量子优势在无监督学习中受限于数据与目标可观测量的依赖性
Limitations of Quantum Advantage in Unsupervised Machine Learning
- 用量子密度矩阵替代经典概率分布，探索量子优势
- 量子优势仅在特定数据和可观测量下存在，非普遍适用
- 对数据挖掘与传感应用有重要启示，适合关注量子优势边界的研究者
机器学习模型用于无需人工干预的大数据分析中的模式识别。无监督学习的目标是找到能最好描述已有数据的概率分布，并据此预测感兴趣的可观测量。经典模型通常将数据拟合到具有大量可调参数的哈密顿量的玻尔兹曼分布。量子扩展模型则用量子密度矩阵替代经典概率分布。只有当利用了经典概率分布所不具备的密度矩阵特征时，才能获得优势。这种优势取决于输入数据及目标可观测量。文中通过具体例子揭示了量子优势的限制。问题依赖性的量子优势程度对数据分析和传感应用具有重要意义。
原文摘要 · Abstract (English)
Machine learning models are used for pattern recognition analysis of big data, without direct human intervention. The task of unsupervised learning is to find the probability distribution that would best describe the available data, and then use it to make predictions for observables of interest. Classical models generally fit the data to Boltzmann distribution of Hamiltonians with a large number of tunable parameters. Quantum extensions of these models replace classical probability distributions with quantum density matrices. An advantage can be obtained only when features of density matrices that are absent in classical probability distributions are exploited. Such situations depend on the input data as well as the targeted observables. Explicit examples are discussed that bring out the constraints limiting possible quantum advantage. The problem-dependent extent of quantum advantage has implications for both data analysis and sensing applications.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。