QUANTUM MACHINE LEARNING AND HYBRID QUANTUM-CLASSICAL OPTIMIZATION FOR COMPLEX SCHEDULING, COMBINATORIAL OPTIMIZATION, AND HIGH-DIMENSIONAL DATA ANALYSIS

Abstract

The rapid expansion of supply chains, logistics networks and enterprise-scale manufacturing platforms has made computational problems harder. The problems involve NP‑hard optimization and high‑dimensional data processing. Classical exact solvers are slow on non‑convex, constraint‑dense search spaces. Metaheuristics such as Simulated Annealing and Genetic Algorithms often stop at local minima. Quantum computing offers an approach by using superposition, entanglement and quantum tunnelling. Nisq‑era hardware limits the use of fault‑tolerant, deep‑circuit algorithms at production scale. This review looks at quantum‑classical optimization and Quantum Machine Learning (QML) frameworks for complex scheduling, combinatorial optimization and high‑dimensional analytics. It covers models like Quadratic Unconstrained Binary Optimization (QUBO) Ising Hamiltonian mappings, Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA) as well as higher‑order mappings and penalty tuning strategies. Special focus is on trainability landscapes studying the Barren Plateau through Dynamical Lie Algebra theory and reviewing ways to help such as Hamiltonian Variational Ansätze, logarithmic‑depth circuits and dynamic parameterised circuits. Industrial workflows such as Job Shop Scheduling, Capacitated Vehicle Routing, AGV dispatching and satellite acquisition scheduling are evaluated with tests against Gurobi, Simulated Annealing, Parallel Tempering and DMRG tensor networks. QML algorithms like Quantum Support Vector Machines, Quantum Support Vector Data Description, Quantum Convolutional Neural Networks and Quantum Principal Component Analysis are examined through the dequantisation framework showing the limits where true quantum advantage appears. Results show that hybrid architectures can reach approximation ratios close, to 0.99 on medium‑scale Max‑Cut instances while dequantisation shows that many claimed speedups actually become polynomial under the same data‑access assumptions meaning real advantage only stays for high‑rank matrices and data that is truly quantum.