# Exponential Quantum Communication Advantage in Distributed Inference and Learning

arXiv: https://arxiv.org/abs/2310.07136 · HTML: https://mlsanity.com/paper/2310.07136/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 119 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [PaLM-E: An Embodied Multimodal Language Model](https://mlsanity.com/paper/2303.03378/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [TPU v4: An Optically Reconfigurable Supercomputer for Machine Learning with Hardware Support for Embeddings](https://mlsanity.com/paper/2304.01433/) (2023)
- [DropGNN: Random Dropouts Increase the Expressiveness of Graph Neural Networks](https://mlsanity.com/paper/2111.06283/) (2021)
- [GSPMD: General and Scalable Parallelization for ML Computation Graphs](https://mlsanity.com/paper/2105.04663/) (2021)
- [On the Expressive Power of Deep Learning: A Tensor Analysis](https://mlsanity.com/paper/1509.05009/) (2015)
- [Pathways: Asynchronous Distributed Dataflow for ML](https://mlsanity.com/paper/2203.12533/) (2022)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Inductive Bias of Deep Convolutional Networks through Pooling Geometry](https://mlsanity.com/paper/1605.06743/) (2016)
- [A Linearly-Convergent Stochastic L-BFGS Algorithm](https://mlsanity.com/paper/1508.02087/) (2015)
- [Online Learning of Quantum States](https://mlsanity.com/paper/1802.09025/) (2018)
- [On quantum backpropagation, information reuse, and cheating measurement collapse](https://mlsanity.com/paper/2305.13362/) (2023)
- [Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms](https://mlsanity.com/paper/1901.05374/) (2019)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [Stochastic Block BFGS: Squeezing More Curvature out of Data](https://mlsanity.com/paper/1603.09649/) (2016)

## Built on by (most cited first, 3 of 3)

- [Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage](https://mlsanity.com/paper/2507.19861/) (2025)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Quantum ring all-reduce: communication and privacy advantages for distributed learning](https://mlsanity.com/paper/2606.20344/) (2026)

## Abstract (arXiv)

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.