Fig. 2: Conjectured complexity \(\boldsymbol{\mathcal{C}}\) as a function of the inner-product distance z, in which H1,000 is a 1,000-local polynomial Hamiltonian.
From: Universality in long-distance geometry and quantum complexity
a, For the proposed critical metric, the complexity grows linearly with the same coefficient at all z (until it saturates at a z exponential in N). b, For the cliff metric, equation (9), at very short distances the complexity grows linearly (orange), then it hits the cut locus and slows to sublinear growth (blue), before transitioning to linear growth again but with a lower slope that matches the critical metric (red).
