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

ArXiv ID: 2406.01335 “View on arXiv”

Authors: Unknown

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.

Keywords: Quantum Machine Learning, Maximum Entropy Principle, Parameterized Quantum Circuits, Statistical Modeling, Quantum Finance, General Finance (Quantum Algorithms)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is highly mathematically dense, featuring advanced quantum physics principles (maximum entropy), linear algebra, and circuit complexity theorems, placing it firmly in the high math quadrant. However, it lacks any actual backtesting, dataset usage, or financial implementation metrics; the empirical evidence is limited to numerical simulations on standard distributions, making it a theoretical lab experiment rather than a street-ready strategy.

  flowchart TD
    A["Research Goal: Develop a<br>trainable and interpretable<br>Quantum Circuit for<br>Statistical Modeling"] --> B["Key Methodology:<br>Maximum Entropy Principle"]
    B --> C["Data Inputs:<br>Statistical Data &<br>Prior Knowledge"]
    C --> D["Computational Process:<br>Statistics-Informed<br>Parameterized Quantum Circuit<br>(SI-PQC)"]
    D --> E["Key Findings:<br>Efficient Preparation &<br>Training of Quantum States"]
    D --> F["Key Findings:<br>Exponential Resource<br>Reduction"]
    D --> G["Key Findings:<br>Simultaneous Learning of<br>Quantum & Classical<br>Parameters"]