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.

References

It is an open question which transformation is the most appropriate for a given problem.

— Combinatorial Optimization with Quantum Computers  (2412.15778 - Chicano et al., 2024) in Section 7 (Discussion and Future Directions)

Beyond this experiment, two directions extend naturally: scaling the automated compilation to industry-standard benchmark families---the combinational circuits and equivalence checking miters of formal hardware verification---would provide a concrete performance comparison at practically relevant circuit sizes and connect the solver to established electronic design automation workflows; and the correspondence between circuit structure and optimization hardness deserves systematic study, since the gadget-based encoding introduces structured connectivity that differs qualitatively from the random or geometric instances of prior MIS hardness analyses, leaving open whether this structure makes the encoded problem harder or easier for quantum annealing dynamics.

— Encoding Circuit Satisfiability in Rydberg Atom Arrays  (2608.12938 - Ji et al., 13 Aug 2026) in Section 6, Conclusion