Quantum Reinforcement Learning Framework for Multi-Rig Drilling Scheduling under Operational Constraints

The purpose of this research is to show the capabilities that quantum computing has to offer for AI. Therefore, the scheduling problem was chosen in order to demonstrate and compare the classical reinforcement learning (CRL) agent with the quantum computing reinforcement learning (QC-RL) agent. This constrained combinatorial optimization problem involves scheduling an oil field with several drilling rigs which are limited in capacity, area limitations, mandatory maintenance periods, weather restrictions and a mobilization costs which is considered along with well priorities and deadlines. Deep reinforcement learning (DRL) can learn adaptive scheduling policies, but value-based agents such as Deep Q-Networks (DQN) are known to exhibit high variance across random initializations. This paper investigates whether a hybrid quantum-classical value function can improve this reliability. We formulate realistic multi-rig drilling scheduling as a Markov Decision Process with action masking over an eight-constraint simulator (24 wells, 6 rigs, 3 areas, 80-day horizon) and compare a classical DQN against a hybrid Quantum DQN in which the value network’s core is a variational quantum circuit via a 4-qubit ZFeatureMap encoding followed by a RealAmplitudes ansatz with 12 trainable quantum parameters, executed using a PyTorch-Qiskit interface. Both agents share an identical training and evaluation protocol (3 seeds × 30 episodes, greedy evaluation) to ensure a controlled comparison. Under greedy evaluation, the hybrid Quantum DQN completes 22.3/24 wells on average versus 17/24 for the classical DQN, achieves an 12.87% higher mean reward (9.12M vs 8.08M), and most significantly reduces the across-seed reward standard deviation by roughly 6.8× (0.202M vs 1.38M). These results indicate that the structurally constrained quantum value function acts as an implicit regularizer, yielding scheduling policies that are markedly more consistent across initializations than a substantially larger classical network. This simulated quantum computing experiment demonstrates the potential for quantum computing in the field of AI.