发表机构
Yau Mathematical Sciences Center, Tsinghua University; Institute for Applied Mathematics, Tsinghua University; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（丘成桐数学科学中心; 应用数学研究所; 北京雁栖湖应用数学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种无后选择的量子自动学习算法，通过将训练路径组织为相干量子电路并采用固定点振幅放大，提高获得学习模型的概率，并提供理论保证与资源成本分析。
AI 中文摘要
量子自动学习（QAL）通过直接更新量子态来训练量子模型，提供了一种避免优化变分电路参数的量子机器学习方法。然而，后选择限制了获得最终学习模型的概率。我们开发了一种无后选择的QAL算法，该算法将完整的训练路径组织成连贯的量子电路，并使用固定点振幅放大来提高获得学习模型的概率。我们提供了关于输出误差和学习损失的理论保证，并确定了在何种条件下，额外的相干资源可以降低重启失败轨迹的成本。该构造为QAL提供了具有明确学习保证和资源成本的相干实现，使得能够以高概率获得具有认证学习质量和受控输出误差的模型。
英文摘要
Quantum automated learning (QAL) trains quantum models by directly updating quantum states, offering an approach to quantum machine learning that avoids optimizing variational circuit parameters. However, post-selection constrains the probability of obtaining the final learned model. We develop a post-selection-free QAL algorithm that organizes a complete training path into a coherent quantum circuit and uses fixed-point amplitude amplification to increase the probability of obtaining the learned model. We provide theoretical guarantees on output error and learning loss, and identify conditions under which additional coherent resources reduce the cost of restarting failed trajectories. The construction gives QAL a coherent implementation with explicit learning guarantees and resource costs, enabling a model with certified learning quality and controlled output error to be obtained with high probability.
Comments16 pages, 7 figures
