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arXiv:2605.26757

Practical Entanglement Distillation Protocols with Quadratic Error Suppression

Elisa Bäumer Marty

quant-phSubmitted May 26, 2026• Announced May 27, 2026• 0 citations
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Abstract

Near-term and early fault-tolerant quantum computing architectures are expected to exhibit highly non-uniform error rates. In particular, local operations within a chip can be substantially more reliable than operations connecting different chips or dilution refrigerators. Such inter-module operations can therefore become a dominant bottleneck, even when quantum error correction is applied. Entanglement distillation provides a natural way to trade additional operations and qubits for higher-fidelity entanglement. Standard distillation protocols, however, are usually formulated in an LOCC resource model, in which several noisy Bell pairs are generated initially and all subsequent processing consists only of local operations and classical communication. Here, we consider a generalized model tailored to modular quantum computing hardware, in which the two modules have access to high-fidelity local operations and to repeated uses of the same noisy inter-module entangling operation during the protocol. We develop practical small-scale entanglement distillation protocols designed to minimize both space and time overhead. Remarkably, our main protocol requires only two qubits per module, yet achieves quadratic error suppression of inter-module errors, assuming local operations are much cleaner. Compared with existing small-scale protocols, our space-optimal protocol provides more space- and time-efficient quadratic error suppression and achieves the best performance in our simulations and experiments on noisy links of current superconducting quantum processors. These results suggest that inter-module-gate-assisted entanglement distillation can be a practical primitive for overcoming noisy links in modular quantum computing architectures.

Comments
9 pages, 4 figures (main text) + 2 pages, 1 figure (appendix)

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Near-term and early fault-tolerant quantum computing architectures are expected to exhibit highly non-uniform error rates. In particular, local operations within a chip can be substantially more reliable than operations connecting different chips or dilution refrigerators. Such inter-module operations can therefore become a dominant bottleneck, even when quantum error correction is applied. Entanglement distillation provides a natural way to trade additional operations and qubits for higher-fidelity entanglement. Standard distillation protocols, however, are usually formulated in an LOCC resource model, in which several noisy Bell pairs are generated initially and all subsequent processing consists only of local operations and classical communication. Here, we consider a generalized model tailored to modular quantum computing hardware, in which the two modules have access to high-fidelity local operations and to repeated uses of the same noisy inter-module entangling operation during the protocol. We develop practical small-scale entanglement distillation protocols designed to minimize both space and time overhead. Remarkably, our main protocol requires only two qubits per module, yet achieves quadratic error suppression of inter-module errors, assuming local operations are much cleaner. Compared with existing small-scale protocols, our space-optimal protocol provides more space- and time-efficient quadratic error suppression and achieves the best performance in our simulations and experiments on noisy links of current superconducting quantum processors. These results suggest that inter-module-gate-assisted entanglement distillation can be a practical primitive for overcoming noisy links in modular quantum computing architectures.
Distributed quantum computing allows the modular construction of large-scale quantum computers and enables new protocols for blind quantum computation.However, such applications in the large-scale, fault-tolerant regime place stringent demands on the fidelity and rate of entanglement generation, which are not met by existing methods for quantum interconnects.In this work, we develop constant-rate entanglement distillation methods to address this bottleneck in the setting of noisy local operations.By using a sequence of two-way entanglement distillation protocols based on quantum error detecting codes with increasing rate, and combining with standard fault tolerance techniques, we achieve constant-rate entanglement distillation.We show that the scheme has constant-rate in expectation, and further numerically optimize to achieve low practical overhead under memory constraints.We find that compared to existing quantum interconnect * Both authors contributed equally to this research.
High-fidelity entanglement shared between distant quantum systems is an essential resource for quantum communication and computation. Entanglement distillation addresses this need by converting multiple noisy Bell pairs into fewer higher-fidelity pairs, using only local quantum operations and classical communication. However, this approach typically requires a substantial overhead in the number of qubits. To bypass this hurdle, we propose to leverage the high-dimensional Hilbert space of a single pair of bosonic systems to store a large amount of entanglement, replacing the need for multi-qubit systems. To distill entanglement in such a setup, we devise a new entanglement distillation protocol, tailored for bosonic systems. The protocol converts a highly-entangled noisy state between two bosonic systems into a lower-dimensional but high-fidelity entangled state, using only local bosonic operations. We show that our protocol significantly enhances the fidelity of the entangled state in the presence of naturally occurring loss and dephasing errors. Compared to methods relying on multiple Bell pairs, our scheme offers a more hardware-efficient strategy, providing a practical route toward the realization of entanglement distillation.
Distributed architectures have been proposed as a pathway to large-scale quantum computers. Combined with the need for fault-tolerance, such architectures require distributed quantum error correction (DQEC) and distributed logical gates. An important challenge is how to realize DQEC primitives in the setting where interaction between modules is restricted to shared Bell pairs that are significantly noisier than on-chip operations. We extend the framework known as fault tolerance by construction to this setting, deriving different strategies for handling the additional noise. Through fault-improvement we recover conventional entanglement distillation, and also find more dynamical protocols that enable space-time trade-offs. We show that integrated decoding halves the required distillation code distance compared to entanglement distillation implemented using separate decoding, thus requiring significantly fewer Bell pairs. As a main focus of the work, we synthesize efficient circuits for an important primitive in distributed fault tolerance: distributed stabilizer measurements. These circuits can be adapted to resource constraints, e.g. on the Bell pair generation rate or the space available for on-chip auxiliary qubits. Noting that full local fault-tolerance is not always needed to preserve the correct scaling of logical error rates, we further optimize the circuits depending on the surrounding context. We consider in particular the surface code and the color code, both as distributed memories and in the case of lattice surgery across separate modules. Here, robustness to certain hook and readout errors reduces the number of required Bell pairs even further, compared to the context-free setting. We numerically benchmark the resulting implementations under circuit level noise with additional interconnect noise.
Distributed quantum computing can potentially address the scalability challenge by networking processors through photon-mediated remote entanglement. Prior approaches assumed that remote Bell pairs require distillation before use, incurring substantial overhead, to achieve sufficiently high fidelity. However, recent results show that lattice-surgery operations at logical qubit boundaries tolerate significantly higher error rates than previously assumed. We quantify the resource trade-offs between distillation overhead and surface-code distance requirements under realistic constraints including probabilistic entanglement generation and memory decoherence. We identify the fidelity crossover point separating the two regimes. Below this threshold, the distillation strategy dominates, reducing resource overhead by up to two orders of magnitude. Above it, no-distillation becomes the more efficient choice, reducing resource overhead by more than half. We briefly describe the application of these methods to ion-trap and neutral-atom platforms. These results provide joint design guidelines for optimizing photonic interconnects and fault-tolerant architectures in distributed quantum computing.
Distributed quantum computing allows the modular construction of large-scale quantum computers and enables new protocols for blind quantum computation. However, such applications in the large-scale, fault-tolerant regime place stringent demands on the fidelity and rate of entanglement generation which are not met by existing methods for quantum interconnects. In this work, we develop constant-rate entanglement distillation methods to address this bottleneck in the setting of noisy local operations. By using a sequence of two-way entanglement distillation protocols based on quantum error detecting codes with increasing rate, and combining with standard fault tolerance techniques, we achieve constant-rate entanglement distillation. We prove the scheme has constant-rate in expectation and further numerically optimize to achieve low practical overhead subject to memory constraints. We find our optimized schemes outperform existing computationally efficient quantum interconnect schemes by an order of magnitude in relevant regimes, leading to a direct speed-up in the execution of distributed quantum algorithms.
Distributed architecture is a promising route to scaling fault-tolerant quantum computing (FTQC) beyond the inherent limitations of single processors. For practical implementation of distributed FTQC, logical Bell pair preparation must be designed not only for efficient Bell pair consumption but also for the spacetime volume of the protocol; however, entanglement distillation protocols have primarily focused on minimizing the consumption of Bell pairs, often resulting in protocols that require a substantial number of local operations. To resolve this issue, we introduce a metric for characterizing the practical cost of preparing high-fidelity logical Bell pairs, link-limited volume (LLV), which is a circuit-volume metric incorporating both the cost of physical Bell pairs and the spacetime volume of local operations. Guided by this metric, we propose entanglement boosting protocol, which achieves efficient preparation of logical Bell pairs encoded in rotated surface code with LLV reduced by orders of magnitude compared to prior state-of-the-art methods. In this protocol, paralleling recent advances in magic state cultivation, we employ soft-information decoders and postselection to suppress the logical error rates of Bell pairs to practical levels in the order of 10−1010^{-10}10−10 from 86 noisy physical Bell pairs at 1% error, while all local operations are implementable within a spatial region of a single surface code patch with 2D local connectivity. We also present a pipelined implementation of entanglement distillation using high-rate quantum error-correcting codes, enabling arbitrarily low logical error rates while also maintaining physically efficient implementations. These results pave the way for the practical implementation of distributed FTQC, reinforcing the benefits of fast interconnect technologies and serving as a guiding principle for the efficient design of protocols and devices.