Bitstring-ChiFc: machine learning Fisher Information Metric from bitstrings

We consider the task of identifying phase transitions in low temperature states in systems on a lattice described by a parameterised family of spin Hamiltonians with no known order parameters given access to an oracle producing bit strings representing the Z-basis measurement of such states. For fixed finite system size such phase transitions are typically reflected by maxima of fidelity susceptibility. Given only the access to bit strings we can only hope to estimate the classical fidelity susceptibility. Here we show the conditions under which classical fidelity susceptibility matches the full fidelity susceptibility and demonstrate a machine learning based method for determining the classical fidelity susceptibility from a dataset of bit strings or an access to an oracle able to produce such bit strings. We investigated numerically the performance of the methods on a few toy models including the Transverse Field Ising Model, Frustrated Ising Ladder, and MaxCut problem represented as an Ising system on a random graph. In this talk we present the numerical results on one of these toy models.