Hierarchical Quantum Optimization via Backbone-Driven Problem Decomposition: Integrating Tabu-Search with QAOA

• URL: http://arxiv.org/abs/2504.09575v1
• Date: Sun, 13 Apr 2025 13:50:38 GMT
• Title: Hierarchical Quantum Optimization via Backbone-Driven Problem Decomposition: Integrating Tabu-Search with QAOA
• Authors: Minhui Gou, Zeyang Li, Hong-Ze Xu, Changbin Lu, Jing-Bo Wang, Yukun Wang, Meng-Jun Hu, Dong E Liu, Wei-Feng Zhuang,
• Abstract summary: 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.
• Score: 6.1238490000465635
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: As quantum computing advances, quantum approximate optimization algorithms (QAOA) have shown promise in addressing combinatorial optimization problems. However, the limitations of Noisy Intermediate Scale Quantum (NISQ) devices hinder the scalability of QAOA for large-scale optimization tasks. To overcome these challenges, we propose Backbone-Driven QAOA, a hybrid framework that leverages adaptive Tabu search for classical preprocessing to decompose large-scale quadratic unconstrained binary (QUBO) problems into NISQ-compatible subproblems. In our approach, adaptive Tabu search dynamically identifies and fixes backbone variables to construct reduced-dimensional subspaces that preserve the critical optimization landscape. These quantum-tractable subproblems are then solved via QAOA, with the resulting solutions iteratively refining the backbone selection in a closed-loop quantum-classical cycle. Experimental results demonstrate that our approach not only competes with, and in some cases surpasses, traditional classical algorithms but also performs comparably with recently proposed hybrid classical-quantum algorithms. Our proposed framework effectively orchestrates the allocation of quantum and classical resources, thereby enabling the solution of large-scale combinatorial optimization problems on current NISQ hardware.

Related papers

• Warm-Starting QAOA with XY Mixers: A Novel Approach for Quantum-Enhanced Vehicle Routing Optimization [11.41994899497275]
  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. We propose an approach that integrates these two strategies, enabling constraint-aware quantum evolution toward high-quality classical solutions. 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 Problems.
  arXiv  Detail & Related papers  (2025-04-28T16:08:38Z)
• Solving Constrained Combinatorial Optimization Problems with Variational Quantum Imaginary Time Evolution [4.266376725904727]
  We show that VarQITE achieves significantly lower mean optimality gaps compared to other conventional methods. We demonstrate that scaling the Hamiltonian can further reduce optimization costs and accelerate convergence.
  arXiv  Detail & Related papers  (2025-04-17T03:09:37Z)
• Benchmarking Metaheuristic-Integrated QAOA against Quantum Annealing [0.0]
  The study provides insights into the strengths and limitations of both Quantum Annealing and metaheuristic-integrated QAOA across different problem domains. The findings suggest that the hybrid approach can leverage classical optimization strategies to enhance the solution quality and convergence speed of QAOA.
  arXiv  Detail & Related papers  (2023-09-28T18:55:22Z)
• A Review on Quantum Approximate Optimization Algorithm and its Variants [47.89542334125886]
  The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve intractable optimization problems. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios. We conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm.
  arXiv  Detail & Related papers  (2023-06-15T15:28:12Z)
• Quantum-Assisted Solution Paths for the Capacitated Vehicle Routing Problem [0.0]
  We discuss the Capacitated Vehicle Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP) Even with today's most powerful classical algorithms, the CVRP is challenging to solve classically. Quantum computing may offer a way to improve the time to solution.
  arXiv  Detail & Related papers  (2023-04-19T13:03:50Z)
• 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)
• QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines [81.4597482536073]
  Quantum approximate optimization algorithms (QAOAs) utilize the power of quantum machines and inherit the spirit of adiabatic evolution. We propose QAOA-in-QAOA ($textQAOA2$) to solve arbitrary large-scale MaxCut problems using quantum machines. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale optimization problems.
  arXiv  Detail & Related papers  (2022-05-24T03:49:10Z)
• Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization [44.96576908957141]
  We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linear iterations problems on quantum computers.
  arXiv  Detail & Related papers  (2022-03-23T18:00:03Z)
• Q-Match: Iterative Shape Matching via Quantum Annealing [64.74942589569596]
  Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) This paper proposes Q-Match, a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm. Q-Match can be applied for shape matching problems iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems.
  arXiv  Detail & Related papers  (2021-05-06T17:59:38Z)
• 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)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)
• Multi-block ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers [3.04585143845864]
  We present a decomposition-based approach to extend the applicability of current approaches to "quadratic plus convex" mixed binary optimization problems. We show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms) The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit.
  arXiv  Detail & Related papers  (2020-01-07T14:43:13Z)

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.