Optimal quantum dataset for learning a unitary transformation

本研究聚焦于量子机器学习中的一个基本问题：如何高效学习一个酉变换。数据集'Optimal quantum dataset for learning a unitary transformation'由百度研究院量子计算研究所创建，旨在解决量子酉变换学习的最小数据集大小问题。该数据集包含n+1个基本张量积状态，足以进行精确训练，通过利用解耦简化了结构，从而在纯状态数据集大小上实现了指数级的改进。此外，数据集大小可减少至常数，为学习酉变换提供了最优量子数据集。应用领域包括量子模拟和量子编译，展示了在混合量子-经典算法框架下的实际应用效果。

This study focuses on a fundamental problem in quantum machine learning: how to efficiently learn a unitary transformation. The dataset titled 'Optimal quantum dataset for learning a unitary transformation' was created by the Quantum Computing Institute of Baidu Research, aiming to address the minimal dataset size problem for quantum unitary transformation learning. This dataset contains n+1 basic tensor product states, which is sufficient for exact training. Its structure is simplified by utilizing decoupling, achieving exponential improvements in the size of pure-state datasets. Furthermore, the dataset size can be reduced to a constant, providing an optimal quantum dataset for unitary transformation learning. Its application fields include quantum simulation and quantum compilation, demonstrating practical application effects under the hybrid quantum-classical algorithm framework.