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Chinese Academy of Sciences

Quantum Algorithm Accelerates Traveling Salesman Problem

Strategic Insights

— 1 min read

Researchers at the Chinese Academy of Sciences have published a study on a quantum algorithm that significantly accelerates the solution of the Traveling Salesman Problem (TSP), a critical NP-hard problem in combinatorial optimization. The study, published in Theoretical Computer Science, introduces a quantum speedup algorithm based on quantum dynamic programming with very few ancillary qubits, achieving exponential acceleration compared to previous initial state preparation algorithms.

The quantum algorithm aims to address the challenge of searching for all Hamiltonian cycles from a vast solution space, which hinders the effectiveness of quantum search algorithms. By preparing a superposition state of all feasible solutions and then amplifying the amplitude of the optimal solution, the researchers propose a novel approach that realizes the theoretical minimum query complexity of quantum search algorithms for a general TSP. The study concludes that the proposed algorithm has feasible circuit implementation, making it a practical solution for the TSP.

Key Takeaways:

  • The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization.
  • The researchers propose a quantum algorithm to generate the uniform superposition state of all N-length Hamiltonian cycles as an initial state within polynomial gate complexity based on pure quantum dynamic programming.
  • The proposed algorithm achieves exponential acceleration compared to the previous initial state preparation algorithm.
  • The study concludes that the algorithm has feasible circuit implementation, making it a practical solution for the TSP.
  • Funders for the research include the National Natural Science Foundation special project of China, National Key R&D Program of China, and National Natural Science Foundation of China (NSFC).
  • The study has been peer-reviewed and published in Theoretical Computer Science.

Statistics:

  • The Traveling Salesman Problem (TSP) is a classical NP-hard problem that affects combinatorial optimization.
  • The researchers propose a quantum algorithm to accelerate the TSP solutions.
  • The algorithm achieves exponential acceleration compared to previous initial state preparation algorithms.
  • The study concludes that the algorithm has feasible circuit implementation.

Sources:

  • NewsRx. Researchers from Chinese Academy of Sciences Report Findings in Engineering (A Quantum Speedup Algorithm for Tsp Based On Quantum Dynamic Programming With Very Few Qubits). Journal of Engineering. October 20, 2025; p 3395.
  • A Quantum Speedup Algorithm for Tsp Based On Quantum Dynamic Programming With Very Few Qubits. Theoretical Computer Science, 2025;1052.

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