Fig. 3: Comparison of quantum methods (QBnB and QTG-based search) with the classical methods COMBO and CTG. | npj Quantum Information

Fig. 3: Comparison of quantum methods (QBnB and QTG-based search) with the classical methods COMBO and CTG.

From: A quantum algorithm for solving 0-1 Knapsack problems

Fig. 3

The subfigures (from left to right) show the measured average performance for different groups g = 2, 3 ≤ g ≤ 6 and 7 ≤ g ≤ 10, respectively. 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); on the other hand, values for QBnB are lower bounds, based on several benevolent assumptions, so a realistic runtime can be expected to be higher; see Supplementary Section F 2. 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 B1. Assuming comparability of classical and quantum cycles, we observe within the studied regimes that QTG-based search starts outperforming COMBO on instances with 7 ≤ g ≤ 10. The trend continues towards larger instances and indicates a generally more favourable slope for the quantum method than for COMBO.

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