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arXiv:2407.01429 · Physical Review Letters

Generalized Quantum Repeater Graph States

Bikun Li, Kenneth Goodenough, Filip Rozpędek, Liang Jiang

Published May 12, 2025• 13 citations
arXivHTMLPDF

Abstract

All-photonic quantum repeaters are essential for establishing long-range quantum entanglement. Within repeater nodes, reliably performing entanglement swapping is a key component of scalable quantum communication. To tackle the challenge of probabilistic Bell state measurement in linear optics, which often leads to information loss, various approaches have been proposed to ensure the loss tolerance of distributing a single ebit. We have generalized previous work regarding repeater graph states with elaborate connectivity, enabling the efficient establishment of exploitable ebits at a finite rate with high probability. We demonstrate that our new scheme significantly outperforms the previous work with much flexibility and discuss the generation overhead of such resource states. These findings offer new insights into the scalability and reliability of loss-tolerant quantum networks.

DOI
10.1103/physrevlett.134.190801

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All-photonic quantum repeaters are essential for establishing long-range quantum entanglement. Within repeater nodes, reliably performing entanglement swapping is a key component of scalable quantum communication. To tackle the challenge of probabilistic Bell state measurement in linear optics, which often leads to information loss, various approaches have been proposed to ensure the loss tolerance of distributing a single ebit. We have generalized previous work regarding repeater graph states with elaborate connectivity, enabling the efficient establishment of exploitable ebits at a finite rate with high probability. We demonstrate that our new scheme significantly outperforms the previous work with much flexibility and discuss the generation overhead of such resource states. These findings offer new insights into the scalability and reliability of loss-tolerant quantum networks.
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.
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.
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.
To realize long-distance quantum communication, it is crucial to design quantum repeater architectures that can deal with transmission losses and operational errors. Code concatenation of photonic graph codes is a promising way to achieve this; however, existing concatenated codes that can correct both transmission losses and operational errors are extremely hardware-demanding. We propose a one-way quantum repeater architecture based on concatenated ring graph codes and linear optical Bell-state measurements. We construct a scheme to generate the concatenated ring graph codes using quantum emitters, where the number of matter qubits scales linearly with concatenation depth. Furthermore, we devise a measurement strategy at each repeater station with a simple experimental setup where photons are measured in the order that they are created and show that entanglement swapping is fault-tolerant to both transmission losses and operational errors. This allows for long-distance quantum communication (>104> 10^4>104 km) at a kHZ rate even in the presence of single qubit error rates ε>10−3ε> 10^{-3}ε>10−3.
Abstract A repeater graph state (RGS) is a class of multipartite entangled states with favourable features for quantum communication, particularly as the enabler of all-photonic quantum repeaters. In this paper, based on an alternative formalism, we show that two RGSs can be fused via a Bell measurement in a fault-tolerant manner. The fusing of multiple RGSs can thus be carried out simultaneously and flexibly, which enables a 2-step rapid generation of an arbitrarily large RGS from relatively small building blocks using heralded but non-deterministic photonic Bell measurements. It then makes possible the distribution of a large multipartite entangled state from multiple sources to many parties via high-loss channels, and hence also a satellite-based entanglement distribution scheme. In such a scheme, stationary memories are only required for ground stations, the growth of memory noise with its scale can be effectively suppressed, and recipients of entangled pairs of qubits may remain anonymous.
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.