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arXiv · 2507.05373

Solving Large-Scale Vehicle Routing Problems with Hybrid Quantum-Classical Decomposition

Andrew Maciejunes·John Stenger·Dan Gunlycke·Nikos Chrisochoides
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Abstract

We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm. A Problem-Level Decomposition partitions a 13-node (156-qubit) VRP into smaller Traveling Salesman Problem (TSP) instances. Each TSP is then further cut via Circuit-Level Decomposition, enabling execution on near-term quantum devices. Our approach achieves up to 95\% reductions in the circuit depth, 96\% reduction in the number of qubits and a 99.5\% reduction in the number of 2-qubit gates. We demonstrate this hybrid algorithm on the standard edge encoding of the VRP as well as a novel amplitude encoding. These results demonstrate the feasibility of solving VRPs previously too complex for quantum simulators and provide early evidence of potential quantum utility.

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Andrew Maciejunes, John Stenger, Dan Gunlycke, Nikos Chrisochoides. 2025-07-07. Solving Large-Scale Vehicle Routing Problems with Hybrid Quantum-Classical Decomposition. https://arxiv.org/abs/2507.05373

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