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arXiv:2209.04888 · Physical Review Letters

Communication-Efficient Quantum Algorithm for Distributed Machine Learning

Hao Tang, Boning Li, Guoqing Wang, Haowei Xu, Changhao Li, Ariel Barr, Paola Cappellaro, Ju Li

Published Apr 12, 2023• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.130.150602

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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.
Linear regression is fundamental to statistical analysis and machine learning, but its application to large-scale datasets necessitates distributed computing. The problem also arises in quantum computing, where handling extensive data requires distributed approaches. This paper investigates distributed linear regression in the quantum coordinator model. Building upon the distributed quantum least squares protocol developed by Montanaro and Shao, I propose improved and extended quantum protocols for solving both ordinary (unregularized) and L2-regularized (Tikhonov) least squares problems. For ordinary least squares methods, my protocol reduces the quantum communication complexity compared to the previous protocol. In particular, this yields a quadratic improvement in the number of digits of precision required for the generated quantum states. This improvement is achieved by incorporating advanced techniques such as branch marking and branch-marked gapped phase estimation developed by Low and Su. Furthermore, I establish a setting for theℓ2\ell _{2}ℓ2​-regularized least squares problem specifically in the quantum coordinator model and derive its quantum communication complexity. I analyze the effect of regularization parameters on the quantum communication complexity.
This paper explores the potential of utilizing quantum error correction (QEC) codes to address the challenges of optimization within distributed machine learning (DML) systems. Traditional DML frameworks are susceptible to communication noise, leading to errors in the optimization process and ultimately impacting the quality of the learned models. This work proposes a novel approach where QEC codes are leveraged to correct these errors during information transmission between distributed nodes. The core concept hinges on decomposing the machine learning task across multiple nodes and employing QEC to ensure the accurate propagation of information, thereby enhancing the robustness and efficiency of the optimization process. We present a theoretical framework outlining the implementation and demonstrate the potential for significant improvements in DML performance compared to conventional methods, particularly in environments with high communication noise. The key innovation lies in directly applying the error correction capabilities of QEC to the communication channel, rather than relying on post-processing techniques. This offers a fundamentally different approach with the potential to unlock the benefits of DML in scenarios previously limited by communication constraints.
The quantum internet aims to interconnect distant devices and enable large-scale computation through distributed quantum algorithms. One of the key obstacles is communication latency during computation. Even separations of a few hundred kilometers introduce millisecond-scale delays, which exceed the coherence times of many solid-state qubit platforms. In contrast, entanglement can be established beforehand and used as a practical resource to reduce communication complexity between remote nodes. Here we examine the utility of entanglement in distributed quantum machine learning for binary classification tasks. Drawing an analogy with the CHSH game, we show that entanglement improves classification accuracy across all datasets considered. We also find that excessive entanglement may degrade performance by reducing the effective dimension of the parameter space. This highlights the importance of using an appropriate amount and structure of entanglement in data embedding. Our findings bridge nonlocality and machine-learning advantage, providing a pathway toward distributed quantum computation beyond coherence-time constraints.
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.
This paper proposes a novel approach to distributed machine learning leveraging the unique properties of quantum decoherence. The core idea is to utilize the controllable rate of decoherence in quantum systems to facilitate information exchange and learning between distributed nodes. This allows for the construction of an algorithm that, under specific conditions, can converge towards a global optimum. Unlike traditional distributed machine learning methods reliant on classical information, this approach incorporates quantum mechanics, potentially leading to significant improvements in learning efficiency. The algorithm hinges on carefully managing decoherence, treating it not as a detrimental effect but as a mechanism for controlled information transfer. We present a theoretical framework for this method, detailing the mathematical formalism and outlining the key steps involved in the distributed learning process. The presented method aims to address the limitations of current distributed learning approaches, particularly in scenarios involving large datasets and complex models, by harnessing the inherent parallelism and potential for quantum speedup. Further research will focus on practical implementation challenges and exploring the algorithm's performance across various network topologies and machine learning tasks.
This paper explores the potential of leveraging quantum entanglement and decoherence for distributed machine learning (DML). Traditional DML faces limitations regarding scalability and robustness due to communication overhead and susceptibility to errors. We propose a novel algorithm that utilizes the inherent properties of quantum entanglement to facilitate information sharing between distributed quantum nodes while simultaneously harnessing the effects of decoherence to introduce a degree of error correction. The core idea is to decompose a machine learning task into sub-problems solved independently by each node. Quantum entanglement ensures correlation between node states, and controlled decoherence is employed to dynamically adjust the correlations, mitigating the impact of noise. We present a mathematical framework outlining the algorithm's operation, including the key equations governing the entanglement distribution, decoherence dynamics, and the iterative learning process. This approach offers a promising pathway toward more efficient and resilient DML systems, potentially surpassing the capabilities of classical methods in specific scenarios. The primary contributions of this work lie in the conceptual design and the formalization of the algorithm, laying the groundwork for future experimental investigations.