Selecting the most appropriate transformation for quantum optimization

Determine, for a specified combinatorial optimization problem, the transformation into an unconstrained pseudo-Boolean function and its subsequent QUBO/Ising representation that is most appropriate, in the sense of yielding the best optimization performance on quantum annealers or gate-based quantum computers.

Background

The paper outlines several steps and choices when mapping combinatorial optimization problems to forms suitable for quantum computation, including representing variables, handling constraints via penalties, and reducing higher-order terms through global (e.g., Rosenberg substitution) or local quadratization techniques. Different formulations can lead to different performance outcomes on quantum hardware.

The authors note recent literature showing that alternative 3SAT-to-QUBO transformations impact solution quality, but there is no established guidance on which transformation is best for a given problem instance. Hence, identifying the most appropriate transformation remains unresolved.