Statistics-Informed Parameterized Quantum Circuit via Maximum Entropy Principle for Data Science and Finance

TL;DR

This paper introduces a statistics-informed parameterized quantum circuit designed using the maximum entropy principle, enhancing efficiency, trainability, and interpretability for data science and finance applications in quantum machine learning.

Contribution

It proposes a novel SI-PQC framework that integrates prior statistical knowledge, reduces resource consumption, and improves model training and interpretability on quantum processors.

Findings

Exponential reduction in resource and time consumption.

Enhanced trainability and interpretability of quantum models.

Effective preparation of arbitrary distributions and mixtures.

Abstract

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.