Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization

2026-07-01

AI Summary

This work addresses the challenges posed by high-dimensional full quantum kernels, which, despite their strong expressive power, often lead to excessive model complexity, poor learnability, and large cumulative regret in Gaussian process bandit optimization. To mitigate these issues, the authors propose an efficient approximation method that combines projected quantum kernels with classical kernel approximations, preserving essential quantum characteristics while enabling a misspecified Gaussian process bandit algorithm that balances expressivity and learnability. The study establishes the first theoretical regret bound that explicitly characterizes the trade-off between approximation error and information gain, offering principled guidance for model complexity selection. Empirical results demonstrate that the proposed approach substantially reduces computational overhead, enhances sample efficiency, and achieves scalable quantum-native optimization suitable for near-term Noisy Intermediate-Scale Quantum (NISQ) era applications.

Abstract

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.

Problem

• quantum kernel
• Gaussian process bandit
• learnability
• expressivity
• regret

Innovation

• projected quantum kernels
• kernel approximation
• Gaussian process bandits
• regret bounds
• quantum-native optimization