum repeaters. While some primitive instances have been successfully prepared, scalable generation of large-scale graph states with programmable connections remains an outstanding challenge. Fusion provides a promising "divide-and-conquer" approach by linking smaller resource states into larger, more complex graphs. However, its practical scalability has been limited by the probabilistic nature of conventional fusion protocols, which necessitates extensive hardware overhead and feed-forward resources to achieve deterministic outcomes. Here, we introduce and experimentally demonstrate a deterministic fusion operation with built-in error mitigation, capable of connecting small time-bin-encoded cluster states--originally generated on-demand from a quantum emitter--into larger, reconfigurable photonic graph states of increased sizes. The fusion operation is realized by nondestructively projecting pairs of flying microwave photonic qubits into Bell states using superconducting circuits with in-situ programmability. Crucially, the protocol features active reset and reuse of matter qubits during graph state generation, thereby circumventing the coherence constraints of the quantum emitter and enabling the generation of genuine multipartite entanglement across 13 photonic qubits. Our results establish a scalable framework for photonic graph-state synthesis, paving the way for fault-tolerant measurement-based quantum computation and distributed quantum networks.
Measurement-based quantum computing relies on the generation of large entangled cluster states that act as a universal resource on which logical circuits can be imprinted and executed through local measurements. A number of strategies for constructing sufficiently large photonic cluster states propose fusing many smaller resource states generated by a series of quantum emitters. However, the fusion process is inherently probabilistic with a 50% success probability in standard guise. A recent proposal has shown that, in the limit of low loss, the probability of achieving successful fusion may be boosted to near unity by redundantly encoding the vertices of linear graph states using Greenberger-Horne-Zeilinger states [Quantum 7, 992 (2023)]. Here we present a protocol for deterministically generating redundantly encoded photonic resource states using single quantum emitters, and study the impact of protocol errors and photonic losses on the generated resource states and type-II photonic fusion. Our work provides a route for efficiently constructing complex entangled photonic qubit states for photonic quantum computing and quantum repeaters.
Abstract The central technological appeal of quantum science resides in exploiting quantum effects, such as entanglement, for a variety of applications, including computing, communication and sensing 1 . The overarching challenge in these fields is to address, control and protect systems of many qubits against decoherence 2 . 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 entanglement 3 is inherently probabilistic and, therefore, subject to severe scalability limitations. Here we report the implementation of a deterministic protocol 4–6 for the creation of photonic entanglement with a single memory atom in a cavity 7 . We interleave controlled single-photon emissions with tailored atomic qubit rotations to efficiently grow Greenberger–Horne–Zeilinger (GHZ) states 8 of up to 14 photons and linear cluster states 9 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 experiment 3,10–13 . In the future, this rate could be increased even further, the scheme could be extended to two atoms in a cavity 14,15 or several sources could be quantum mechanically coupled 16 , to generate higher-dimensional cluster states 17 . Overcoming the limitations encountered by probabilistic schemes for photonic entanglement generation, our results may offer a way towards scalable measurement-based quantum computation 18,19 and communication 20,21 .
Graph states are versatile resources for various quantum information processing tasks, including measurement-based quantum computing and quantum repeaters. Although the type-II fusion gate enables all-optical generation of graph states by combining small graph states, its non-deterministic nature hinders the efficient generation of large graph states. In this work, we present a graph-theoretical strategy to effectively optimize fusion-based generation of any given graph state, along with a Python package OptGraphState. Our strategy comprises three stages: simplifying the target graph state, building a fusion network, and determining the order of fusions. Utilizing this proposed method, we evaluate the resource overheads of random graphs and various well-known graphs. Additionally, we investigate the success probability of graph state generation given a restricted number of available resource states. We expect that our strategy and software will assist researchers in developing and assessing experimentally viable schemes that use photonic graph states.
Fusion measurements are a key primitive for linear-optical quantum computing and quantum networks. Type-I and type-II fusion gates are widely used to combine small entangled resource states into larger photonic states, but without ancillary resources their success probability is limited to 1/2. Existing 3/4-efficient type-I schemes rely on entangled Bell-pair ancillary states, whose preparation is itself probabilistic and resource-intensive. Here we propose a boosted type-I fusion gate using only four ancillary single photons and standard linear-optical primitives. For multiqubit GHZ and graph states, the gate succeeds directly with probability 5/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to 11/16 after one stage and asymptotically to 3/4. We quantify the practical advantage of this scheme by estimating the photonic resources required for generating representative large entangled photonic states and show that the proposed gate significantly reduces the required overhead compared with existing schemes. These results expand the set of resource-efficient linear-optical primitives and enable a substantial reduction in the resource requirements for scalable photonic quantum computing and quantum communication.
Since linear-optical two-photon gates are inherently probabilistic, measurement-based implementations are particularly well suited for photonic platforms: a large highly-entangled photonic resource state, called a graph state, is consumed through measurements to perform a computation. The challenge is thus to produce these graph states. Several generation procedures, which use either interacting quantum emitters or efficient spin-photon interface, have been proposed to create these photonic graph states deterministically. Yet, these solutions are still out of reach experimentally since the state-of-the-art is the generation of a linear graph state. Here, we introduce near-deterministic solutions for the generation of graph states using the current quantum emitter capabilities. We propose hybridizing quantum-emitter-based graph state generation with all-photonic fusion gates to produce graph states of complex topology near-deterministically. Our results should pave the way towards the practical implementation of resource-efficient quantum information processing, including measurement-based quantum communication and quantum computing.