Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Generalized quantum parity codes for ultrafast long-distance quantum communication

Yun-Jiang Wang, Zhuo-Yan Xiao, Xing-Yu Xiong, Sha Shi, Dongsheng Wang

Published Jan 6, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.111.012606

Related papers

Loss-Tolerant Quantum Communication via Bosonic-GKP-Parity-Encoding

S. Nibedita Swain, Timothy C. Ralph

Quantum repeaters constitute a promising platform for enabling long-distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, we initially investigate the bosonic Gottesman Kitaev Preskill (GKP) code as a promising platform for loss correcting quantum repeaters, compatible with room temperature implementation, and analyse how loss and other noise sources propagate through the circuit using Heisenberg evolution. We analyse three quantum repeater protocols in which transmission loss is suppressed at the cost of logical errors, identifying a relay-like teleamplifier as the optimal scheme. This enables long distance quantum communication via densely packed nodes without higher-level encoding, and we evaluate the resulting secure key rates exploiting analog syndrome information. Furthermore, we propose a concatenated Bell-state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement with teleamplifier and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible secure key distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits. Our parity encoded GKP repeater protocol achieves a substantially higher secret key rate than existing GKP based repeater schemes while maintaining a comparable resource overhead.

quant-pharXiv:2604.09002•Apr 13, 2026•0 citations

Long-distance quantum communication using concatenated ring graph codes

Love A. Pettersson, Anders Søndberg Sørensen

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 ($> 10^4$ km) at a kHZ rate even in the presence of single qubit error rates $ε> 10^{-3}$.

arXiv:2503.19822•Mar 25, 2025•0 citations

Long-distance quantum communication sending single photons and keeping many

Stefan Häussler, Peter van Loock

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.

quant-pharXiv:2512.18767•Dec 23, 2025•0 citations

Resource-efficient fault-tolerant one-way quantum repeater with code concatenation

Kah Jen Wo, Guus Avis, Filip Rozpędek +6 more

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.

arXiv:2306.07224•npj Quantum Information•Dec 12, 2023•14 citations

All-optical long-distance quantum communication with Gottesman-Kitaev-Preskill qubits

Kosuke Fukui, Rafael N. Alexander, Peter van Loock

Quantum repeaters are a promising platform for realizing long-distance quantum communication and thus could form the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. Repeater protocols that encode information in single- or multiphoton states are limited by transmission losses and the cost of implementing entangling gates or Bell measurements. In this work, we consider implementing a quantum repeater protocol using Gottesman-Kitaev-Preskill (GKP) qubits. These qubits are natural elements for quantum repeater protocols, because they allow for deterministic Gaussian entangling operations and Bell measurements, which can be implemented at room temperature. The GKP encoding is also capable of correcting small displacement errors. At the cost of additional Gaussian noise, photon loss can be converted into a random displacement error channel by applying a phase-insensitive amplifier. Here we show that a similar conversion can be achieved in two-way repeater protocols by using phase-sensitive amplification applied in the postprocessing of the measurement data, resulting in less overall Gaussian noise per (sufficiently short) repeater segment. We also investigate concatenating the GKP code with higher-level qubit codes while leveraging analog syndrome data, postselection, and path-selection techniques to boost the rate of communication. We compute the secure key rates and find that GKP repeaters can achieve a comparative performance relative to methods based on photonic qubits while using orders-of-magnitude fewer qubits.

arXiv:2011.14876•Physical Review Research•Aug 5, 2021•79 citations

Long-distance quantum communication using concatenated ring graph codes

Love A. Pettersson, Anders Søndberg Sørensen

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.

Physical Review Applied•Sep 24, 2025•1 citation
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.
Quantum repeaters constitute a promising platform for enabling long-distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, we initially investigate the bosonic Gottesman Kitaev Preskill (GKP) code as a promising platform for loss correcting quantum repeaters, compatible with room temperature implementation, and analyse how loss and other noise sources propagate through the circuit using Heisenberg evolution. We analyse three quantum repeater protocols in which transmission loss is suppressed at the cost of logical errors, identifying a relay-like teleamplifier as the optimal scheme. This enables long distance quantum communication via densely packed nodes without higher-level encoding, and we evaluate the resulting secure key rates exploiting analog syndrome information. Furthermore, we propose a concatenated Bell-state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement with teleamplifier and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible secure key distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits. Our parity encoded GKP repeater protocol achieves a substantially higher secret key rate than existing GKP based repeater schemes while maintaining a comparable resource overhead.
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.
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.
Quantum repeaters are a promising platform for realizing long-distance quantum communication and thus could form the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. Repeater protocols that encode information in single- or multiphoton states are limited by transmission losses and the cost of implementing entangling gates or Bell measurements. In this work, we consider implementing a quantum repeater protocol using Gottesman-Kitaev-Preskill (GKP) qubits. These qubits are natural elements for quantum repeater protocols, because they allow for deterministic Gaussian entangling operations and Bell measurements, which can be implemented at room temperature. The GKP encoding is also capable of correcting small displacement errors. At the cost of additional Gaussian noise, photon loss can be converted into a random displacement error channel by applying a phase-insensitive amplifier. Here we show that a similar conversion can be achieved in two-way repeater protocols by using phase-sensitive amplification applied in the postprocessing of the measurement data, resulting in less overall Gaussian noise per (sufficiently short) repeater segment. We also investigate concatenating the GKP code with higher-level qubit codes while leveraging analog syndrome data, postselection, and path-selection techniques to boost the rate of communication. We compute the secure key rates and find that GKP repeaters can achieve a comparative performance relative to methods based on photonic qubits while using orders-of-magnitude fewer qubits.
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.