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

TL;DR

The paper tackles multi-period SKU allocation as a large-scale QUBO problem by integrating a quantum-derived similarity kernel and slack-bit capacity encoding within a Coherent Ising Machine framework. It demonstrates that a hybrid quantum-inspired approach can produce feasible, high-profit supply chain allocations across 8 planning periods for 500 SKUs, outperforming several classical and simulated-quantum baselines. Key contributions include the RX-embedding-based quantum similarity, soft capacity enforcement, and a comprehensive ablation study validating the necessity of each component. The work highlights the practical potential of physics-inspired optimizers for industrial-scale optimization, while also acknowledging scalability and hardware integration challenges for real-world deployment.

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.

Figures (8)

• Figure 1: End-to-end pipeline of the quantum similarity-driven QUBO framework
• Figure 2: RX-embedding used to compute the pairwise similarity between two SKU feature vectors $x_1$ and $x_2$. Each wire represents a qubit; for qubit $i$ we apply $R_x(x_{1,i})$ followed by $R_x(-x_{2,i})$ and then measure the output probability distribution. The entry $p_{00\ldots0}$ of the resulting probability vector is used as the similarity measure in the QUBO.
• Figure 3: Quanfluence quantum QUBO results: (left) multi-period capacity utilization; (right) quantum similarity matrix capturing SKU interdependencies.
• Figure 4: Quanfluence cosine QUBO results showing capacity allocation across periods (left) and the cosine similarity matrix between SKUs (right).
• Figure 5: SQA cosine QUBO results showing capacity allocation across periods (left) and the cosine similarity matrix between SKUs (right).