Near-Term Quantum Computing Applications for Solving Complex Scheduling Problems in Hospital Resource Allocation

Abstract

Abstract
Hospital resource allocation and scheduling covering operating rooms, staff shifts, bed assignments, and equipment utilization pose large-scale combinatorial optimization challenges with high stakes for patient outcomes, throughput, staff wellbeing and cost efficiency. Classical optimization methods (integer programming, heuristics, meta-heuristics) have had success but increasingly hit scalability limits in the face of growing complexity, uncertainty and real-time demands. Meanwhile, quantum computing (in its near-term “Noisy Intermediate-Scale Quantum” or NISQ era) and quantum-inspired optimization offer new opportunities for tackling scheduling problems via quadratic unconstrained binary optimization (QUBO), variation quantum circuits, quantum annealing and hybrid quantum-classical frameworks. In this article, we propose a comprehensive framework for applying near-term quantum/quantum-inspired algorithms to hospital scheduling problems, present full mathematical formulations of scheduling models mapped to QUBO and variational circuits, review literature across healthcare scheduling and quantum optimization, discuss implementation architecture (including hybrid pipelines, cloud quantum access, latency, hardware limitations), and present use-case scenarios (operating room scheduling, bed assignment, staff shift optimization) with insights for hospital administrators and practitioners.Ths paper discusses practical constraints data quality, integration, regulatory compliance, interpretability and lay out a roadmap for near-term adoption of quantum-enabled scheduling in healthcare. Our findings suggest that while fully fault-tolerant quantum advantage remains in the future, near-term hybrid/quantum-inspired solutions can deliver meaningful improvements in scheduling efficiency, resource utilisation and responsiveness in hospital settings.