Quantum Circuit Learning for Volatility Modeling: Multifractal Analysis of Realized Volatility Time Series

Herein, we propose a quantum circuit learning framework for modeling the realized volatility (RV) of Bitcoin and investigate the statistical properties of the predicted time series through multifractal analysis. Unlike conventional GARCH-type models, which require a pre-specified functional form for the volatility process, a parameterized quantum circuit directly approximates the volatility function from empirical data, eliminating the need for explicit model selection. Using five-minute Bitcoin price data, we construct daily RV, train a single-qubit parameterized quantum circuit, and generate a long synthetic time series from the optimized quantum circuit. Multifractal Detrended Fluctuation Analysis is applied to calculate the generalized Hurst exponent h(q), the singularity spectrum f(α), and the multifractal scaling exponent τ(q). The predicted return series exhibits h(2)≈0.5, consistent with near-random dynamics, and both the predicted and the empirical return series display multifractality that partially persists after random shuffling. The increment series of RV shows pronounced anti-persistence with h(2)≈0.05–0.1, consistent with the rough volatility hypothesis. These results demonstrate that a simple single-qubit parameterized quantum circuit captures qualitatively some observed properties in Bitcoin volatility dynamics.