Quadratic Unconstrained Binary Optimization (QUBO) is a fundamental framework for solving combinatorial optimization problems, with significant applications in quantum computing. Many real-world optimization tasks can be naturally expressed as QUBOs, making them well-suited for quantum annealing, a promising paradigm for harnessing quantum hardware to find optimal solutions efficiently. A key challenge in utilizing QUBO models effectively is the formulation of an appropriate QUBO matrix \( Q \) that correctly encodes a given problem \( p \) , ensuring that the optimal solution \( x^* \) of \( p \) corresponds to the minimum value of \( x^T Q x \) . In this paper, we propose an algorithm for learning QUBO formulations from data, enabling automated discovery of problem encodings that align with optimal solutions, reducing the need for manual problem modeling and enhancing adaptability to diverse optimization tasks. Experimental results show that our learned QUBO formulations yield accurate representations of the underlying problems, paving the way for more effective problem encoding strategies in quantum computing applications.

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Learning QUBO Formulations from Data

  • Jonas Nüßlein,
  • Sebastian Zielinski,
  • Claudia Linnhoff-Popien

摘要

Quadratic Unconstrained Binary Optimization (QUBO) is a fundamental framework for solving combinatorial optimization problems, with significant applications in quantum computing. Many real-world optimization tasks can be naturally expressed as QUBOs, making them well-suited for quantum annealing, a promising paradigm for harnessing quantum hardware to find optimal solutions efficiently. A key challenge in utilizing QUBO models effectively is the formulation of an appropriate QUBO matrix \( Q \) that correctly encodes a given problem \( p \) , ensuring that the optimal solution \( x^* \) of \( p \) corresponds to the minimum value of \( x^T Q x \) . In this paper, we propose an algorithm for learning QUBO formulations from data, enabling automated discovery of problem encodings that align with optimal solutions, reducing the need for manual problem modeling and enhancing adaptability to diverse optimization tasks. Experimental results show that our learned QUBO formulations yield accurate representations of the underlying problems, paving the way for more effective problem encoding strategies in quantum computing applications.