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Moth（Moth）
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研究量子数据重新上传分类器中傅里叶锁定问题，指出其是优化瓶颈。通过两种费舍尔诊断表征，实验发现锁定现象及频谱迁移率等情况。提出频率分级同伦协议调整频率，解决傅里叶锁定问题，提高逃逸率。
AI 中文摘要
数据重新上传参数化量子电路（DRU-PQC）是通用函数逼近器，但其表现力会产生振荡的、非凸的损失景观，阻碍基于梯度的优化。我们表明，DRU-PQC中的主要优化瓶颈不是能力不足，而是一种我们称为傅里叶锁定（FL）的结构故障模式：由于编码权重和纠缠层是非线性耦合的，高频目标上的随机初始化会使编码参数陷入虚假的局部最小值。两种费舍尔诊断方法可表征FL。输入空间量子费舍尔信息$F_x$测量编码状态的有效频率内容；测量特征的费舍尔判别比测量它们与类标签的对齐程度。在两个独立的50种子实验中，锁定是实实在在的：被困电路在整个运行过程中使$F_x$保持冻结，而逃逸电路会迁移其频率内容（直接训练：$r_{pb} = -0.48$；课程学习：$d = 1.34$；两者$p < 0.001$）。复制的特征是这种频谱迁移率，而不是$F_x$的任何端点值，并且被困电路保留完全非退化的参数空间量子费舍尔信息矩阵（$r_{pb} \approx 0$）：失败是响应状态的频谱未对齐，而不是几何灵敏度的丧失。一种频率分级同伦协议，对目标频率进行调整（$f: 1.0 \to 3.0$），使早期损失景观凸化；逃逸电路随着课程学习提高$F_x$，逃逸率增加两倍（18%对6%）。傅里叶锁定是一个频率对齐问题，其补救方法是频率调整。
英文摘要
Data re-uploading parameterized quantum circuits (DRU-PQCs) are universal function approximators, yet their expressivity produces oscillatory, non-convex loss landscapes that resist gradient-based optimization. We show that the primary optimization bottleneck in DRU-PQCs is not insufficient capacity but a structural failure mode we term Fourier locking (FL): because encoding weights and entangling layers are nonlinearly coupled, random initialization on high-frequency targets collapses the encoding parameters into spurious local minima. Two Fisher diagnostics characterize FL. The input-space quantum Fisher information $F_x$ measures the effective frequency content of the encoded state; the Fisher discriminant ratio of the measured features measures their alignment with the class labels. In two independent 50-seed experiments, the locking is literal: trapped circuits hold $F_x$ frozen for the entire run, while escaping circuits migrate their frequency content (direct training: $r_{pb} = -0.48$; curriculum: $d = 1.34$; both $p < 0.001$). The replicated signature is this spectral mobility, not any endpoint value of $F_x$, and trapped circuits retain a fully non-degenerate parameter-space QFIM ($r_{pb} \approx 0$): the failure is spectral misalignment of a responsive state, not a loss of geometric sensitivity. A frequency-staged homotopy protocol that paces the target frequency ($f: 1.0 \to 3.0$) convexifies the early loss landscape; escaping circuits raise $F_x$ in step with the curriculum, and the escape rate triples (18% vs. 6%). Fourier locking is a frequency-alignment problem, and its remedy is frequency pacing.
Comments14 pages, 5 figures, 1 table. Submitted to PRX Quantum. Code and data: https://github.com/moth-quantum/fourier_locking_study. ORCID: 0009-0000-0081-9786
