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arXiv:2608.15620

Finite-energy GKP-QPC architectures for photonic quantum memories and repeaters

Kaustav Chatterjee, Ulrik Lund Andersen

quant-phSubmitted Aug 16, 2026• Announced Aug 18, 2026• 0 citations
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Abstract

Photonic quantum networks require error-correction architectures that remain useful with finite-energy bosonic states, pure-loss fiber transmission, and explicit resource accounting. In this light, we study a concatenated architecture in which each physical rail is a finitely squeezed Gottesman--Kitaev--Preskill (GKP) qubit transmitted through a pure-loss fiber segment, corrected by teleportation-based GKP error correction with finitely squeezed ancillae, and decoded by an outer quantum parity code (QPC). The GKP layer converts continuous homodyne syndromes into effective rail-level Pauli marginals, while the QPC layer suppresses the residual qubit-level errors. For the concatenated code family considered here, we find a finite-squeezing threshold of $5.06\,\mathrm{dB}$ at zero propagation loss. In the memory setting, the QPC layer lowers the squeezing at which repeated error correction becomes beneficial from $6.7\,\mathrm{dB}$ for bare GKP correction to $5.2\,\mathrm{dB}$ for QPC$(3,3)$ and $4.3\,\mathrm{dB}$ for QPC$(5,5)$, and improves the average-fidelity ratio by up to $75$--$90\%$ in the relevant intermediate-noise regime. In the repeater setting, avoiding pre-amplification gives larger secret-key fractions at moderate squeezing, but also produces an optimal squeezing because highly squeezed GKP peaks become sensitive to loss-induced inward displacement. Resource-normalized rates show that QPC concatenation can exceed the repeaterless PLOB benchmark by orders of magnitude and extend the communication reach, at short repeater spacing, to distances of order $10^4$km with $14$dB squeezing. However, QPC concatenation becomes detrimental when each elementary hop is too lossy. These results provide quantitative design rules for finite-squeezing GKP--QPC quantum memories and repeaters.

Comments
15 pages, 12 figures

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Photonic quantum networks require error-correction architectures that remain useful with finite-energy bosonic states, pure-loss fiber transmission, and explicit resource accounting. In this light, we study a concatenated architecture in which each physical rail is a finitely squeezed Gottesman--Kitaev--Preskill (GKP) qubit transmitted through a pure-loss fiber segment, corrected by teleportation-based GKP error correction with finitely squeezed ancillae, and decoded by an outer quantum parity code (QPC). The GKP layer converts continuous homodyne syndromes into effective rail-level Pauli marginals, while the QPC layer suppresses the residual qubit-level errors. For the concatenated code family considered here, we find a finite-squeezing threshold of 5.06 dB5.06\,\mathrm{dB}5.06dB at zero propagation loss. In the memory setting, the QPC layer lowers the squeezing at which repeated error correction becomes beneficial from 6.7 dB6.7\,\mathrm{dB}6.7dB for bare GKP correction to 5.2 dB5.2\,\mathrm{dB}5.2dB for QPC(3,3)(3,3)(3,3) and 4.3 dB4.3\,\mathrm{dB}4.3dB for QPC(5,5)(5,5)(5,5), and improves the average-fidelity ratio by up to 757575--90%90\%90% in the relevant intermediate-noise regime. In the repeater setting, avoiding pre-amplification gives larger secret-key fractions at moderate squeezing, but also produces an optimal squeezing because highly squeezed GKP peaks become sensitive to loss-induced inward displacement. Resource-normalized rates show that QPC concatenation can exceed the repeaterless PLOB benchmark by orders of magnitude and extend the communication reach, at short repeater spacing, to distances of order 10410^4104km with 141414dB squeezing. However, QPC concatenation becomes detrimental when each elementary hop is too lossy. These results provide quantitative design rules for finite-squeezing GKP--QPC quantum memories and repeaters.
Reliable quantum memory is essential for scalable quantum networks and fault-tolerant photonic quantum computing. We present a quantitative analysis of an all-optical quantum memory architecture in which a Gottesman-Kitaev-Preskill (GKP) encoded qubit is stored in a fibre loop and periodically stabilized using teleportation-based error correction. By modelling fibre propagation as a pure-loss channel and representing each correction round as an effective logical map acting on the Bloch vector, we obtain a compact description of the full multi-round memory channel. We show that syndrome decoder optimization plays a crucial role in the experimentally relevant finite-squeezing regime. The optimal decoder deviates from standard square-grid GKP decoder in both tile-size and tile-shape, leading to significant improved logical performance. Using this optimized decoding strategy, we identify a squeezing-dependent optimal spacing between correction nodes that maximizes the memory lifetime. Remarkably, this optimal segment length is largely independent of the desired storage time, providing a simple and practical design rule for fibre-loop quantum memory. We further find a squeezing threshold of approximately 6.7 dB below which intermediate error correction becomes counterproductive, while above threshold the achievable storage time increases approximately exponentially with squeezing. For example, at 17 dB squeezing, storage times exceeding 400 ms can be achieved with logical infidelity below 1%. These results establish clear performance benchmarks and reveal the fundamental trade-off between photon loss, squeezing, and correction frequency in continuous-variable architectures. Our findings provide actionable design principles for near-term photonic quantum memory and clarify the path toward scalable all-optical fault-tolerant quantum storage.
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.
Quantum communication between two distant parties will serve as a cornerstone of the future quantum internet. However, generating enough entangled Bell pairs over long distances is a critical bottleneck. Although photons are ideal carriers of quantum information, overcoming photon loss and the exponential attenuation of signals remains a major challenge. We propose an all-photonic quantum repeater architecture that enables quantum communication over 1,000 km with an equidistant repeater spacing of 9 km. This repeater spacing is enabled by elementary entangled Bell pairs protected through the concatenation of continuous-variable and discrete-variable quantum error correction codes, namely, the bosonic Gottesman-Kitaev-Preskill (GKP) code and the [[7,1,3]] Steane code, whose combination yields a synergistic improvement in robustness against photon loss. This architecture incorporates a new ranking criterion and a multi-reflection mirror-based optical cavity as a free-space photonic memory module, which we model in terms of its length and mirror-reflection efficiency. Additionally, we propose two heuristic construction methods for the elementary entangled Bell pairs. One method introduces up to two-qubit correlated errors within each logical qubit but requires a large number of GKP qubits, while the other allows up to three-qubit correlated errors within each logical qubit but requires fewer GKP qubits. To more accurately capture realistic physical conditions during photonic resource preparation, we include switching-induced imperfections in our simulations, in addition to other standard optical imperfections. In the presence of these imperfections, our realization requires only a few thousand GKP qubits per repeater station per protocol run, a resource requirement significantly smaller than the corresponding resource requirements of prior third-generation all-photonic repeater proposals.
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.
Scalable fault-tolerant quantum error correction based on Gottesman-Kitaev-Preskill (GKP) codes requires finite-rate outer codes that can exploit analog GKP information under realistic circuit noise. However, quantum low-density parity-check (qLDPC) outer codes have not been systematically compared as candidates for circuit-level GKP concatenation. Here, we benchmark BB and tricycle codes using a unified simulation framework that progresses from code-capacity noise to repeated noisy syndrome extraction and schedule-resolved displacement propagation. Across all three noise models, analog-informed belief-propagation with ordered-statistics decoding (BP-OSD) yields higher finite-size crossing estimates than hard-decision decoding. In the full circuit model, the analog-informed crossings are σth≃0.212σ_{\mathrm{th}}\simeq0.212σth​≃0.212 for the selected BB sequence and 0.1420.1420.142 for the tricycle sequence, corresponding to squeezing requirements of approximately 10.46 dB10.46\,\mathrm{dB}10.46dB and 13.94 dB13.94\,\mathrm{dB}13.94dB, respectively. These results show that analog GKP information continues to improve decoding under circuit-level noise. Under the common simulation assumptions used here, the selected BB sequence also yields a higher finite-size crossing estimate than the selected tricycle sequence.
Long-distance quantum communication will require the use of quantum repeaters to overcome the exponential attenuation of signal with distance. One class of such repeaters utilizes quantum error correction to overcome losses in the communication channel. Here we propose a strategy of using the bosonic Gottesman-Kitaev-Preskill (GKP) code in a two-way repeater architecture with multiplexing. The crucial feature of the GKP code that we make use of is the fact that GKP qubits easily admit deterministic two-qubit gates, hence allowing for multiplexing without the need for generating large cluster states as required in previous all-photonic architectures based on discrete-variable codes. Moreover, alleviating the need for such clique clusters entails that we are no longer limited to extraction of at most one end-to-end entangled pair from a single protocol run. In fact, thanks to the availability of the analog information generated during the measurements of the GKP qubits, we can design better entanglement swapping procedures in which we connect links based on their estimated quality. This enables us to use all the multiplexed links so that large number of links from a single protocol run can contribute to the generation of the end-to-end entanglement. We find that our architecture allows for high-rate end-to-end entanglement generation and is resilient to imperfections arising from finite squeezing in the GKP state preparation and homodyne detection inefficiency. In particular we show that long-distance quantum communication over more than 1000 km is possible even with less than 13 dB of GKP squeezing. We also quantify the number of GKP qubits needed for the implementation of our scheme and find that for good hardware parameters our scheme requires around ${10}^{3}\ensuremath{-}{10}^{4}$ GKP qubits per repeater per protocol run.