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Logical Photon Encoding Schemes for All-photonic Quantum Repeaters and Networks

Ching-Lin Chan, Charu Jain, Ezra Kissel, Wenji Wu, Edwin Barnes, Sophia E. Economou, Inder Monga

Published Aug 17, 2026• 0 citations
Publisher

Abstract

The paper conducts a comparative study of logical photon encoding schemes for all-photonic entanglement-based quantum repeaters and networks. We aim to quantitatively understand the relative performance and resource requirements of different encoding schemes in all-photonic quantum networks, employing quantum emitters to deterministically generate the required photonic graph states. The performance metrics include entanglement generation rate and resource requirement between the endpoints of the network.

DOI
10.1145/3833409.3833442

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The paper conducts a comparative study of logical photon encoding schemes for all-photonic entanglement-based quantum repeaters and networks. We aim to quantitatively understand the relative performance and resource requirements of different encoding schemes in all-photonic quantum networks, employing quantum emitters to deterministically generate the required photonic graph states. The performance metrics include entanglement generation rate and resource requirement between the endpoints of the network.
By encoding logical qubits into specific types of photonic graph states, one can realize quantum repeaters that enable fast entanglement distribution rates approaching classical communication. However, the generation of these photonic graph states requires a formidable resource overhead using traditional approaches based on linear optics. Overcoming this challenge, a number of new schemes have been proposed that employ quantum emitters to deterministically generate photonic graph states. Although these schemes have the potential to significantly reduce the resource cost, a systematic comparison of the repeater performance among different encodings and different generation schemes is lacking. Here, we quantitatively analyze the performance of quantum repeaters based on two different graph states, i.e. the tree graph states and the repeater graph states. For both states, we compare the performance between two generation schemes, one based on a single quantum emitter coupled to ancillary matter qubits, and one based on a single quantum emitter coupled to a delayed feedback. We identify the numerically optimal scheme at different system parameters. Our analysis provides a clear guideline on the selection of the generation scheme for graph-state-based quantum repeaters, and lays out the parameter requirements for future experimental realizations of different schemes.
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.
Developing and deploying advanced Quantum Repeater (QR) technologies will be necessary to scale quantum networks to longer distances. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically classified into memory-based or all-photonic QRs; and each type of QR may be best suited for a specific type of underlying quantum technology, a particular scale of quantum networks, or a specific regime of operational parameters. We perform theoretical analysis and simulations of quantum repeaters and networks to investigate the relative performance and resource requirements of different quantum network paradigms. Our results will help guide the optimization of quantum hardware and components and shed light on the role of a robust control plane. We present our research findings on theoretical analysis and simulations of memory-based first-generation trapped-ion quantum repeaters and networks, and all-photonic entanglement-based quantum repeaters and networks. We study the relative performance in terms of entanglement generation rate and fidelity, as well as the resource requirements of these two different quantum network paradigms.
Developing and deploying advanced Quantum Repeater (QR) technologies will be necessary to scale quantum networks at longer distances. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically classified into “memory-based” or “all-photonic” QRs, and each type of QR may be best suited for a specific type of underlying quantum technology, a particular scale of quantum network, or a specific regime of operational parameters. Modeling and simulation of quantum repeaters and networks can help in understanding the relative performance and resource requirements of different types of QRs, identify tradeoffs of alternative quantum network architectures, optimize quantum hardware, and assist in the design of a robust control plane. This paper introduces a quantum repeater simulation toolkit based on NetSquid, which includes component models and protocols to study advanced quantum repeater networks. We present our initial research findings on modeling and simulation of “allphotonic” entanglement-based QRs and “memory-based” first generation trapped ion QRs. We study the relative performance and resource requirements of these two different types of QRs and networks. The performance metrics include entanglement generation rate and fidelity between the endpoints of the network. For fair comparison of resource requirements of different types of QRs, entanglement generation rate is normalized by the total number of matter qubits involved.
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.
All-photonic quantum repeater is not yet commercially applicable due to difficulty in the generation of repeater graph states (RGS) and the probabilistic nature of Bell-state measurement. In recent years, several deterministic protocols have been proposed to generate RGS. However, they can only create bare RGS and a rate-distance analysis for the deterministic approach is currently missing. We present a deterministic generation scheme of encoded RGS and show that after optimization, the repeater using our scheme performs at least 4.9 times better than the traditional probabilistic generation scheme in terms of secret key rate, with a significant reduction in the total number photons by 2 orders of magnitude. The duration of our generation protocol is only half of the existing deterministic schemes. We also describe in detail an experimental method using cavity QED-enhanced resonance fluorescence and time-bin encoding to implement our protocol.