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arXiv:2512.10584

Volatility time series modeling by single-qubit quantum circuit learning

Tetsuya Takaishi

Published Dec 11, 2025• 0 citations
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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.

DOI
10.48550/arxiv.2512.10584

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Quantum circuit learning (QCL) is a hybrid quantum-classical machine learning technique designed for noisy intermediate-scale quantum (NISQ) devices. In QCL, classical data are encoded into quantum states and processed through parameterized quantum gates, and the resulting quantum measurement outcomes are used to optimize circuit parameters via classical optimization algorithms for machine learning. Sparse identification of nonlinear dynamics (SINDy) is a method for estimating classical nonlinear dynamical systems from time series data. In SINDy, system dynamics is approximately represented as a linear combination of a predefined set of basis functions, with their coefficients sparsely estimated from the time-series data. In this study, we propose sparse identification of quantum Hamiltonian dynamics (SIQHDy), a SINDy-inspired quantum circuit learning algorithm for estimating quantum Hamiltonian dynamics from time-series data. In SIQHDy, quantum Hamiltonian dynamics is approximately represented as a product of basis quantum circuits, with their parameters sparsely estimated from time-series data of quantum measurement outcomes. We numerically demonstrate that SIQHDy can successfully estimate the dynamics of single-, two-, and five-qubit systems and that the advantage of sparsity becomes evident when using time-series data with measurement noise.
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Quantum computing promises a paradigm shift in computational power. However, a major challenge is mitigating the inherent noise and errors in quantum circuits. As quantum computers operate, their fragile qubits are highly susceptible to environmental disturbances, leading to errors that affect the outcomes of repeated circuit executions. Understanding and predicting these errors is crucial for improving the accuracy and reliability of quantum computing systems. In this work, we analyze and predict the output patterns of a single qubit quantum circuit by treating the results of repeated executions as a time series. Specifically, we collect measurement data from multiple runs of a quantum circuit and construct a time series from these observations. By training a predictive model, we aim to forecast future outcomes, providing insights into the error behavior of the quantum circuit. Additionally, we analyze time series data from two different circuits executed on the same qubit to investigate potential relationships and assess whether one dataset can be used to predict the other. Our findings reveal key characteristics of quantum circuit outputs, including stationarity, autocorrelation, seasonality, trends, linearity, and causality. The analysis highlights intriguing behaviors within the dataset. Furthermore, we evaluate multiple time series prediction methods and determine that XGBoost (Extreme Gradient Boosting) outperforms other approaches, demonstrating its effectiveness in accurately predicting quantum computing outputs in subsequent runs.
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