对比四类时间序列模型,发现量子模型暂无优势。
Variational Quantum Conditional Boltzmann Machines for Time-Series Forecasting: Architectures, Symmetric Hyperparameter Evaluation, and a Nonlinear Benchmark

- 设计四类能量模型,含量子与混合架构,完整推导条件分布与训练梯度。
- 在金融模拟与非线性基准上,量子模型均未超越最优经典模型。
- 对称超参调优与同预算对比均显示量子无显著优势,小优势仍可能存。
本研究构建并评估了四种条件能量基预测架构:经典高斯-伯努利CRBM、混合量子-经典QCRBM、全寄存器QQRBM,以及带滞后特征的QFeatureQRBM。完整推导其条件分布、对比散度梯度与混合训练方法,衔接能量基理论与量子计算实现。不同于以往研究,本评估采用对称超参优化:对经典与量子特有超参进行同等程度的网格搜索,覆盖十三组结构化实验。测试数据包括基于真实金融数据生成的高斯过程(GP)数据集和输入驱动的NARMA-10非线性基准。在两类数据上均未发现系统性量子优势:所有量子架构均未能超越最优经典基线。全量子的QQRBM与QFeatureQRBM表现显著更差;而混合的QCRBM在两个数据集上与最强经典CRBM统计无差异。功效分析表明,在样本量n=12时仅能检测中等至大效应,小优势无法排除。同参数预算比较亦得相同结论:经典CRBM在四个预算中的三个最低,且任意预算下CRBM与QCRBM无显著差异。
原文摘要 · Abstract (English)
In this study, we developed and evaluated four conditional energy-based forecasting architectures: a classical Gaussian-Bernoulli CRBM, a hybrid quantum-classical QCRBM, a full-register QQRBM, and a lag-feature QFeatureQRBM with complete derivations of their conditional distributions, Contrastive-Divergence gradients, and hybrid training, bridging the energy-based formulation and the implementation-level quantum computation. Unlike prior comparisons, our evaluation enforces symmetric hyperparameter optimisation: classical and quantum-specific hyperparameters receive an equally thorough grid search across thirteen structured experiments. We test on two data classes, a Gaussian-process dataset (GP) generated with real financial data and the input-driven NARMA-10 nonlinear benchmark. Across both regimes we find no systematic evidence of a quantum advantage at the available sample size: no quantum architecture improves on the best classical baseline. The fully quantum QQRBM and QFeatureQRBM are significantly worse, whereas the hybrid QCRBM is statistically indistinguishable from the strongest classical CRBM on both datasets. A power analysis bounds this null result: at n = 12 only medium-to-large effects are detectable, so small advantages cannot be excluded. An iso-parameter (matched-budget) comparison reaches the same conclusion: the classical CRBM is lowest at three of the four budgets and no CRBM-vs-QCRBM difference is significant at any budget.
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