Fig. 3: Rank of the quantum geometric tensor (QGT) and converged infidelity for infidelity minimizations on the spin-1 bilinear-biquadratic (BLBQ) chain.
From: Efficiency of neural quantum states in light of the quantum geometric tensor
a–c The rank of the QGT (dr) is shown as a function of the hidden layer density α for lengths L = 8, 10, and 12. The insets show the QGT rank normalized w.r.t. the number of parameters Np. d–f The converged infidelity (I) is shown as a function of the ratio dr/dq, where dq is the upper bound for the QGT rank (or the effective quantum dimension), with dq = 554, 4477, and 36,895, respectively, for L = 8, 10, and 12. The QGT rank dr (which is also the dimension of the relevant manifold around the converged solution) is computed as the number of eigenvalues of the QGT greater than 10−5. Each panel shows the data for the antiferromagnetic-Heisenberg (AFH) (red squares), Affleck-Kennedy-Lieb-Tasaki (AKLT) (red triangles), and the two critical phases (blue circles and blue diamonds for θ = π/4 and \(\arctan (2)\) respectively) of the spin-1 BLBQ chain with open boundary conditions, for a given length of the chain.
