The significance of the result lies in how it sidesteps the central limitation of conventional photonic graph-state synthesis. In linear optical systems, the standard tool for combining smaller resource states into bigger ones is the fusion operation, a divide-and-conquer strategy first formalized by Browne and Rudolph in 2005. Fusion works by interfering photons and measuring the outcomes, which links the constituent states into a larger graph. The catch is probability: with ordinary beam splitters and detectors, fusion succeeds only some of the time. Failed attempts destroy the participating photons, forcing experimenters to build elaborate multiplexing schemes, extensive feed-forward electronics, and massive hardware overheads simply to make the overall process behave deterministically. Resource-cost analyses, such as the 2015 study by Li and colleagues, have quantified how punishing these overheads become for fault-tolerant linear optical quantum computing.

The Tsinghua group, led by Hongyi Zhang and Luming Duan of the Center for Quantum Information at the Institute for Interdisciplinary Information Sciences, took a different route. Rather than relying on passive linear optics, they implemented the fusion operation on a superconducting circuit device, where microwave photons interact with engineered quantum circuits in a controllable, coherent way. Their scheme non-destructively projects pairs of flying microwave photons into Bell states, the maximally entangled two-qubit states that serve as the connective tissue of graph-state fusion. Because the projection is deterministic and the photons survive the operation, every fusion attempt contributes to the final state, eliminating the exponential losses that plague probabilistic protocols.

The photons themselves are encoded in time bins, a format in which the logical states of a qubit are represented by a photon arriving in one of two well-defined temporal modes. Time-bin encoding is attractive for propagating qubits because it is robust against many channel imperfections and fits naturally with sequential generation schemes. The team generated small time-bin-encoded cluster states on demand, meaning that each elementary building block could be produced precisely when the protocol required it. On-demand availability is crucial for a scalable architecture: if the photonic qubits must wait in flight while the apparatus catches up, decoherence erodes the fragile quantum correlations before the graph can be completed.

Managing decoherence is, in fact, a central theme of the experiment. Superconducting qubits, the stationary quantum circuits that mediate the photon-photon interactions, have finite coherence times, and a long graph-state synthesis sequence would normally exhaust them. The researchers therefore built active reset and reuse of the superconducting qubits into the protocol. After each qubit has performed its role in generating or fusing photonic qubits, it is rapidly reset to a known state and pressed back into service. This recycling circumvents the effects of decoherence that would otherwise accumulate over the many rounds of photon emission and fusion needed to build a large graph, and it echoes the complete methods sets developed in other platforms, such as the scalable ion trap techniques demonstrated by Home and colleagues in 2009.

Programmability is the second pillar of the demonstration. Because the fusion operation can be applied selectively to chosen pairs of photonic qubits, the same hardware can produce different graph topologies under software control. The team showed this by fusing two linear cluster states of three qubits each, joining qubit 2 and qubit 4 to create a new vertex and thereby producing a five-vertex caterpillar graph state, a structure whose entanglement pattern resembles a chain with additional rungs. Verifying such states is itself a formidable task: full quantum state tomography of a five-qubit density matrix would be prohibitively costly because of the sheer dimension of the Hilbert space, so the experimenters instead measured a subset of stabilizer operators, the commuting observables that uniquely characterize stabilizer states such as graph states. One stabilizer, involving Z and X operators across all five qubits, was deliberately omitted from the measurement set for exactly this reason.

To certify that the generated states were genuinely multipartite entangled, meaning that the entanglement cannot be reduced to any mixture of states over smaller partitions, the team computed fidelities with respect to the ideal target states and compared them against the standard threshold of 0.5. The measurements, performed with datasets of five times ten to the seventh power shots and analyzed with bootstrap standard errors derived by parametric resampling, confirmed genuine multipartite entanglement. Pushing further through repetitive fusion, the researchers scaled the approach to 13 photonic qubits, establishing what they describe as a scalable framework for photonic graph-state synthesis. The stabilizer formalism used for entanglement detection draws on well-established tools, including the entanglement-witness techniques of Toth and Guhne.

The microwave domain in which this demonstration takes place deserves particular attention. Circuit quantum electrodynamics has matured into a platform where itinerant microwave photons can be generated, routed, and measured with high fidelity, and where quantum non-demolition detection of individual propagating photons became possible in 2018 through the work of Kono and colleagues and Besse and colleagues. Deterministic quantum state transfer and remote entanglement using microwave photons were demonstrated by Kurpiers and colleagues in 2018, and universal gate sets for itinerant microwave photons followed in 2022. The Tsinghua result extends this trajectory from point-to-point operations to the synthesis of extended entangled photonic structures, a capability that connects naturally to proposals for microwave quantum networks and to hybrid architectures in which superconducting processors interface with flying qubits.

At the same time, the achievement sits within a broader international effort to make photonic graph states deterministic. Single quantum emitters, including quantum dots, trapped atoms in optical cavities, Rydberg superatoms, and solid-state emitters, have all been used to generate cluster states sequentially, with notable demonstrations by Cogan and colleagues, Thomas and colleagues, and Yang and colleagues between 2022 and 2025. Thomas, Ruscio, Morin, and Rempe showed in 2024 that deterministically generated photonic graph states from a single atom can themselves be fused, and temporal fusion of emitter-produced resource states was reported in 2025. The Tsinghua experiment adds a distinct architectural idea to this landscape: instead of growing one large state from a single emitter, it fuses independently generated small states through a deterministic Bell-state projection, combining the strengths of on-demand sources with the modularity of fusion-based quantum computation, a model formalized by Bartolucci and colleagues in 2023.

The implications reach toward several long-sought applications. Measurement-based quantum computing, proposed by Raussendorf and Briegel in 2001 as the one-way quantum computer, consumes a large entangled graph state as its computational substrate, and fusion-based schemes with high fault-tolerance thresholds have been proposed for one-dimensional cluster states. All-photonic quantum repeaters, introduced by Azuma, Tamaki, and Lo in 2013, replace matter-based quantum memories with graph states, removing the memory bottlenecks of conventional repeater chains. Graph states also serve as resources for quantum metrology, as Shettell and Markham showed in 2020. A deterministic, programmable fusion engine that can be reconfigured at will brings each of these visions closer to practical realization, particularly if the underlying photonic qubits can eventually be converted to the optical telecom band for long-distance distribution. The work was supported by China’s Quantum Science and Technology major project, the National Natural Science Foundation of China, Tsinghua University, and the Ministry of Education, and the underlying data have been made openly available, offering the community a concrete foundation on which to build the next generation of entangled photonic resources.

Subject of Research: Deterministic fusion of microwave photons on superconducting circuits for scalable photonic graph-state generation

Article Title: Deterministic and programmable fusion for the scalable generation of photonic graph states

Article References: Li, Y., Yang, Y., Bao, Z., Yang, J., Sun, L., Song, Y., Wu, Y., Zhang, H., & Duan, L. (2026). Deterministic and programmable fusion for the scalable generation of photonic graph states. Nature Physics. https://doi.org/10.1038/s41567-026-03471-5

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03471-5

Keywords: photonic graph states, quantum entanglement, superconducting qubits, microwave photons, fusion operation, cluster states, measurement-based quantum computing, quantum repeaters, time-bin encoding, circuit quantum electrodynamics, stabilizer measurements, genuine multipartite entanglement

Photonic graph states are a class of multipartite entangled quantum states whose applications span quantum computing, secure communication, and precision sensing. Despite their recognized utility, producing large-scale graph states of photons has been severely impeded by intrinsic photon losses characteristic of optical platforms. The probabilistic nature of photon emission and subsequent transmission losses result in incomplete or corrupted entanglement structures, a barrier that conventional deterministic methods have struggled to overcome.

The fundamental issue stems from the fact that photon detection, which confirms entanglement, is intrinsically destructive. Attempting to fill missing photon “slots” after partial detection collides with the no-cloning principle and quantum measurement postulates, which forbid the non-invasive inspection or replacement of quantum particles without disturbing their delicate quantum states. Overcoming this destructive nature requires a radical rethink of how entangled photonic states are constructed in practice.

Led by Associate Professor Elizabeth Goldschmidt and Professor Eric Chitambar, the Illinois team embraced this paradigm shift. Instead of striving for a perfect, pre-generated entangled state, they proposed embracing the limitations of real-world hardware and harnessing the destructive measurement process itself to their advantage. This mindset heralded the development of the “emit-then-add” technique, wherein photons are added sequentially to a virtual graph state only after their successful heralded detection, ensuring that the graph is constructed from verified, existing photons.

Central to their scheme is the concept of “virtual graph states.” Unlike physical photonic states existing simultaneously in a shared quantum system, virtual graph states exist temporally and are mediated via the long coherence times of spin qubits in quantum emitters. Each photon is emitted, detected, and verified before the next photon is incorporated into the entangled state, dramatically mitigating photon loss impacts. This approach shifts the primary bottleneck from photon loss probabilities—which can be alarmingly high—to the coherence properties of the quantum emitters’ spin qubits, which often maintain coherence over extended durations.

This heralded add-on strategy represents a departure from conventional approaches that require non-destructive, quantum non-demolition measurements—currently beyond state-of-the-art capabilities for photon detection. By embracing destructive measurements and coupling them to virtual graph state construction, the Illinois group charts a more immediately accessible route to functional photonic graph states. Their framework is not only theoretically elegant but promise practical feasibility with existing quantum hardware such as trapped ions and neutral atom emitters, which have historically been handicapped by suboptimal photon collection efficiencies.

Graduate students Max Gold and Jianlong Lin, co-lead authors on the study, provide further insight into the counterintuitive nature of this process. Because the photons do not coexist simultaneously, the emergent multi-photon entanglement is not embodied in a conventional time-synchronized state. Instead, the spin qubit’s coherence “stitches” these photons together in a virtual, non-classical state transcending the traditional temporal constraints on quantum correlation. This fundamentally shifts perspectives on how entanglement can be distributed and measured in quantum networks and computational devices.

The researchers have illustrated a compelling potential application of their protocol in secure two-party computation. By repeatedly generating small graph states that are verified before usage, parties can perform computations that leverage quantum correlations with strict security guarantees against adversaries, even under photon loss scenarios. This concrete use case highlights the practical import of their proposal, going beyond the purely theoretical allure of large entangled states.

Measurement-based quantum computing, a leading model in quantum computation architectures, stands to be revolutionized by these heralded graph states. The proposed methodology not only underpins scalable quantum gate implementations but also opens avenues to fault-tolerant error correction and distributed quantum sensing, where entanglement serves as a critical resource enhancing sensitivity beyond classical limits.

Moreover, this work signals a call to the broader quantum information science community to focus on realistic hardware constraints. Often, theoretical proposals assume idealized components unavailable in laboratory settings, creating a disconnect between theory and implementation. Goldschmidt’s group explicitly addresses this divide by developing a protocol aligned with current emitter technologies and measurement limitations, inspiring optimism for near-term experimental realization.

The Illinois team is emboldened by the wide compatibility of their scheme across various quantum emitter platforms. Their method’s feasibility is underscored particularly for systems with inherently low photon collection efficiencies—a persistent hurdle in quantum optics. Early experimental efforts headed by Jianlong Lin aim to demonstrate this protocol with standard quantum hardware, potentially marking one of few successful practical demonstrations of photonic graph states with bona fide technological applications.

While the experimental endeavors advance, Max Gold continues to explore the theoretical landscape, seeking additional scenarios where heralded photonic graph states could innovate quantum algorithms or communication protocols. Their combined efforts promise a robust pipeline from foundational theory through laboratory validation to potential technological deployment in quantum computing and secure communication infrastructures.

This landmark research encapsulates a shift toward pragmatism in quantum photonics, marrying theoretical innovation with hardware realism. By constructing entangled photonic states constructively and heraldedly, rather than attempting to overcome unavoidable system losses through brute force, the Illinois researchers demonstrate a pathway that could shape the next decade of quantum technology development, making complex photonic entanglement accessible to operational quantum devices worldwide.

Subject of Research: Photonic graph states and quantum emitters for quantum information processing
Article Title: Heralded photonic graph states with inefficient quantum emitters
News Publication Date: 15 January 2026
Web References:

• https://www.nature.com/articles/s41534-026-01181-7
• http://dx.doi.org/10.1038/s41534-026-01181-7

References:
Goldschmidt, E., Chitambar, E., Gold, M., Lin, J. (2026). Heralded photonic graph states with inefficient quantum emitters. npj Quantum Information. https://doi.org/10.1038/s41534-026-01181-7

Keywords
Quantum information, photonic graph states, quantum entanglement, quantum emitters, heralded photon detection, virtual graph states, measurement-based quantum computing, quantum communication, spin qubits, quantum sensing, trapped ions, neutral atoms.