Fig. 1. Quantum speedup ratio.

Plot of the zero temperature dynamics quantum speedup ratio β_C/β_Q which assumes an Θ(η^α) relationship between problem size and basis size so that cost of the best exact quantum simulations of electron dynamics can be expressed as $\left({\eta }^{{\beta }_{\mathrm{Q}}}t\right){\left(Nt/ϵ\right)}^{o\left(1\right)}$ and the cost of the best classical mean-field algorithms for electron dynamics can be expressed as $\left({\eta }^{{\beta }_{\mathrm{C}}}t\right){\left(Nt/ϵ\right)}^{o\left(1\right)}$. These costs are compared under the same assumptions for sampling time-dynamics output as those mentioned in Table 1. See Supplementary Note 5 for more details.