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arXiv:2505.14628

Large-Scale Tree-Type Photonic Cluster State Generation with Recurrent Quantum Photonic Neural Networks

Jacob Ewaniuk, Bhavin J. Shastri, Nir Rotenberg

Published May 20, 2025• 0 citations
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Abstract

Large, multi-dimensional clusters of entangled photons are among the most powerful resources for emerging quantum technologies, as they are predicted to enable global quantum networks or universal quantum computation. Here, we propose an entirely new architecture and protocol for their generation based on recurrent quantum photonic neural networks (QPNNs) and focusing on tree-type cluster states. Unlike other approaches, QPNN-based generators are not limited by the the coherence of quantum emitters or by probabilistic multi-photon operations, enabling arbitrary scaling only limited by loss (which, unavoidably, also affects all other methods). We show that a single QPNN can learn to perform all of the many different operations needed to create a cluster state, from photon routing to entanglement generation, all with near-perfect fidelity and at loss-limited rates, even when it is created from imperfect photonic components. Although these losses ultimately place a limit on the size of the cluster states, we show that state-of-the-art photonics should already allow for clusters of 60 photons, which can grow into the 100s with modest improvements to losses. Finally, we present an analysis of a one-way quantum repeater based on these states, determining the requisite platform quality for a global quantum network and highlighting the potential of the QPNN to play a vital role in high-impact quantum technologies.

DOI
10.48550/arxiv.2505.14628

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Large, multi-dimensional clusters of entangled photons are among the most powerful resources for emerging quantum technologies, as they are predicted to enable global quantum networks or universal quantum computation. Here, we propose an entirely new architecture and protocol for their generation based on recurrent quantum photonic neural networks (QPNNs) and focusing on tree-type cluster states. Unlike other approaches, QPNN-based generators are not limited by the the coherence of quantum emitters or by probabilistic multi-photon operations, enabling arbitrary scaling only limited by loss (which, unavoidably, also affects all other methods). We show that a single QPNN can learn to perform all of the many different operations needed to create a cluster state, from photon routing to entanglement generation, all with near-perfect fidelity and at loss-limited rates, even when it is created from imperfect photonic components. Although these losses ultimately place a limit on the size of the cluster states, we show that state-of-the-art photonics should already allow for clusters of 60 photons, which can grow into the 100s with modest improvements to losses. Finally, we present an analysis of a one-way quantum repeater based on these states, determining the requisite platform quality for a global quantum network and highlighting the potential of the QPNN to play a vital role in high-impact quantum technologies.
A photonic cluster state with a tree-type entanglement structure constitutes an efficient resource for quantum error correction of photon loss. But the generation of a tree cluster state with an arbitrary size is notoriously difficult. Here, we propose a protocol to deterministically generate photonic tree states of arbitrary size by using only a single quantum emitter. Photonic entanglement is established through both emission and rescattering from the same emitter, enabling fast and resource-efficient entanglement generation. The same protocol can also be extended to generate more general tree-type entangled states.
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.
We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states.Encoding a qubit in a photonic tree cluster protects the information from transmission loss and enables long-range quantum communication through a chain of repeater stations.As opposed to conventional approaches that are limited by the two-way communication time, the overall transmission rate of the current quantum repeater protocol is determined by the local processing time enabling very high communication rates.We further show that such a repeater can be constructed with as little as two stationary qubits and one quantum emitter per repeater station, which significantly increases the experimental feasibility.We discuss potential implementations with diamond defect centers and semiconductor quantum dots efficiently coupled to photonic nanostructures and outline how such systems may be integrated into repeater stations.
Photonic cluster states are fundamental resource for measurement-based quantum computing (MBQC), which is a promising approach for scalable quantum computing. These highly entangled states enable computation with applying local measurements rather than gate operations, which makes them essential for fault-tolerant quantum computing. Generation of the photonic cluster states requires high-quality entanglement and stability, which can be done by making use of cavity quantum electrodynamics (cavity QED), which is embedding quantum dots (QDs) into photonic microcavities. This method enables controlled single-photon emission and the entanglement of them, helping with key challenges in generating photonic cluster states. Enhancing the generation of the photonic cluster state requires improvement in the quality factor (Q-factor) and therefore, cooperativity of cavity and QD systems. A high Q-factor helps with reduction in photon loss and decoherence, ensuring more stable and high-fidelity quantum states. It also enables better light-matter interactions, improving cluster state quality. Cooperativity, which is a measure for the light-matter coupling strength relative to dissipation, directly impacts photon emission efficiency. Optimization of these parameters improves entanglement generation, which is essential for producing high-quality photonic cluster states. Therefore, optimized cavities are essential for improving the generation of the photonic cluster states. Scalability is also an important parameter for the generation of the large-scale cluster states used in quantum computing. In this paper, after reviewing MBQC, cluster states, and the generation of the photonic cluster states, we investigate the deterministic generation of the photonic cluster state resource for the purpose of MBQC, and highlights the importance of the inverse design techniques for this goal.
Reconfigurable photonic integrated circuits (PICs) for quantum optical information processing are now routinely made in foundries with hundreds or thousands of components. Such PICs rely on linear optics, meaning that all photon-photon interactions are probabilistic, and hence that complex protocols that, for example, produce entanglement or graph states do so at low rates. Adding optical nonlinearities to the circuits provides an activation function analogous to that of classical neural networks, enabling deterministic photon-photon protocols in ideal circuits. Here, we discuss the next step: quantum photonic neural networks made from more realistic – i.e. imperfect – components. We show that these are capable of near-deterministic entanglement generation, when imperfections such as losses, imperfect routing and sub-optimal nonlinearities are balanced against network size. These results provide a design for real quantum photonic neural networks and demonstrate that they may play important roles in emerging quantum technologies.
We introduce the architecture and timing algorithm to realize a time-bin-encoded quantum photonic neural network (QPNN): a reconfigurable nonlinear photonic circuit inspired by the brain and trained to process quantum information. Unlike the typical spatially-encoded QPNN, time-encoded networks require the same number of photonic elements (e.g. phase shifters or switches) regardless of their size or depth. Here, we present a model of such a network and show how to include imperfections such as losses, routing errors and most notably distinguishable photons. As an example, we train the QPNN to realize a controlled-NOT gate, based on a hypothetical ideal Kerr nonlinearity. We then extend our model to a realistic two-photon nonlinearity due to scattering from a single, semiconductor quantum dot coupled to a photonic waveguide. We show that, using this realistic nonlinearity, the QPNN can be trained to act as a Bell-state analyzer which operates with a fidelity of 0.96 and at a rate only limited by losses. We further show that time gating can raise this fidelity to over 0.99, while still maintaining an efficiency exceeding 0.9. Overall, this work lays a framework for the first QPNN encoded in time, and provides a clear path to the scaling of these networks.