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Physical Review Applied

Long-distance quantum communication using concatenated ring graph codes

Love A. Pettersson, Anders Søndberg Sørensen

Published Sep 24, 2025• 1 citation
Publisher

Abstract

This study develops a method to overcome the effect of loss in optical fibers, which is one of the main obstacles to long-distance quantum communication. The work discusses an architecture for quantum repeaters, in which information is encoded in error-correcting codes capable of handling both photon loss and logical errors. Advantages of this approach are that it can work with very limited resources at each repeater station, and is more robust to errors than previous techniques. The results can promote long-distance quantum communication at very high rates.

DOI
10.1103/fxcg-xxry

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Physical Review A•Jan 6, 2025•0 citations
This study develops a method to overcome the effect of loss in optical fibers, which is one of the main obstacles to long-distance quantum communication. The work discusses an architecture for quantum repeaters, in which information is encoded in error-correcting codes capable of handling both photon loss and logical errors. Advantages of this approach are that it can work with very limited resources at each repeater station, and is more robust to errors than previous techniques. The results can promote long-distance quantum communication at very high rates.
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.
Fiber-based classical communication is all-optical and uses light pulses reamplified and reshaped every 50-100 km in classical repeaters. Most compatible with this would be a quantum communication system which is also all-optical with quantum processing units placed in similar intervals. However, existing all-optical quantum communication protocols either require complicated quantum error correction steps for logical-qubit recoveries at every few kilometers or, over larger quantum repeater segments, they would at least depend on sharing complex multi-photon entangled states. Here we propose an all-optical memory-based quantum repeater for long-distance quantum communication, with quantum memories at each repeater station realized in the form of fiber loops combined with suitable quantum error correction codes for photon-loss protection. By sending only single-photon states through the fibers connecting the stations, such repeaters can operate in the classical infrastructure's long-segment regime. We analyze the performance of our scheme for the Gottesman-Kitaev-Preskill code, including a concatenation with the Steane code, as well as the single-photon quantum parity code for total distances up to 10000 km.
Abstract We propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.
One-way quantum repeaters where loss and operational errors are counteracted by quantum error-correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error-correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimized resource overhead by interspersing repeater nodes that each specialize in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.
Despite the tremendous progress of quantum cryptography, efficient quantum communication over long distances (≥ 1000 km) remains an outstanding challenge due to fiber attenuation and operation errors accumulated over the entire communication distance. Quantum repeaters (QRs), as a promising approach, can overcome both photon loss and operation errors, and hence significantly speedup the communication rate. Depending on the methods used to correct loss and operation errors, all the proposed QR schemes can be classified into three categories (generations). Here we present the first systematic comparison of three generations of quantum repeaters by evaluating the cost of both temporal and physical resources, and identify the optimized quantum repeater architecture for a given set of experimental parameters for use in quantum key distribution. Our work provides a roadmap for the experimental realizations of highly efficient quantum networks over transcontinental distances.
To achieve an ultrafast long-distance quantum communication, the one-way quantum repeater scheme based on linear optics is a promising framework. However, photon loss becomes the dominant error in communication as the distance increases. To resolve this problem, a quantum parity code has been developed, which, however, suffers from a significant fluctuation in the success transmission probability as the code length increases. Here, to utilize all the available qubits to boost the coding gain, we propose a generalized version of quantum parity code by using the concatenated structure in a flexible way. Compared to quantum parity code, the generalized one does not increase the hardware overhead but offers superior performance with the continuous increase of code length. The gain comes from optimizing the length distribution of the inner codes. Given the current limited ability to realize quantum codes, generalized quantum parity code assisted by one-way quantum repeaters offers a promising way to achieve ultrafast long-distance quantum communication.