The problem that has stymied previous efforts is brutally simple: loss. When a multi-qubit state is spread across several photons, with one qubit per photon as in conventional polarization encoding, the probability that all photons survive the journey falls exponentially with both photon number and distance. Lose a single photon and the entire encoded state is gone. For four-qubit states, this exponential penalty has made fiber transmission over application-relevant distances effectively impossible without loss-tolerant architectures such as all-photonic quantum repeaters, which remain far from deployment.

The Hannover team, led by Philip Rübeling, Robert Johanning, and Michael Kues, sidestepped the exponential scaling by packing multiple qubits into single photons. In their scheme, each of two photons carries two qubits, encoded in multi-level time bins—discrete temporal slots in which the photon can arrive. Because the number of photons stays fixed at two regardless of how many qubits are encoded, the transmission rate no longer collapses exponentially as the quantum state grows. The researchers compared their multi-level encoding directly against a four-qubit multi-photon encoding and confirmed the predicted advantage: a fundamentally different, more forgiving loss scaling that enables longer transmission distances.

Generating the cluster state itself was made dramatically more efficient by a clever trick at the source. Conventionally, cluster states are carved out of hyper-entangled photon pairs using a controlled-phase gate, an operation that introduces additional optical loss and experimental complexity. Instead, the team exploited coherent control of the parametric generation process itself. They carved four coherent excitation pulses from a continuous-wave laser using an electro-optic amplitude modulator, with irregular spacings of 100, 200, and 100 picoseconds, and applied a phase shift of π/2 to the fourth pulse using an electro-optic phase modulator. When these pulses drove cascaded second-harmonic generation and spontaneous parametric down-conversion in a periodically poled lithium niobate waveguide, the photon pairs emerged already in the cluster state—no gate required. Shifting the phase manipulation from the fragile photon pairs to the robust classical excitation pulses cuts both loss and complexity, two currencies that quantum networks cannot afford to waste.

Once generated, the signal and idler photons were separated by a wavelength-selective switch into distinct 15-gigahertz channels centered at 193.7 and 193.1 terahertz, distributing two qubits of the cluster state to each of two processing nodes. The idler photon then faced the gauntlet: a 4.5-kilometer deployed fiber link running in a round trip across the Leibniz University Hannover campus between the Institute of Photonics and the Institute of Solid State Physics—buildings only 600 meters apart linearly—followed by an additional 25 kilometers of fiber on a spool. A dispersion compensation module corrected the distortion introduced by the fiber, and an active stabilization system using a motorized optical delay line tamed thermal drifts. Without this feedback, applied every 15 minutes from the photons’ time-of-flight, the fiber length wandered by roughly 100 picoseconds; with it, jitter was squeezed down to just 2.8 picoseconds, keeping the time bins crisply distinguishable over a 90-hour acquisition.

Verifying that the transmitted state was still genuinely entangled posed its own challenge. Certification required projective measurements on each qubit in two mutually unbiased bases, which for time-bin qubits normally means imbalanced fiber interferometers—rigid devices matched to a single time-bin spacing, operating at only 50 percent efficiency, and, for this multi-level encoding, requiring four separately stabilized interferometers. The team’s answer is perhaps the experiment’s most transferable innovation: chirped pulse modulation, a reconfigurable Fourier-domain pulse-shaping technique. An electro-optic phase modulator sits between two chirped fiber Bragg gratings of opposite dispersion, each of about 10 nanoseconds per nanometer. The first grating stretches the pulse so that its spectrum maps onto time, the modulator imprints a radio-frequency phase pattern, and the second grating recompresses everything back into the time domain—producing coherent copies of the time bins that act as a tunable beam splitter for temporal quantum states.

The elegance of chirped pulse modulation lies in its flexibility. By driving the modulator with an arbitrary waveform generator at 1.25 gigahertz, the team superimposed the 100-picosecond time bins of one qubit level; at 3.75 gigahertz, they addressed the 300-picosecond bins of the other level, all while leaving the orthogonal qubit untouched. A single segmented waveform, repeated every 180 nanoseconds, cycled through nine different beam-splitter settings, allowing 48 projective measurements across three basis settings to be acquired in parallel. This parallelism made the measurement robust against count-rate fluctuations from polarization drifts and pump power noise, and the entire beam splitter could be reconfigured in under 2.5 nanoseconds by changing the radio-frequency waveform.

The results were emphatic. From the stabilizer values computed across all 48 measurements, the team derived an entanglement witness of −0.57 ± 0.03, certifying genuine four-qubit entanglement after transmission with a confidence of 19 standard deviations—a threshold crossed far beyond any reasonable statistical doubt. The witness implies a lower bound on the fidelity with the ideal cluster state of 78.5 percent. To demonstrate that the state is not merely a curiosity but a working computational resource, the researchers executed primitives of one-way quantum computing on the transmitted cluster state, performing partial projective measurements and observing two-qubit interference visibilities between 89.7 and 96.8 percent. All four measured configurations clearly violated the CHSH inequality, whose threshold sits at 70.7 percent, proving that residual bipartite entanglement survives even after parts of the cluster state have been measured away.

The implications ripple outward. Because the entire scheme operates at telecommunication wavelengths in standard single-mode fiber, it is natively compatible with the existing global fiber infrastructure—unlike spatial encodings such as orbital angular momentum, which cannot propagate in single-mode fiber at all. The two-node topology demonstrated here is already sufficient for compelling applications, including blind quantum computing, where a client delegates computation to a server without revealing the computation itself, and quantum key agreement. The authors note that the main distance limitation is currently optical loss in the processing setup itself, which could be alleviated with integrated photonic components, optimized source phase-matching, and spectral multiplexing. Scaling to around ten qubits appears feasible with state-of-the-art technology, which would open the door to distributed blind Grover algorithms and multi-qubit quantum communication. The demonstration stops short of a fault-tolerant, directly scalable architecture, and the beam splitter’s cross-talk and spectral walk-off currently cap the observed visibilities. But the conceptual barrier has fallen: complex, multi-qubit entangled states can now travel the same glass arteries that carry today’s internet, and the quantum networks long sketched on whiteboards have moved measurably closer to the fiber in the ground.

Subject of Research: Fiber transmission of multi-level time-bin encoded photonic cluster states for quantum networking

Article Title: Transmission of multi-level time-bin encoded cluster states over 29 km of partially deployed optical fiber

Article References: Rübeling, P., Johanning, R., Heine, J., Marchukov, O. V., & Kues, M. (2026). Transmission of multi-level time-bin encoded cluster states over 29 km of partially deployed optical fiber. Light: Science & Applications, 15(1), Article 384. https://doi.org/10.1038/s41377-026-02465-5

Image Credits: AI Generated

DOI: 10.1038/s41377-026-02465-5

Keywords: cluster states, quantum entanglement, time-bin encoding, optical fiber, quantum networks, photonic quantum computing, blind quantum computing, chirped pulse modulation, spontaneous parametric down-conversion, entanglement witness, quantum communication, telecom infrastructure

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