📄 中文摘要
量子机器学习模型通过角度编码自然地表示截断的傅里叶级数，具备足够电路深度时提供通用函数逼近能力。对于一元固定频率编码，电路深度与目标频率幅度ω_max和精度ε的关系为O(ω_max * (ω_max + ε^{-2}))。可训练频率的方法理论上将这一复杂度降低至与目标频谱大小相匹配，仅需与目标频谱中的频率数量相同的编码门。尽管这种效率令人信服，其实际有效性依赖于一个关键假设：基于梯度的优化能够将前因子驱动至任意目标值。通过系统实验，展示了这一假设的局限性。
量子机器学习中的长距离频率调谐
出处: Long Range Frequency Tuning for QML
发布: 2026年3月2日
📄 English Summary
Long Range Frequency Tuning for QML
Quantum machine learning models utilizing angle encoding inherently represent truncated Fourier series, offering universal function approximation capabilities with sufficient circuit depth. For unary fixed-frequency encodings, the circuit depth scales as O(ω_max * (ω_max + ε^{-2})) with respect to the target frequency magnitude ω_max and precision ε. Trainable-frequency approaches theoretically reduce this complexity to align with the target spectrum size, requiring only as many encoding gates as there are frequencies in the target spectrum. Despite this compelling efficiency, their practical effectiveness relies on a key assumption: that gradient-based optimization can drive prefactors to arbitrary target values. Systematic experiments demonstrate the limitations of this assumption.