Qubit-Scalable CVRP via Lagrangian Knapsack Decomposition and Noise-Aware Quantum Execution

TL;DR

This paper presents a practical framework for scaling hybrid quantum vehicle routing optimization by decomposing the problem, learning control strategies, and adaptively selecting hardware configurations to improve solution quality under noise constraints.

Contribution

It introduces an end-to-end decomposition and learning-based control framework that enables scalable, noise-aware quantum optimization for CVRP, addressing current hardware limitations.

Findings

Decomposition yields stable bounded-width subproblems across instance sizes.

Learned multiplier updates improve routing quality over classical control.

Hardware-aware configuration reduces optimality gaps in noisy quantum environments.

Abstract

Hybrid quantum optimization for vehicle routing faces a practical bottleneck: direct QUBO encodings of CVRP quickly exceed near-term qubit and gate budgets, while quantum evaluations are expensive, noise-limited, and sensitive to backend and circuit configuration. We address this gap with an end-to-end decomposition pipeline that converts CVRP into bounded-width quantum subproblems and treats quantum execution as a decision problem within the optimization loop. Starting from a Fisher--Jaikumar assignment linearization, we apply Lagrangian relaxation to dualize customer-assignment couplers, yielding independent per-vehicle knapsack subproblems that admit QUBO/Ising evaluation. To replace brittle subgradient tuning, we learn a multiplier-update controller using expert-guided pretraining followed by reinforcement-learning fine-tuning, with rewards based on execution-realized progress and route reconstruction. We also introduce a constrained contextual bandit as a hardware-aware execution layer that selects backend and circuit configuration with feasibility screening, enabling adaptation across heterogeneous noisy resources and parallel multi-QPU scheduling. Computational results on multiple CVRPLIB families show that the decomposition yields stable bounded-width subproblems across instance sizes, learned multiplier updates improve end-to-end routing quality relative to classical subgradient control under matched budgets, and hardware-mode configuration reduces median optimality gaps relative to static execution choices in our test set. We do not claim quantum advantage. Instead, the contribution is a practical end-to-end framework for scaling hybrid quantum CVRP optimization through OR decomposition, learning-augmented dual control, and adaptive hardware-aware execution.