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arXiv:2601.02870

Quantum-Enhanced Neural Contextual Bandit Algorithms

Yuqi Huang, Vincent Y. F Tan, Sharu Theresa Jose

cs.LGcs.ITquant-phSubmitted Jan 6, 2026• Announced Jan 7, 2026• 0 citations
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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 $Ω((TK)^3)$ for QNTK-UCB, a substantial reduction compared to $Ω((TK)^8)$ 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.

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Combinatorial bandits offer a principled framework for sequential decisionmaking under uncertainty.However, in drug discovery, classical algorithms often struggle to model complex fragment interactions and suffer from high sample complexity.This paper introduces three quantum-enhanced combinatorial bandit algorithms that leverage the expressive power of parameterized quantum circuits.Quantum Thompson Sampling (Q-TS) samples actions directly from a quantum posterior.Quantum Combinatorial UCB (Q-CUCB) uses the diagonal elements of the quantum Fisher information matrix as an intrinsic uncertainty measure.Quantum-Neural Bandit (Q-Neural) combines quantum feature extraction with a classical neural network for context-aware decisions.Experiments on data from the ChEMBL database demonstrate that while classical linear methods achieve the lowest mean regret, the quantum methods excel in stability, near-optimal performance, and interpretability-unique advantages that are critical for reliable drug discovery.This work establishes quantum combinatorial bandits as a versatile tool offering benefits beyond raw regret minimization.
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