Quantum machine learning has demonstrated significant potential in solving practical problems, particularly in statistics-focused areas such as data science and finance. However, challenges remain in preparing and learning statistical models on a quantum processor due to issues with trainability and interpretability. In this letter, we utilize the maximum entropy principle to design a statistics-informed parameterized quantum circuit (SI-PQC) for efficiently preparing and training of quantum computational statistical models, including arbitrary distributions and their weighted mixtures. The SI-PQC features a static structure with trainable parameters, enabling in-depth optimized circuit compilation, exponential reductions in resource and time consumption, and improved trainability and interpretability for learning quantum states and classical model parameters simultaneously. As an efficient subroutine for preparing and learning in various quantum algorithms, the SI-PQC addresses the input bottleneck and facilitates the injection of prior knowledge.

翻译：量子机器学习在解决实际问题方面展现出巨大潜力，尤其在数据科学与金融等统计密集型领域。然而，由于可训练性与可解释性方面的挑战，在量子处理器上制备和学习统计模型仍存在困难。本文利用最大熵原理设计了一种统计信息参数化量子电路（SI-PQC），用于高效制备和训练量子计算统计模型，包括任意分布及其加权混合。该SI-PQC采用具有可训练参数的静态结构，支持深度优化的电路编译，实现资源与时间消耗的指数级降低，并在同步学习量子态与经典模型参数时提升可训练性与可解释性。作为各类量子算法中用于制备与学习的高效子程序，SI-PQC解决了输入瓶颈问题，并促进了先验知识的注入。