Problem
Research questions and friction points this paper is trying to address.
Quantum Approximate Optimization Algorithm
Vehicle Routing Problem
Feasibility
Constraint Preservation
Combinatorial Optimization
Improving Feasibility in Quantum Approximate Optimization Algorithm for Vehicle Routing via Constraint-Aware Initialization and Hybrid XY-X Mixing
🤖 AI Summary
This work addresses the poor feasibility ratio and constraint violation issues of the standard Quantum Approximate Optimization Algorithm (QAOA) when applied to the Vehicle Routing Problem (VRP), where conventional Pauli-X mixers often disrupt local constraint structures. To overcome these limitations, the authors propose a constraint-aware QAOA framework that incorporates a lightweight initialization strategy to encode one-hot constraints, thereby reducing the initial state space, and introduces an XY-X mixing Hamiltonian that preserves constraint satisfaction while maintaining exploratory freedom over feasible configurations. Empirical results demonstrate that the proposed approach consistently outperforms standard QAOA across ideal, finite-sampling, and noisy settings, yielding significantly higher proportions of feasible solutions and improved solution quality. Although hardware noise partially diminishes this advantage, the performance gain is expected to increase as error rates decrease with advancing quantum hardware.
📝 Abstract
The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it poses a major feasibility challenge for standard QAOA because feasible solutions occupy only a tiny fraction of the search space, and the conventional Pauli-$X$ mixer can disrupt partial solution structures that satisfy key local constraints. To address this issue, we propose a constraint-aware QAOA framework with two complementary components. First, we design a lightweight initialization strategy that encodes a selected subset of simple yet informative local one-hot constraints into the initial state, thereby reducing the initial superposition space and increasing the probability mass on states with important local structure. Second, we introduce a hybrid XY-$X$ mixer that preserves the constraint structure imposed at initialization while retaining exploratory flexibility over the remaining unconstrained degrees of freedom during QAOA evolution. We evaluate the proposed framework against standard QAOA under three progressively more realistic regimes: ideal statevector simulation, finite-shot sampling, and noisy finite-shot sampling. Across all regimes, the proposed method consistently achieves lower average energy and higher feasible-solution ratios than standard QAOA, indicating more effective guidance toward structurally valid, lower-cost VRP solutions. However, the performance gap narrows in the noisy regime. Because this setting adopts a hardware-inspired error model based on near-best-reported laboratory-level qubit gate and readout fidelities, the observed attenuation suggests that the practical advantage of the more structured mixer is likely to grow as quantum hardware improves and error rates decline.
Innovation
Methods, ideas, or system contributions that make the work stand out.
constraint-aware initialization
hybrid XY-X mixer
Quantum Approximate Optimization Algorithm
Vehicle Routing Problem
feasibility enhancement
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