Quantum-enhanced multi-echelon inventory control
Zefree Lazarus Mayaluri, Sasmita Mishra · Journal of Simulation · 2026
We develop a Quantum-enhanced Policy Iteration (QPI) framework for multi-echelon inventory control in stochastic supply-chain networks. QPI formulates policy evaluation as the Bellman linear system AπVπ=Rπ, where Aπ=I−γPπ, and embeds quantum evaluation within a hybrid quantum–classical policy-improvement loop. The framework uses block-encoded access to the policy-induced transition kernel and supports two evaluation routes: an HHL-style quantum linear-system solver (QLSS) for targeted value estimation and a variational quantum algorithm (VQA) based on a diagonal inventory-cost observable. Under sparsity, bounded conditioning, efficient sparse-access/block-encoding oracles, and selective readout, the QLSS branch has query/gate complexity O˜sκpolylogS/ε; state preparation, oracle synthesis, and readout are treated separately, and no QRAM is assumed. In matched Qiskit Aer benchmarks, Sparse-LU, HHL-QLSS, and VQA required 610.7, 10.5, and 13.7 s for M=5, n=10, and 7420.2, 25.1, and 38.9 s for M=6, n=10, respectively. Policy-loop and synthetic-noise experiments further characterised numerical stability and sensitivity under emulator conditions.