用压缩量子核提升量子优化的效率与可学习性
Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization
- 用投影与经典近似降低量子核维度，减少模型复杂度
- 实测在样本效率上优于完整量子核，且计算开销大幅下降
- 适合需要高效量子控制或变分量子算法的科研人员
我们研究基于量子核的高斯过程（GP）贝叶斯优化，假设平均收益函数位于由量子核诱导的再生核希尔伯特空间（RKHS）中。该设定源于含噪声中等规模量子（NISQ）时代的任务，如量子控制、态制备和变分量子算法。尽管量子核可通过领域特定归纳偏置实现‘量子优势’，但直接使用全维高维核会增加模型复杂度和信息增益，导致累积遗憾升高、学习性能下降。为此，我们提出投影量子核与经典核近似技术，在保留关键量子特性的同时降低特征维度。利用这些近似核，我们构建了非匹配高斯过程贝叶斯优化算法，并推导出关于近似误差与信息增益权衡的遗憾界。该遗憾界为最优模型复杂度选择提供了理论指导。实验表明，所提方法在样本效率上优于完整量子核，同时显著降低计算开销，使量子原生应用的可扩展高斯过程优化成为可能。
原文摘要 · Abstract (English)
We investigate Gaussian process (GP) bandit optimization with quantum kernels, assuming the mean reward function lies in the reproducing kernel Hilbert space (RKHS) induced by the quantum kernel. This setting is motivated by NISQ-era tasks such as quantum control, state preparation and variational quantum algorithms. While quantum kernels can offer a `quantum advantage' via domain-specific inductive biases, naïvely using full, high-dimensional kernels increases model complexity and information gain, leading to higher cumulative regret and poor learnability. To address this, we propose projected quantum kernels and classical kernel approximation techniques that reduce feature dimensionality while preserving key quantum properties. Using these approximate kernels, we develop misspecified GP bandit algorithms and derive regret bounds that characterize the trade-off between approximation error and information gain. The regret bounds provide principled guidance for selecting the optimal model complexity. Empirically, our methods outperform full quantum kernels in sample efficiency, while substantially reducing computational overhead, enabling scalable GP optimization for quantum-native applications.
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