Quantum-Enhanced Combinatorial Multi-Armed Bandit Algorithms for Drug Discovery

Combinatorial bandits offer a principled framework for sequential decision-making 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.