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arXiv:2504.18121 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Integrating Entanglement Purification into All-Photonic Quantum Repeaters

Naphan Benchasattabuse, Michal Hajdušek, Rodney Van Meter

Published Aug 30, 2025• 0 citations
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Abstract

We propose a purification-enhanced all-photonic quantum repeater scheme based on repeater graph states (RGS) framework that leverages the recently proposed half-RGS building block. This framework addresses a longstanding open question—how to naturally integrate entanglement purification with an all-photonic scheme—by enabling long-distance purification without disrupting the core design. Our framework utilizes optimistic purification performed directly on the half-RGS primitives across long distances without waiting for heralding outcomes. The overhead is modest: the RGS generation slows down proportionally with the number of purification rounds, and each round requires only one additional quantum emitter per half-RGS source. However, since the generation time is negligible compared to the end-to-end communication delay, the total latency remains effectively dominated by communication time, similar to frameworks without purification. Our framework enables flexible purification scheduling along the connection path, making it compatible with memory-based strategies, a rich body of research on purification scheduling and optimization that was previously thought inapplicable to the RGS scheme. Through numerical evaluation, we compare the performance of our framework with purification between memories at end nodes.

DOI
10.1109/qce65121.2025.00100

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We propose a purification-enhanced all-photonic quantum repeater scheme based on repeater graph states (RGS) framework that leverages the recently proposed half-RGS building block. This framework addresses a longstanding open question—how to naturally integrate entanglement purification with an all-photonic scheme—by enabling long-distance purification without disrupting the core design. Our framework utilizes optimistic purification performed directly on the half-RGS primitives across long distances without waiting for heralding outcomes. The overhead is modest: the RGS generation slows down proportionally with the number of purification rounds, and each round requires only one additional quantum emitter per half-RGS source. However, since the generation time is negligible compared to the end-to-end communication delay, the total latency remains effectively dominated by communication time, similar to frameworks without purification. Our framework enables flexible purification scheduling along the connection path, making it compatible with memory-based strategies, a rich body of research on purification scheduling and optimization that was previously thought inapplicable to the RGS scheme. Through numerical evaluation, we compare the performance of our framework with purification between memories at end nodes.
The all-photonic quantum repeater scheme, utilizing a type of graph state called the repeater graph state (RGS), promises resilience to photon losses and operational errors, offering a fast Bell pair generation rate limited only by the RGS creation time (rather than enforced round-trip waits). While existing research has predominantly focused on RGS generation and secret key sharing rate analysis, there is a need to extend investigations to encompass broader applications, such as distributed computation and teleportation, the main tasks envisioned for the Quantum Internet. Here we propose a new emitter-photonic qubit building block and an RGS protocol that addresses several key considerations: end node involvement in connection establishment, decoding of logical qubits within the RGS, and computing the Pauli frame corrections at each participating node to ensure the desired correct end-to-end Bell pair state. Our proposed building block significantly reduces the total number of emissive quantum memories required for end nodes and seamlessly integrates all-photonic and memory-based repeaters under the same communication protocol. We also present an algorithm for decoding logical measurement results, employing graphical reasoning based on graph state manipulation rules.
The all-photonic quantum repeater scheme based on repeater graph states (RGS) offers a promising approach for constructing quantum networks without relying on long-coherence-time quantum memories, which remain a significant technological challenge. Despite substantial progress in defining new schemes for generating RGSs, and in analyzing their performance for the task of secret key generation, the integration of all-photonic schemes with memory-equipped quantum repeaters remains underexplored. We propose an architecture that enables seamless interoperability between all-photonic and memory-based quantum repeaters through an emitter-photon qubit building block, significantly reducing the number of quantum memories required at end nodes from a multiplicative dependence on the trial rate and number of RGS arms to an additive scaling. The core idea of our architecture is to abstract the all-photonic sections of the network as link-level connections between memory-equipped nodes, enabling integration into existing network-level protocols. Additionally, we outline the content and semantics of the messages necessary for a communication protocol based on graph state manipulation rules for computing Pauli frame corrections for obtaining the correct Bell pair. Our approach also provides a simplified method for calculating state fidelity directly from graph state properties.
All-photonic repeater scheme based on a repeater graph state (RGS) promises tolerance to photon losses as well as operational errors. An attractive promise of this scheme is that it offers a fast Bell pair generation rate, limited only by the RGS creation time. This is in stark contrast to the traditional quantum repeater with quantum memories, where the Bell pair generation time is limited by the round-trip wait time leading to poor Bell pair generation performance and quality due to the decoherence of quantum memories. Prior research has focused on lowering the cost of RGS generation and improving upon the probabilistic generation to a deterministic generation with required photon counts to be the same as the number of qubits in the RGS. The operations of creating and manipulating the RGS into an end-to-end Bell pair are complex and have not been fully figured out in detail. Here, we focus on improving the practicality of the RGS scheme in real-world implementation and address three open questions of the RGS scheme, namely; how do end nodes participate in the connection, what classical information needs to be exchanged and processed between nodes, and how to make RGS scheme work hand in hand with the traditional quantum repeaters with memories.
Quantum repeaters are essential for establishing long-distance quantum communication to overcome the exponential decay of entanglement due to photon loss. Traditional repeater architectures rely on physical quantum memory, which introduces decoherence and poses significant practical implementation challenges. The repeater graph state (RGS) architecture offers a promising memory-less alternative that is inherently resilient to photon losses. A key challenge in implementing RGS lies in the requirement for highly efficient graph state generators and complex qubit measurement. In this work, we aim to investigate the strategies for extracting the maximum number of Bell pairs from the RGS structure via its qubit connection to resolve the well-known bottleneck problem of RGS in which only a single Bell pair can be extracted from a complete bipartite graph state. From simulations, we observe that the maximum number of extracted Bell pairs depends on its connection topology, where the Bell-pair yield tends to be maximal at low to moderate edge densities. As the number of network hops increases, the RGS must be equipped with higher inner-qubit connectivity to maintain a sufficient yield of extractable Bell pairs. Thus, the expected resource requirement shifts toward the use of RGSs with higher inner-qubit connectivity.
Graph states constitute the main building block for quantum computing with photons. Quantum emitters with a hosted spin can deterministically generate photonic graph states, strongly lowering the overhead of multiplexing highly probabilistic linear-optics graph state generation. However, they generally suffer from various noise sources, resulting in reduced fidelities of the produced states. To mitigate this issue, we develop purification schemes for entangled photonic states. We first develop purification schemes to purify arbitrary photonic GHZ and other CSS states, which we generalize to all photonic graph states and stabilizer states. The proposed purification schemes have a high success probability of up to 1/21/21/2 and require only linear optics and photon detectors. We optimize cascaded purification schemes for various graph states, taking into account phenomenological Pauli errors or physical noise in time-bin-encoded graph state generation with quantum emitters.
All-photonic quantum repeaters use multi-qubit photonic graph states, called repeater graph states (RGS), instead of matter-based quantum memories, for protection against predominantly loss errors. The RGS comprises tree-graph-encoded logical qubits for error correction at the repeaters and physical {\em link} qubits to create entanglement between neighboring repeaters. The two methods to generate the RGS are probabilistic stitching -- using linear optical Bell state measurements (fusion) -- of small entangled states prepared via multiplexed-probabilistic linear optical circuits fed with single photons, and a direct deterministic preparation using a small number of quantum-logic-capable solid-state emitters. The resource overhead due to fusions and the circuit depth of the quantum emitter system both increase with the size of the RGS. Therefore engineering a resource-efficient RGS is crucial. We propose a new RGS design, which achieves a higher entanglement rate for all-photonic quantum repeaters using fewer qubits than the previously known RGS would. We accomplish this by boosting the probability of entangling neighboring repeaters with tree-encoded link qubits. We also propose a new adaptive scheme to perform logical BSM on the link qubits for loss-only errors. The adaptive BSM outperforms the previous schemes for logical BSM on tree codes when the qubit loss probability is uniform. It reduces the number of optical modes required to perform logical BSM on link qubits to improve the entanglement rate further.