AI 中文总结
本研究提出量子电路学习框架，利用单量子比特参数化量子电路建模比特币已实现波动率，经多重分形分析验证其可捕捉比特币波动率动态的部分关键特性。
AI 中文摘要
本文提出一种用于对比特币已实现波动率（RV）建模的量子电路学习框架，并通过多重分形分析研究预测时间序列的统计特性。与需要预先指定波动率过程函数形式的传统GARCH类模型不同，参数化量子电路可直接从经验数据近似波动率函数，无需显式模型选择。利用五分钟间隔的比特币价格数据构建日度RV，训练一个单量子比特参数化量子电路，并从优化后的量子电路生成长合成时间序列。采用多重分形去趋势波动分析计算广义赫斯特指数$h(q)$、奇异性谱$f(\alpha)$及多重分形标度指数$\tau(q)$。预测收益率序列的$h(2)\approx0.5$，接近随机动态；预测序列与经验序列均呈现多重分形性，且随机打乱后部分保留。RV增量序列表现出明显反持续性，$h(2)\approx0.05$--$0.1$，符合粗糙波动率假说。上述结果表明，简单的单量子比特参数化量子电路能够定性捕捉比特币波动率动态的部分观测特性。
英文摘要
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.
Comments26 figures
Journal refFractal Fractional. 2026, 10(7), 442
DOI：10.3390/fractalfract10070442
