Quantum Optimization Methods for the Generalized Traveling Salesman Problem

• URL: http://arxiv.org/abs/2604.25531v1
• Date: Tue, 28 Apr 2026 11:58:35 GMT
• Title: Quantum Optimization Methods for the Generalized Traveling Salesman Problem
• Abstract summary: This paper studies quantum optimization baselines for the Generalized Traveling Salesman Problem (GTSP)<n>We propose a novel GTSP QUBO formulation focused on maintaining feasible solutions for quantum annealing.<n>We implement a constrained QAOA variant using an XY-mixer, which preserves the stepwise Hamming weight in the ideal circuit model.
• Score: 2.4029307306254513
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies quantum optimization baselines for the Generalized Traveling Salesman Problem (GTSP), a clustered routing problem that naturally models variant selection and sequencing problems under discrete alternatives. We propose a novel GTSP QUBO formulation focused on maintaining feasible solutions for quantum annealing, as well as a hardware-executable gate-based pipeline utilizing the Quantum Approximate Optimization Algorithm (QAOA). We implement a constrained QAOA variant using an XY-mixer, which preserves the stepwise Hamming weight in the ideal circuit model, while feasibility with respect to the full GTSP constraints is tracked explicitly during post-processing. We compare the two quantum optimization paradigms on problem instances from GTSPLIB, an established benchmark dataset, and validate against classical state-of-the-art solvers. To mitigate current quantum hardware size limitations, we further extend a preprocessing method to reduce the node count in instance clusters, constructing new NISQ-friendly instances from reduced subsets. Across all tested instances, quantum solvers often produce competitive solution quality when tested on smaller graphs, but exhibit higher runtimes and a sharp degradation in feasibility and scalability as instance size grows. Our evaluation highlights where quantum optimizers can already succeed and which algorithmic bottlenecks, like sampling rates, runtime issues, and other practical failure modes, remain as open problems.

Related papers

• Tensor Network Assisted Distributed Variational Quantum Algorithm for Large Scale Combinatorial Optimization Problem [19.046113542182436]
  We propose the Distributed Variational Quantum Algorithm (DVQA) for solving Combinatorial Optimization Problems (COPs)<n>A key innovation of DVQA is its use of the truncated higher-order singular value decomposition to preserve inter-variable dependencies without relying on complex long-range entanglement.<n> Empirically, DVQA achieves state-of-the-art performance in simulations and has been experimentally validated on the Wu Kong quantum computer for portfolio optimization.
  arXiv  Detail & Related papers  (2026-01-20T13:31:02Z)
• A Non-Variational Quantum Approach to the Job Shop Scheduling Problem [0.3078691410268859]
  We introduce Iterative-QAOA, a variant of QAOA designed to mitigate near-term hardware limitations.<n>We benchmark the algorithm on Just-in-Time Job Shop Scheduling Problem (JIT-JSSP) instances on IonQ Forte Generation QPUs.<n>We find that Iterative-QAOA robustly converges to find optimal solutions as well as high-quality, near-optimal solutions for all problem instances evaluated.
  arXiv  Detail & Related papers  (2025-10-30T16:14:13Z)
• RhoDARTS: Differentiable Quantum Architecture Search with Density Matrix Simulations [44.13836547616739]
  Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers.<n> choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task.<n>Quantum Architecture Search (QAS) algorithms enable automatic generation of quantum circuits tailored to the provided problem.
  arXiv  Detail & Related papers  (2025-06-04T08:30:35Z)
• Branch-and-bound digitized counterdiabatic quantum optimization [39.58317527488534]
  Branch-and-bound algorithms effectively solve convex optimization problems, relying on the relaxation the objective function to obtain tight lower bounds.<n>We propose a branch-and-bound digitized counterdiabatic quantum optimization (BB-DCQO) algorithm that addresses the relaxation difficulties.
  arXiv  Detail & Related papers  (2025-04-21T18:19:19Z)
• Hierarchical Quantum Optimization via Backbone-Driven Problem Decomposition: Integrating Tabu-Search with QAOA [6.1238490000465635]
  We propose Backbone-DrivenOA to overcome limitations of Noisy Intermediate Scale Quantum (NISQ) devices.<n>In our approach, adaptive Tabu search dynamically identifies and fixes backbone variables to construct reduced-dimensional subspaces.<n>Our proposed framework effectively orchestrates the allocation of quantum and classical resources, thereby enabling the solution of large-scale optimization problems.
  arXiv  Detail & Related papers  (2025-04-13T13:50:38Z)
• Non-Variational Quantum Random Access Optimization with Alternating Operator Ansatz [3.5773675235837974]
  Quantum Random Access Optimization (QRAO) has been proposed to reduce the space requirements of quantum optimization.<n>We show that instance-independent fixed" parameters achieve good performance, removing the need for variational parameter optimization.<n>Our results pave the way for the practical execution of QRAO on early fault-tolerant quantum computers.
  arXiv  Detail & Related papers  (2025-02-06T18:25:31Z)
• Measurement-Based Quantum Approximate Optimization [0.24861619769660645]
  We focus on measurement-based quantum computing protocols for approximate optimization. We derive measurement patterns for applying QAOA to the broad and important class of QUBO problems. We discuss the resource requirements and tradeoffs of our approach to that of more traditional quantum circuits.
  arXiv  Detail & Related papers  (2024-03-18T06:59:23Z)
• Multiobjective variational quantum optimization for constrained problems: an application to Cash Management [45.82374977939355]
  We introduce a new method for solving optimization problems with challenging constraints using variational quantum algorithms. We test our proposal on a real-world problem with great relevance in finance: the Cash Management problem. Our empirical results show a significant improvement in terms of the cost of the achieved solutions, but especially in the avoidance of local minima.
  arXiv  Detail & Related papers  (2023-02-08T17:09:20Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Scaling Quantum Approximate Optimization on Near-term Hardware [49.94954584453379]
  We quantify scaling of the expected resource requirements by optimized circuits for hardware architectures with varying levels of connectivity. We show the number of measurements, and hence total time to synthesizing solution, grows exponentially in problem size and problem graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.
  arXiv  Detail & Related papers  (2022-01-06T21:02:30Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.