This is the dataset, which was used for generating the figures with results in our work (to be published in PRResearch) https://doi.org/10.48550/arXiv.2307.15173 The data is generated by a simulation protocol implemented in Python. For the imaginary time evolution figures, the data contains the values of the fidelity with respect to the true ground state and the energy of the variational state as a function of the time for N = 1,2 and 3 layers of the variational circuit. For the real time evolution figures, the data contains the values of the fidelity with respect to the exactly time-evolved state, the fermion numbers, calculated in the variational state, as a function of time, and the bipartite entropy as a function of time.