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

arXiv: https://arxiv.org/abs/2406.01335 · HTML: https://mlsanity.com/paper/2406.01335/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 51 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Builds on (most cited first, 9 of 9)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Nonlinear transformation of complex amplitudes via quantum singular value transformation](https://mlsanity.com/paper/2107.10764/) (2021)
- [Quantum Expectation-Maximization for Gaussian Mixture Models](https://mlsanity.com/paper/1908.06657/) (2019)
- [Efficient phase-factor evaluation in quantum signal processing](https://mlsanity.com/paper/2002.11649/) (2020)

## Abstract (arXiv)

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.