AI 中文总结
研究针对篮子期权定价中量子幅度估计受态制备电路深度限制的问题，提出基于张量列车秩信息的结构感知量子态制备框架，设计浅变分电路，能线性缩放态制备深度，保持低定价误差，还兼容相关训练和定价工作流程。
AI 中文摘要
篮子期权定价通常依赖蒙特卡罗估计，量子幅度估计（QAE）能实现二次加速。但QAE的实际效益受限于态制备电路的深度。我们提出了一种用于基于QAE的篮子期权定价的结构感知量子态制备框架。该框架利用张量列车（TT）秩信息设计浅变分态制备电路。在独立情况下，TT秩从硬件高效的量子态模板中去除不必要的纠缠链接。在相关篮子设置中，我们在本地制备资产边际并训练一个紧凑的潜在块以匹配篮子累积分布函数。篮子CDF目标针对篮子前推分布而非完整联合态，使态制备与篮子依赖收益直接对齐。数值实验表明，所提出的电路将精确幅度加载的指数态制备深度缩放替换为线性缩放，同时保持低百分比的篮子定价误差。额外的基于采样的训练实验和端到端QAE集成研究支持与样本估计训练和基于标准QAE的定价工作流程的兼容性。
英文摘要
Basket option pricing often relies on Monte Carlo estimation, for which quantum amplitude estimation (QAE) provides a quadratic speed-up. However, the practical benefit of QAE can be limited by the depth of the state-preparation circuit. We propose a structure-aware quantum state-preparation framework for QAE-based basket option pricing. The framework uses tensor-train (TT) rank information to design shallow variational state-preparation circuits. In the independent regime, TT ranks remove unnecessary entangling links from a hardware-efficient ansatz. In correlated basket settings, we instead prepare asset-wise marginals locally and train a compact latent block to match the basket cumulative distribution function. The Basket-CDF objective targets the basket pushforward distribution rather than the full joint state, directly aligning state preparation with basket-dependent payoffs. Numerical experiments show that the proposed circuits replace the exponential state-preparation depth scaling of exact amplitude loading with linear scaling, while maintaining low-percent basket-pricing errors. Additional sampling-based training experiments and an end-to-end QAE integration study support compatibility with sample-estimated training and standard QAE-based pricing workflows.
Comments39 pages, 8 figures, 6 tables
