Steiner Traveling Salesman Problem with Quantum Annealing

2025-04-03

AI Summary

This paper addresses the NP-hard Steiner Traveling Salesman Problem (STSP), which extends the classical TSP by allowing optional Steiner nodes to reduce the tour cost while visiting all mandatory nodes. To tackle its quantum-solvability challenges, we propose the first quantum annealing framework for STSP: we formulate a compact Quadratic Unconstrained Binary Optimization (QUBO) model and develop a preprocessing pipeline based on graph compression and critical node selection, substantially reducing problem size and embedding overhead. The end-to-end solution is implemented on D-Wave quantum hardware. Our key contributions are: (1) the first QUBO modeling and empirical validation of STSP on quantum annealers; (2) a hardware-aware network reduction technique tailored to quantum annealing constraints, including qubit connectivity and precision limits; and (3) experimental validation on real quantum devices, demonstrating both solution efficacy and promising scalability for larger instances.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

The Steiner Traveling Salesman Problem (STSP) is a variant of the classical Traveling Salesman Problem. The STSP involves incorporating steiner nodes, which are extra nodes not originally part of the required visit set but that can be added to the route to enhance the overall solution and minimize the total travel cost. Given the NP-hard nature of the STSP, we propose a quantum approach to address it. Specifically, we employ quantum annealing using D-Wave's hardware to explore its potential for solving this problem. To enhance computational feasibility, we develop a preprocessing method that effectively reduces the network size. Our experimental results demonstrate that this reduction technique significantly decreases the problem complexity, making the Quadratic Unconstrained Binary Optimization formulation, the standard input for quantum annealers, better suited for existing quantum hardware. Furthermore, the results highlight the potential of quantum annealing as a promising and innovative approach for solving the STSP.

Problem

• Solving Steiner Traveling Salesman Problem using quantum annealing
• Reducing network size to enhance computational feasibility
• Exploring quantum annealing potential for NP-hard STSP

Innovation

• Quantum annealing for STSP solution
• Preprocessing reduces network size
• QUBO formulation for quantum hardware