Fig. 5: Runs-per-success versus inverse absolute error 1/ε_λ.

We implemented VQSE for the states of: a n = 6, b n = 8, and c n = 10 qubits corresponding to Fig. 4. The insets depict the same data in the small 1/ε_λ regime. Runs-per-success is defined as the total number of runs divided by the number of runs with a relative error smaller than a target ε_λ. For all three cases, we can see that as 1/ε_λ increases, the adaptive Hamiltonian has the lowest number of runs-per-success, and hence the best performance. In all cases, the x-axis is plotted on a log scale.