Quantum Similarity-Driven QUBO Framework for Multi-Period Supply Chain Allocation using Time-Multiplexed Coherent Ising Machines and Simulated Quantum Annealing

Abstract: Multi-period stock-keeping unit (SKU) allocation in supply chains is a combinatorial optimization problem that is both NP-hard and operationally critical, requiring simultaneous attention to profitability, feasibility, and diversity. Quadratic unconstrained binary optimization (QUBO) provides a principled framework for such tasks, yet prior studies often rely on simplified assumptions or omit real operational constraints. This work proposes a hybrid QUBO framework integrating three advances: (i) a quantum-derived similarity kernel, obtained from a variational RX embedding, to discourage redundant SKU selections; (ii) exact per-period capacity enforcement via slack-bit encoding to maintain feasibility; and (iii) execution on a time-multiplexed Coherent Ising Machine (CIM) benchmarked against simulated quantum annealing (SQA) and classical optimization algorithms. The resulting model, with over one million quadratic terms and about 4,100 variables, captures profit, risk, and capacity interactions within a unified formulation. On a dataset of 500 SKUs across eight planning periods, Quanfluence's CIM achieved an energy of minus 2.95 times 10 to the power of 16, producing robust solutions with 288 distinct SKUs (approximately 60 percent of the catalog), 226,813 allocated units, and 12.75 million dollars profit, all with zero capacity violations. These results demonstrate that hybrid quantum-classical QUBO methods can deliver feasible and profitable supply-chain allocations at an industrial scale.