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arXiv:2606.20344

Quantum ring all-reduce: communication and privacy advantages for distributed learning

María Gragera Garcés, Lirandë Pira

quant-phcs.DCcs.LGSubmitted Jun 18, 2026• Announced Jun 19, 2026• 0 citations• Revised Jun 23, 2026 (v2)
v1 · Jun 18, 2026v2 · Jun 23, 2026
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Abstract

Machine learning models have scaled to unprecedented sizes, making training across distributed devices the de facto standard in the field. In this work, we explore how quantum communications can make distributed training both more communication-efficient and information-theoretically private, for both classical and quantum learning models. Ring all-reduce is the foundational communication primitive for large-scale distributed training. We present a quantum version that reduces per-link online communication by a provably optimal factor of two using pre-shared entanglement and superdense coding, without requiring the learning model or gradient computation to change. Beyond bandwidth, the primitive enables privacy guarantees that are information-theoretically impossible for any classical protocol, achieving composable ε-secure aggregation, via verified entanglement, at a 2x overhead in GHZ copies. Our hybrid quantum-classical communication architecture yields simultaneous communication and security advantages for large scale distributed training, regardless of whether the learning itself is quantum or classical. Finally, we characterise quantum advantages in gradient conflict detection for server-to-client communication under bandwidth constraints, a setting that arises after ring all-reduce is completed, when full gradient broadcast to external clients is infeasible. Two variants of the problem admit different separations. For margin-based alignment testing (\textsc{GapIP}_τ), the quantum advantage is quadratic in the margin parameter: \widetilde{O}(τ^{-1}\log P) qubits versus \widetilde{O}(\min(\τ^{-2},P)) bits. For sign-consistency auditing against a private parameter matching (\textsc{TieAudit}_ε), the advantage represents an exponential separation in communication complexity: Ω(\sqrt{P}) bits whereas O(ε^{-2}\log P) qubits suffice.

Comments
23 pages, 1 figure / v2: Minor expository corrections; results unchanged

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Machine learning models have scaled to unprecedented sizes, making training across distributed devices the de facto standard in the field. In this work, we explore how quantum communications can make distributed training both more communication-efficient and information-theoretically private, for both classical and quantum learning models. Ring all-reduce is the foundational communication primitive for large-scale distributed training. We present a quantum version that reduces per-link online communication by a provably optimal factor of two using pre-shared entanglement and superdense coding, without requiring the learning model or gradient computation to change. Beyond bandwidth, the primitive enables privacy guarantees that are information-theoretically impossible for any classical protocol, achieving composable ε-secure aggregation, via verified entanglement, at a 2x overhead in GHZ copies. Our hybrid quantum-classical communication architecture yields simultaneous communication and security advantages for large scale distributed training, regardless of whether the learning itself is quantum or classical. Finally, we characterise quantum advantages in gradient conflict detection for server-to-client communication under bandwidth constraints, a setting that arises after ring all-reduce is completed, when full gradient broadcast to external clients is infeasible. Two variants of the problem admit different separations. For margin-based alignment testing (\textsc{GapIP}_τ), the quantum advantage is quadratic in the margin parameter: \widetilde{O}(τ^{-1}\log P) qubits versus \widetilde{O}(\min(\τ^{-2},P)) bits. For sign-consistency auditing against a private parameter matching (\textsc{TieAudit}_ε), the advantage represents an exponential separation in communication complexity: Ω(\sqrt{P}) bits whereas O(ε^{-2}\log P) qubits suffice.
Training and inference with large machine learning models that far exceed the memory capacity of individual devices necessitates the design of distributed architectures, forcing one to contend with communication constraints. We present a framework for distributed computation over a quantum network in which data is encoded into specialized quantum states. We prove that for models within this framework, inference and training using gradient descent can be performed with exponentially less communication compared to their classical analogs, and with relatively modest overhead relative to standard gradient-based methods. We show that certain graph neural networks are particularly amenable to implementation within this framework, and moreover present empirical evidence that they perform well on standard benchmarks. To our knowledge, this is the first example of exponential quantum advantage for a generic class of machine learning problems that hold regardless of the data encoding cost. Moreover, we show that models in this class can encode highly nonlinear features of their inputs, and their expressivity increases exponentially with model depth. We also delineate the space of models for which exponential communication advantages hold by showing that they cannot hold for linear classification. Our results can be combined with natural privacy advantages in the communicated quantum states that limit the amount of information that can be extracted from them about the data and model parameters. Taken as a whole, these findings form a promising foundation for distributed machine learning over quantum networks.
AI-driven medical diagnostics increasingly requires collaborative model training across institutions, yet centralizing patient data conflicts with privacy regulations. Federated Learning enables distributed training without raw data sharing, but remains vulnerable to gradient inversion and model leakage attacks. Furthermore, harvest-now-decrypt-later attacks render computationally secure protocols insufficient for protecting long-lived medical records. Quantum communication offers information-theoretic security immune to such threats, making Quantum Federated Learning (QFL) a compelling framework for healthcare. However, practical deployment is constrained by communication overhead and quantum channel noise. We present a systematic quantitative study of communication, convergence, and noise trade-offs in QFL, introducing two complementary strategies to reduce quantum transmissions: (1) structured parameter reduction via light-cone feature selection in parameterized quantum circuits, and (2) a Hybrid QFL architecture that dynamically switches between centralized and decentralized aggregation. We show that Hybrid QFL reduces total quantum transmissions from 3 TNMP3\,TNMP3TNMP, the cost of pure Centralized QFL, to {3t+2(T−t)} NMP\{3t + 2(T - t)\}\,NMP{3t+2(T−t)}NMP over TTT rounds while preserving near-centralized convergence. We further demonstrate that decentralized aggregation is more noise-resilient under depolarizing noise, and evaluate Steane code-based quantum error correction in high-noise regimes. Our results provide an integrated design framework for communication-efficient, noise-aware QFL, clarifying practical trade-offs for scalable quantum-secure distributed learning in healthcare.
The growing demands of remote detection and an increasing amount of training data make distributed machine learning under communication constraints a critical issue. This work provides a communication-efficient quantum algorithm that tackles two traditional machine learning problems, the least-square fitting and softmax regression problems, in the scenario where the dataset is distributed across two parties. Our quantum algorithm finds the model parameters with a communication complexity of O(log_{2}(N)/ε), where N is the number of data points and ε is the bound on parameter errors. Compared to classical and other quantum methods that achieve the same goal, our methods provide a communication advantage in the scaling with data volume. The core of our methods, the quantum bipartite correlator algorithm that estimates the correlation or the Hamming distance of two bit strings distributed across two parties, may be further applied to other information processing tasks.
In the healthcare sector, the scarcity of data and privacy concerns present formidable challenges to the widespread adoption of machine learning. In the present-day scenario, Federated Learning (FL) emerges as a pivotal solution, fostering the rapid evolution of distributed machine learning paradigms while adeptly addressing the problem of data governance and privacy. It allows distributed clients to collaboratively train a global model by synchronizing their local updates without sharing private data. In recent years, federated learning and quantum computing have individually shown great promise to revolutionize various sectors, including healthcare, finance, and manufacturing, where privacy protection is paramount. In this article, we propose a communication-efficient Quantum Federated Learning (QFL) framework based on a variational circuit that enables clients to efficiently train and transmit quantum model parameters, thereby reducing communication rounds significantly and enhancing QFL performance using quantum natural gradient descent (QNGD) optimization. This paper demonstrates the feasibility of a QFL framework for predicting the presence of coronary heart disease, diagnosing whether a patient is suffering from diabetes or not, and differentiating malignant and benign cancer by distributing the UCI datasets unbalanced among healthcare institutions. The proposed framework has the potential to incorporate privacy, security, and the expedited processing of distributed data. QNGD outperformed classical GD by reducing communication rounds by a range of 5% to 60%. In addition to reducing the communication rounds by optimizing the QFL training algorithm and achieving quicker convergence, it also determines the important features regardless of the data imbalance among the clients.
The privacy in classical federated learning can be breached through the use of local gradient results combined with engineered queries to the clients. However, quantum communication channels are considered more secure because a measurement on the channel causes a loss of information, which can be detected by the sender. Therefore, the quantum version of federated learning can be used to provide better privacy. Additionally, sending an NNN-dimensional data vector through a quantum channel requires sending log⁡N\log NlogN entangled qubits, which can potentially provide efficiency if the data vector is utilized as quantum states. In this paper, we propose a quantum federated learning model in which fixed design quantum chips are operated based on the quantum states sent by a centralized server. Based on the incoming superposition states, the clients compute and then send their local gradients as quantum states to the server, where they are aggregated to update parameters. Since the server does not send model parameters, but instead sends the operator as a quantum state, the clients are not required to share the model. This allows for the creation of asynchronous learning models. In addition, the model is fed into client-side chips directly as a quantum state; therefore, it does not require measurements on the incoming quantum state to obtain model parameters in order to compute gradients. This can provide efficiency over models where the parameter vector is sent via classical or quantum channels and local gradients are obtained through the obtained values these parameters.
Federated learning enables collaborative model training across multiple clients without sharing raw data, thereby enhancing privacy. However, the exchange of model updates can still expose sensitive information. Quantum teleportation, a process that transfers quantum states between distant locations without physical transmission of the particles themselves, has recently been implemented in real-world networks. This position paper explores the potential of integrating quantum teleportation into federated learning frameworks to bolster privacy. By leveraging quantum entanglement and the no-cloning theorem, quantum teleportation ensures that data remains secure during transmission, as any eavesdropping attempt would be detectable. We propose a novel architecture where quantum teleportation facilitates the secure exchange of model parameters and gradients among clients and servers. This integration aims to mitigate risks associated with data leakage and adversarial attacks inherent in classical federated learning setups. We also discuss the practical challenges of implementing such a system, including the current limitations of quantum network infrastructure and the need for hybrid quantum-classical protocols. Our analysis suggests that, despite these challenges, the convergence of quantum communication technologies and federated learning presents a promising avenue for achieving unprecedented levels of privacy in distributed machine learning.