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 certain 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 time and space complexity overheads relative to standard gradient-based methods. To our knowledge, this is the first example of exponential quantum advantage for a generic class of machine learning problems with dense classical data that holds 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 find that, interestingly, the communication advantage nearly vanishes for simpler linear classifiers. These 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.

翻译：随着大型机器学习模型的规模远超单个设备的内存容量，分布式架构的设计成为必要，但必须应对通信约束问题。我们提出了一种量子网络上的分布式计算框架，其中数据被编码为专门的量子态。我们证明，在该框架内的某些模型中，利用梯度下降进行推理和训练所需的通信量相比经典对应方法呈现指数级减少，且相对于标准梯度方法，时间和空间复杂度开销较为适中。据我们所知，这是首个针对通用类机器学习问题（包含密集经典数据）的指数级量子优势实例，该优势与数据编码成本无关。此外，我们表明这类模型能够编码输入的高度非线性特征，且其表达能力随模型深度呈指数级增长。有趣的是，我们还发现对于更简单的线性分类器，通信优势几乎消失。这些结果可与通信量子态中固有的隐私优势相结合，限制从中提取关于数据和模型参数的信息量。总体而言，这些发现为量子网络上的分布式机器学习奠定了有前景的基础。