Extended Data Fig. 2: Numerical simulation of the adiabatic preparation of the ground state of H2 with the simulator (particularized for a 2D lattice).
Red dashed lines follow the adiabatic evolution of the initial state \(\left|{\psi }_{0}\right\rangle \) and arrows point to the direction of evolution. a, Preparation of the bosonic state through steps I(a)–I(c) (see Methods and Extended Data Table 1). Continuous lines indicate the exact energy of the two lowest energy states. For the adiabatic evolution we use Trotterized time as ΔtU = 0.5 and evolution with |ΔU|/(U2Δt) = 3 × 10−4. b, Steps II–III of the preparation of the fermionic state. In the simulation, we use the Trotterized time evolution in intervals of ΔtV0 = 0.05. In step II, the kinetic term is adiabatically introduced in steps of \(\Delta {t}_{{\rm{F}}}/({{\rm{V}}}_{0}^{2}\Delta t)=0.005\). In step III, the electronic repulsion is tuned up as \(\Delta V/({{\rm{V}}}_{0}^{2}\Delta t)=0.02\). Here yellow (blue) continuous lines follow the exact energy levels of Hqc, as calculated by imaginary-time evolution with (without) the effect of electronic repulsion. The top insets show the Mott excitation (a) fermionic population (b) in the lattice at the times indicated in the figure. The final point of the evolution shown in b corresponds to d/a0 = 1. Parameters: N = 60, U/Jc = 1.5, d/a = 10.