这篇论文教你用更省事的核函数解决量子优化问题，省计算省样本，还能量化精度损失，做量子控制或VQA的人值得看看。
该论文研究量子核诱导的高斯过程（GP）Bandit优化问题，假设均值奖励函数位于量子核的RKHS中。针对NISQ时代任务（如量子控制、状态制备），作者指出全量子核因高维度过高导致信息增益大、累积遗憾高。他们提出投影量子核和经典核近似技术，降低特征维度同时保留关键量子性质。基于近似核开发的误指定GP Bandit算法，推导出遗憾界以权衡近似误差与信息增益。实验表明，该方法在样本效率上超越全量子核，并显著降低计算开销。
Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization
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.