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Warm-Starting QAOA with XY Mixers: A Novel Approach for Quantum-Enhanced Vehicle Routing Optimization
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Warm-Starting QAOA with XY Mixers: A Novel Approach for Quantum-Enhanced Vehicle Routing Optimization
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Quantum optimization algorithms, such as the Quantum Approximate Optimization Algorithm, are emerging as promising heuristics for solving complex combinatorial problems. To improve performance, several extensions to the standard QAOA framework have been proposed in recent years. Two notable directions include: warm-starting techniques, which incorporate classical approximate solutions to guide the quantum evolution, and custom mixer Hamiltonians, such as XY mixers, which constrain the search to feasible subspaces aligned with the structure of the problem. In this work, we propose an approach that integrates these two strategies: a warm-start initialization with an XY mixer ansatz, enabling constraint-preserving quantum evolution biased toward high-quality classical solutions. The method begins by reformulating the combinatorial problem as a MaxCut instance, solved approximately using the Goemans-Williamson algorithm. The resulting binary solution is relaxed and used to construct a biased superposition over valid one-hot quantum states, maintaining compatibility with the XY mixer's constraints. We evaluate the approach on 5-city instances of the Traveling Salesperson Problem, a canonical optimization problem frequently encountered as a subroutine in real-world Vehicle Routing Problems. Our method is benchmarked against both the standard XY-mixer QAOA and a warm-start-only variant based on MaxCut relaxation. Results show that the proposed combination consistently outperforms both baselines in terms of the percentage and rank of optimal solutions, demonstrating the effectiveness of combining structured initializations with constraint-aware quantum evolution for optimization problems.
Forward citations
Cited by 6 Pith papers
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Fundamental Limitations of QAOA on Constrained Problems and a Route to Exponential Enhancement
Standard QAOA faces an intrinsic feasibility bottleneck on permutation problems that CE QAOA overcomes with an exponential gain in feasible probability for sublinear-to-linear depths under mild hypergraph growth.
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Constrained Quantum Optimization via Iterative Warm-Start XY-Mixers
A warm-started XY-mixer aligned to a biased W-state, iterated via sample-based probability updates, raises optimal-solution sampling rates for one-hot constrained QAOA and finds optima on 144-qubit hardware with post-...
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Bitflip-gauge warm-start QAOA that aligns the ansatz with amplitude-damping noise improves 100-qubit Ising approximation ratios over non-gauge iterative warm-start at no extra circuit cost.
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Improving Feasibility in Quantum Approximate Optimization Algorithm for Vehicle Routing via Constraint-Aware Initialization and Hybrid XY-X Mixing
Constraint-aware initialization and hybrid XY-X mixer in QAOA for VRP yield lower average energies and higher feasible-solution ratios than standard QAOA across ideal, finite-shot, and noisy simulations.
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A Nested Amplitude Amplification Protocol for the Binary Knapsack Problem
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Fundamental Limitations of QAOA on Constrained Problems and a Route to Exponential Enhancement
Generic QAOA's claimed exponential feasibility bottleneck on permutation-constrained problems is not proven; the main bound has a 2^N normalization error and is false as stated.
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