Quantum Circuit Learning for Bitcoin Realized Volatility Dynamics

Summary

This study models Bitcoin realized volatility with a parameterized quantum circuit and examines whether the generated series reflects statistical features observed in market data. From five-minute Bitcoin prices, the authors calculate daily realized volatility, train a single-qubit circuit, and use it to generate a long synthetic series. They apply Multifractal Detrended Fluctuation Analysis to study scaling behavior, including generalized Hurst exponents, multifractal spectra, and scaling exponents.

The predicted return series has a second-order Hurst exponent near one half, consistent with near-random dynamics. Both predicted and empirical returns show multifractality that remains partly after shuffling, while realized-volatility increments are strongly anti-persistent, in line with the rough-volatility hypothesis. The results suggest qualitative capture of selected Bitcoin volatility properties. The document does not report forecasting accuracy against conventional models or evidence of trading profitability, and its conclusions concern a simple circuit and one asset.

Key ideas

• A single-qubit parameterized quantum circuit is trained to model Bitcoin realized volatility.
• Daily realized volatility is constructed from five-minute Bitcoin prices.
• Multifractal detrended fluctuation analysis assesses properties of the generated series.
• Predicted returns appear near-random by the reported second-order Hurst exponent and retain partial multifractality after shuffling.
• Realized-volatility increments exhibit pronounced anti-persistence, consistent with rough volatility.

Tags

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


# 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 $h(2)\approx 0.5$, 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 $h(2)\approx 0.05$--$0.1$, 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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.