Figure 1

The approximation ratios (top) and in-constraint probabilities (bottom) obtained in the optimization of the instances on 14 (left) and 20 (right) qubits using different quantum optimization algorithms executed in a noiseless simulator, the Quantinuum H1-1 machine and its emulator. In each box plot, the box shows quartiles, the line is the median and the whiskers show minimum and maximum. Each plot is showing the statistics over 10 problem instances, with the exception of XY-QAOA where only three 14-qubit and three 20-qubit runs have been executed due to high circuit depth. We observe that all results significantly improve on random guess. The in-constraint probability of QAOA is below random guess for 14 qubits due to the choice of parameters; see discussion in “Quantum circuit needs to preserve constraints”.