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arXiv:2412.18882 · Physical Review A

Boosted fusion gates above the percolation threshold for scalable graph-state generation

Yong-Peng Guo, Geng-Yan Zou, Xing Ding, Qi-Hang Zhang, Mo-Chi Xu, Runze Liu, Jun-Yi Zhao, Zhen-Xuan Ge, Li-Chao Peng, Ke-Mi Xu, Yi-Yang Lou, Zhen Ning, Lin‐Jun Wang, Hui Wang, Yong-Heng Huo, Yu-Ming He, Chao‐Yang Lu, Jian-Wei Pan

Published Feb 11, 2026• 5 citations
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Abstract

Fusing small resource states into a larger, fully connected graph-state is essential for scalable photonic quantum computing. Theoretical analysis reveals that this can only be achieved when the success probability of the fusion gate surpasses a specific percolation threshold of 58.98% by using three-photon GHZ states as resource states. However, such an implementation of a fusion gate has never been experimentally realized before. Here, we successfully demonstrate a boosted fusion gate with a theoretical success probability of 75%, using deterministically generated auxiliary states. The success probability is experimentally measured to be 71.0(7)%. We further demonstrate the effectiveness of the boosted fusion gate by fusing two Bell states with a fidelity of 67(2)%. Our work paves a crucial path toward scalable linear optical quantum computing.

DOI
10.1103/xt7c-qv52

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Fusing small resource states into a larger, fully connected graph-state is essential for scalable photonic quantum computing. Theoretical analysis reveals that this can only be achieved when the success probability of the fusion gate surpasses a specific percolation threshold of 58.98% by using three-photon GHZ states as resource states. However, such an implementation of a fusion gate has never been experimentally realized before. Here, we successfully demonstrate a boosted fusion gate with a theoretical success probability of 75%, using deterministically generated auxiliary states. The success probability is experimentally measured to be 71.0(7)%. We further demonstrate the effectiveness of the boosted fusion gate by fusing two Bell states with a fidelity of 67(2)%. Our work paves a crucial path toward scalable linear optical quantum computing.
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 1/21/21/2. Existing 3/43/43/4-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 5/85/85/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to 11/1611/1611/16 after one stage and asymptotically to 3/43/43/4. 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.
Fusion gates enable the creation of large entangled photonic states for linear-optical quantum computing and communication protocols. However, their success probability is limited to 1/21/21/2 without additional photonic resources. Previous schemes for boosting type-I fusion have used four ancillary single photons or a two-qubit Bell state, whose preparation is probabilistic and resource intensive. Here we propose a boosted type-I fusion gate using only two independent ancillary single photons and no entangled ancillary input. It achieves a direct success probability of 5/85/85/8, matching that of the previous four-single-photon proposal while using half as many ancillary photons. The circuit is predominantly passive, with a single active element that applies a phase shift or swaps two modes according to intermediate photodetection outcomes. Unlike the previous schemes, successful outputs occupy fixed modes and require no further conditional output routing. In particular, we show that the gate is more robust to heralded ancillary-photon loss than previously proposed boosted gates and reduces the average number of single photons required to generate a six-qubit ring graph state by more than 4.6%4.6\%4.6% compared with other type-I schemes. It therefore offers a resource-efficient primitive for scalable fusion-based photonic quantum information processing.
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.
In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from 50%50\%50% to 1−1/d1-1/d1−1/d for qudits of dimension ddd without relying on existing approaches using ancilla photons and quantum codes. In particular, we show that a 2D cluster state of qubits can be generated from 5-qudit 1D cluster states using pairwise fusion gates while preserving their boosted success probability. We numerically demonstrate that this approach can improve the loss tolerance of a percolation-based scheme while keeping the photon number per resource state constant.
Probabilistic entangling measurements are key operations in linear-optical quantum technologies, enabling the generation and manipulation of high-dimensional quantum states. While prior research has focused predominantly on specific entangled states, notably graph states and Greenberger-Horne-Zeilinger (GHZ) states, broader classes of states with variable entanglement remain underexplored. In this work, we present a linear-optical approach for generating and fusing GHZ-like states, which generalize standard GHZ states to include variable entanglement degrees. We introduce two schemes based on modified fusion gates that allow flexible control over generation efficiency and the entanglement of the output states. These results offer a promising pathway toward resource-efficient entangled-state generation for scalable quantum computing and 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.