The use of quantum calculations to optimize the complex supply chain networks

Abstract

This article presents a quantum-enhanced framework for optimizing complex supply chain networks (SCNs) under stochastic demand, addressing computational intractability in classical approaches. We propose a hybrid quantum-classical methodology integrating the Quantum Approximate Optimization Algorithm (QAOA) with hierarchical graph decomposition, enabling industrial-scale optimization (?100 nodes) on NISQ-era hardware. Key innovations include: (1) First quantum-native stochastic demand modeling via amplitude estimation, achieving quadratic speedup (O(log(1/?)/?)) over Monte Carlo methods; (2) A novel decomposition algorithm coordinating quantum subproblems through augmented Lagrangian optimization; (3) Error-adapted QAOA with zero-noise extrapolation, improving quantum volume utilization to 85%. Empirical validation demonstrates 42% faster computation versus classical solvers (CPLEX) while maintaining solution quality within 4.7% of optimality. The framework exhibits near-linear scalability (efficiency = 0.92) and outperforms heuristics in high-connectivity, volatile-demand scenarios. Mathematical contributions include a stochastic Hamiltonian formulation for normally distributed demand and noise-aware parameter optimization. This work establishes quantum computing as a viable tool for real-time SCN optimization, particularly for multi-period networks with uncertainty. Future research will explore multi-objective extensions, quantum machine learning integration, and dynamic reconfiguration protocols.