Volatility time series modeling by single-qubit quantum circuit learning

ArXiv ID: 2512.10584 “View on arXiv”

Authors: Tetsuya Takaishi

Abstract

We employ single-qubit quantum circuit learning (QCL) to model the dynamics of volatility time series. To assess its effectiveness, we generate synthetic data using the Rational GARCH model, which is specifically designed to capture volatility asymmetry. Our results show that QCL-based volatility predictions preserve the negative return-volatility correlation, a hallmark of asymmetric volatility dynamics. Moreover, analysis of the Hurst exponent and multifractal characteristics indicates that the predicted series, like the original synthetic data, exhibits anti-persistent behavior and retains its multifractal structure.

Keywords: Quantum Circuit Learning, Volatility Modeling, GARCH, Hurst Exponent, Multifractal Analysis, Equities (Volatility)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats
• Why: The paper involves dense mathematical notation, including quantum circuit parameters and statistical models like RGARCH, indicating high math complexity. However, the empirical rigor is limited due to the use of synthetic data and a focus on theoretical property preservation rather than backtesting on real market data.

  flowchart TD
    A["Research Goal: Model Volatility Dynamics using QCL"] --> B{"Methodology: Single-Qubit QCL vs Rational GARCH"}
    B --> C["Synthetic Data Generation: Rational GARCH Model"]
    C --> D["Computational Process: QCL Training & Prediction"]
    D --> E{"Key Outcomes & Analysis"}
    E --> F["Prediction preserves negative return-volatility correlation<br/>(Asymmetric Volatility)"]
    E --> G["Prediction exhibits anti-persistent Hurst Exponent"]
    E --> H["Prediction retains Multifractal structure"]