Fig. 2: Transverse field Ising on a chain.
From: Foundation neural-networks quantum states as a unified Ansatz for multiple hamiltonians
a Simultaneous ground state energy optimization of \({{{\mathcal{R}}}}=5\) systems on a chain of N = 100 sites, with h/J = 0.8, 0.9, 1.0, 1.1 and 1.2. The relative error with respect to the exact ground state energy of each system is shown as a function of the optimization steps. The inset displays the relative error of the total energy as a function of the number of systems \({{{\mathcal{R}}}}\), defined by equispaced values of h/J in the interval h/J ∈ [0.8, 1.2], with a fixed batch size of M = 10000. b Square magnetization evaluated with a FNQS trained at h/J = 0.8, 0.9, 1.0, 1.1 and 1.2 (red diamonds) and tested on previously unseen values of the external field (blue circles). The inset shows the square magnetization predictions of an architecture trained exclusively on h/J = 0.8 and 1.2, evaluated at intermediate external field values. c Fidelity susceptibility per site [see Eq. (22)] as a function of the external field for a FNQS trained on \({{{\mathcal{R}}}}=6000\) equispaced values of h/J in the interval h/J ∈ [0.85, 1.15] for a cluster of N = 100 sites. The inset shows the data collapse of the same quantity for N = 40, 80, and 100.
