Fig. 5: Comparison of QTG-based search with the classical solvers GUROBI and CP-SAT for different numbers of groups g where the classical solvers are given an optimal solution as an initial bound and COMBOs runtime as a time limit.

See Section “Results” for a description of the instance set. Note that the values for QTG are realistic estimates, based on simulation (for g = 2) and calibrated estimates (for g ≥ 3). For larger values of g, computational effort for full QTG simulation is excessive, so we provide estimates for QTG derived from CTG and justified in Supplementary Section B 1. Assuming comparability of classical and quantum cycles, we observe within the studied regimes that QTG-based search starts outperforming even the heuristic versions of classical solvers on instances with 7 ≤ g ≤ 10. Note that the solvers have different success probabilities wihtin the given runtime, see Fig. 4.