From Cables to Qubits: A Decomposed Variational Quantum Optimization Pipeline

TL;DR

This paper presents a decomposed variational quantum pipeline for cable routing optimization that leverages problem structure to improve scalability and feasibility, comparing QUBO and PUBO formulations.

Contribution

It introduces a novel modular quantum optimization pipeline for CROP, explicitly deriving QUBO and PUBO models and analyzing their trade-offs.

Findings

PUBO eliminates auxiliary qubits but increases circuit depth.

Decomposed pipeline accelerates solution time and improves feasibility.

PUBO formulations achieved full routing feasibility in experiments.

Abstract

The Cable Routing Optimization Problem (CROP) is a Multi-Commodity Flow Problem (MCFP) central to industrial layouts and smart manufacturing. Historically, quantum optimization has modeled MCFPs as Quadratic Unconstrained Binary Optimization problems (QUBOs). Recent studies suggest that mapping routing problems to Polynomial Unconstrained Binary Optimization problems (PUBOs) can improve efficiency. However, solving full-scale MCFPs with quantum optimization remains computationally challenging. To bridge this gap, we introduce a Decomposed Variational Quantum Pipeline that exploits the block-diagonal structure of CROP, breaking the multi-cable routing task into modular, single-commodity subproblems. We explicitly derive both the QUBO and PUBO representations for CROP and demonstrate that our pipeline can evaluate both formulations within the same pipeline. Our empirical study highlights a trade-off: PUBO eliminates auxiliary qubits at the cost of circuit depth. In our experiments, the decomposed pipeline accelerates time-to-solution, reliably generating feasible cable layouts while trading strict optimality for computational scalability. PUBO formulations achieved full routing feasibility across all tested seeds, while global QUBO formulations showed substantially lower robustness.