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arXiv:2604.26175

Hardware-Efficient Quantum Optimization for Transportation Networks via Compressed Adiabatic Evolution

Talha Azfar, Ruimin Ke, Sean He, Cara Wang, José Holguín-Veras

quant-phSubmitted Apr 28, 2026• Announced Apr 30, 2026• 0 citations
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Abstract

Transportation systems such as urban logistics, vehicle routing, and infrastructure planning require solving large-scale combinatorial optimization problems under complex constraints. Problems such as the vehicle routing problem (VRP), traveling salesman problem (TSP), and facility location problem (FLP) involve large discrete search spaces and the need to generate multiple feasible solutions in real time. In this work, we develop a hardware-grounded hybrid quantum optimization framework that uses Approximate Quantum Compilation (AQC) to compress early segments of digitized adiabatic evolution into shallow circuits. The compressed prefix is combined with variational layers, enabling a systematic study of how initialization, circuit depth, and expressivity interact on near-term quantum hardware. All experiments are performed on an IBM gate-based quantum computer, and circuits are evaluated as stochastic generators of candidate transportation plans. Results show that moderate prefix compression reduces two-qubit gate depth while maintaining or improving feasible solution discovery, particularly for routing problems. These benefits depend on compatibility between the compressed prefix and the variational ansatz: while standard QAOA effectively leverages AQC initialization, linear-chain QAOA shows limited improvement. Overall, this work demonstrates that hybrid AQC-QAOA methods provide a practical pathway for hardware-efficient quantum optimization, positioning quantum algorithms as candidate generators within transportation decision-making workflows.

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Transportation systems such as urban logistics, vehicle routing, and infrastructure planning require solving large-scale combinatorial optimization problems under complex constraints. Problems such as the vehicle routing problem (VRP), traveling salesman problem (TSP), and facility location problem (FLP) involve large discrete search spaces and the need to generate multiple feasible solutions in real time. In this work, we develop a hardware-grounded hybrid quantum optimization framework that uses Approximate Quantum Compilation (AQC) to compress early segments of digitized adiabatic evolution into shallow circuits. The compressed prefix is combined with variational layers, enabling a systematic study of how initialization, circuit depth, and expressivity interact on near-term quantum hardware. All experiments are performed on an IBM gate-based quantum computer, and circuits are evaluated as stochastic generators of candidate transportation plans. Results show that moderate prefix compression reduces two-qubit gate depth while maintaining or improving feasible solution discovery, particularly for routing problems. These benefits depend on compatibility between the compressed prefix and the variational ansatz: while standard QAOA effectively leverages AQC initialization, linear-chain QAOA shows limited improvement. Overall, this work demonstrates that hybrid AQC-QAOA methods provide a practical pathway for hardware-efficient quantum optimization, positioning quantum algorithms as candidate generators within transportation decision-making workflows.
The Vehicle Routing Problem (VRP) is a fundamental combinatorial optimization challenge with broad applications in logistics and transportation. In this work, we present a quantum-assisted framework that integrates the Quantum Approximate Optimization Algorithm (QAOA) with a link-based formulation of VRP. Our approach encodes flow conservation and subtour elimination directly into the cost Hamiltonian, preserving graph structure while minimizing resource requirements for practical hardware implementation. We design and implement the full pipeline on a gate-based quantum computer, including problem formulation, encoding, circuit synthesis, and execution on IBM Quantum System One. Experimental results on small VRP instances highlight the effects of penalty scaling, coefficient normalization, and circuit depth on solution feasibility under hardware noise. While scalability remains constrained by circuit complexity and decoherence, the study demonstrates a practical pathway for implementing VRP on quantum hardware and identifies methodological directions for advancing near-term quantum optimization.
The Traveling Salesman Problem (TSP) is a cornerstone of combinatorial optimization with widespread applications in logistics and transportation. As problem sizes increase, classical algorithms often fail to deliver high-quality solutions within practical time constraints. This paper explores the use of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical algorithm, to address TSP instances under realistic conditions. We present a QUBO-based formulation of the TSP that integrates practical constraints reflecting real-world conditions—such as vehicle capacity, road accessibility, and time windows—while maintaining compatibility with limitations of current quantum hardware. Our analysis is conducted in a simulated environment, leveraging high-performance computing (HPC) resources to evaluate the algorithm’s performance across varying problem sizes and circuit depths. This approach enables a comprehensive assessment of QAOA’s capabilities and limitations in solving constrained TSP scenarios, thereby laying the groundwork for its deployment on future large-scale quantum hardware.
The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality solutions within reasonable timeframes. This study investigates the potential of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical method, to solve TSP under realistic constraints. We adopt a QUBO-based formulation of TSP that integrates real-world logistical constraints reflecting operational conditions, such as vehicle capacity, road accessibility, and time windows, while ensuring compatibility with the limitations of current quantum hardware. Our experiments are conducted in a simulated environment using high-performance computing (HPC) resources to assess QAOA's performance across different problem sizes and quantum circuit depths. In order to improve scalability, we propose clustering QAOA (Cl-QAOA), a hybrid approach combining classical machine learning with QAOA. This method decomposes large TSP instances into smaller sub-problems, making quantum optimization feasible even on devices with a limited number of qubits. The results offer a comprehensive evaluation of QAOA's strengths and limitations in solving constrained TSP scenarios. This study advances quantum optimization and lays groundwork for future large-scale applications.
In the ever-evolving landscape of global trade and supply chain management, logistics optimization stands as a critical challenge. This study takes on the Vehicle Routing Problem (VRP), a variant of the Traveling Salesman Problem (TSP), by proposing a novel hybrid solution that seamlessly combines classical and quantum computing methodologies. Through a comprehensive analysis of our approach, including algorithm selection, data collection, and computational processes, we provide in-depth insights into the efficiency, and effectiveness of our hybrid solution compared to traditional methods. The results after analysis of 14 datasets highlight the advantages and limitations of this approach, demonstrating its potential to address NP-hard problems and contribute significantly to the field of optimization algorithms in logistics. This research offers promising contributions to the advancement of logistics optimization techniques and their potential implications for enhancing supply chain efficiency.
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-XXX 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-XXX 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.
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.