Variational Quantum Rainbow Deep Q-Network for Optimizing Resource Allocation Problem

TL;DR

This paper introduces a quantum-enhanced deep reinforcement learning method, VQR-DQN, that leverages quantum circuits to improve resource allocation efficiency, outperforming classical approaches on benchmark problems.

Contribution

It presents the Variational Quantum Rainbow DQN, integrating quantum circuits with deep Q-learning to enhance representational power for complex resource allocation tasks.

Findings

Achieves 26.8% reduction in makespan over random baselines

Outperforms Double DQN and classical Rainbow DQN by 4.9-13.4%

Demonstrates theoretical link between quantum circuit expressibility and policy quality

Abstract

Resource allocation remains NP-hard due to combinatorial complexity. While deep reinforcement learning (DRL) methods, such as the Rainbow Deep Q-Network (DQN), improve scalability through prioritized replay and distributional heads, classical function approximators limit their representational power. We introduce Variational Quantum Rainbow DQN (VQR-DQN), which integrates ring-topology variational quantum circuits with Rainbow DQN to leverage quantum superposition and entanglement. We frame the human resource allocation problem (HRAP) as a Markov decision process (MDP) with combinatorial action spaces based on officer capabilities, event schedules, and transition times. On four HRAP benchmarks, VQR-DQN achieves 26.8% normalized makespan reduction versus random baselines and outperforms Double DQN and classical Rainbow DQN by 4.9-13.4%. These gains align with theoretical connections between circuit expressibility, entanglement, and policy quality, demonstrating the potential of quantum-enhanced DRL for large-scale resource allocation. Our implementation is available at: https://github.com/Analytics-Everywhere-Lab/qtrl/.