Quantum-Enhanced Neural Contextual Bandit Algorithms

TL;DR

This paper introduces QNTK-UCB, a quantum neural tangent kernel-based algorithm for stochastic contextual bandits, which improves scalability and sample efficiency by leveraging quantum properties and avoids unstable quantum training.

Contribution

The paper proposes the QNTK-UCB algorithm that uses a static quantum neural tangent kernel to enhance scalability and stability in quantum neural contextual bandits, outperforming classical methods.

Findings

QNTK-UCB achieves better regret bounds with ((TK)^3) scaling.

Empirical results show superior sample efficiency in quantum tasks.

The approach exploits quantum inductive bias for improved online learning.

Abstract

Stochastic contextual bandits are fundamental for sequential decision-making but pose significant challenges for existing neural network-based algorithms, particularly when scaling to quantum neural networks (QNNs) due to issues such as massive over-parameterization, computational instability, and the barren plateau phenomenon. This paper introduces the Quantum Neural Tangent Kernel-Upper Confidence Bound (QNTK-UCB) algorithm, a novel algorithm that leverages the Quantum Neural Tangent Kernel (QNTK) to address these limitations. By freezing the QNN at a random initialization and utilizing its static QNTK as a kernel for ridge regression, QNTK-UCB bypasses the unstable training dynamics inherent in explicit parameterized quantum circuit training while fully exploiting the unique quantum inductive bias. For a time horizon $T$ and $K$ actions, our theoretical analysis reveals a significantly improved parameter scaling of $\Omega((TK)^3)$ for QNTK-UCB, a substantial reduction compared to $\Omega((TK)^8)$ required by classical NeuralUCB algorithms for similar regret guarantees. Empirical evaluations on non-linear synthetic benchmarks and quantum-native variational quantum eigensolver tasks demonstrate QNTK-UCB's superior sample efficiency in low-data regimes. This work highlights how the inherent properties of QNTK provide implicit regularization and a sharper spectral decay, paving the way for achieving ``quantum advantage'' in online learning.