发表机构
Centre of Finance DHBW Stuttgart; Zentrum für Digitale Innovationen DHBW Ravensburg; DATEV eG（德国双应用科技大学斯图加特分校金融中心; 德国双应用科技大学拉芬斯堡分校数字创新中心; DATEV 合作社）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究开发并评估四种用于时间序列预测的架构，通过对称超参数优化在两个数据集测试，发现当前样本量下无量子优势证据，经典CRBM表现良好，混合QCRBM与最强经典CRBM无显著差异，还通过分析得出相关结论。
AI 中文摘要
在本研究中，我们开发并评估了四种基于条件能量的预测架构：经典高斯 - 伯努利CRBM、混合量子 - 经典QCRBM、全寄存器QQRBM和具有滞后特征的QFeatureQRBM，并完整推导了它们的条件分布、对比散度梯度和混合训练，将基于能量的公式与实现级量子计算联系起来。与之前的比较不同，我们的评估实施对称超参数优化，在13个结构化实验中对经典和量子特定超参数进行同样全面的网格搜索。我们在两个数据集上进行测试，一个由真实金融数据生成的高斯过程数据集（GP）和输入驱动的NARMA - 10非线性基准。在这两种情况下，在可用样本量下没有发现量子优势的系统证据：没有量子架构比最佳经典基线有所改进。完全量子的QQRBM和QFeatureQRBM明显更差，而混合QCRBM在两个数据集上与最强的经典CRBM在统计上没有区别。功效分析限制了这个零结果：在n = 12时，只能检测到中等到大的效应，所以不能排除小的优势。等参数（匹配预算）比较得出相同结论：经典CRBM在四个预算中的三个最低，并且在任何预算下CRBM与QCRBM之间的差异都不显著。
英文摘要
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.
Comments45 pages
