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Kibble-Zurek mechanism relates the domain of non-equilibrium dynamics withthe critical properties at equilibrium. It establishes a power law connectionbetween non-equilibrium defects quenched through a continuous phase transitionand the quench rate via the scaling exponent. We present a novel numericalscheme to estimate the scaling exponent wherein the notion of defects is mappedto errors, previously introduced to quantify a variety of gapped quantumphases. To demonstrate the versatility of our method we conduct numericalexperiments across a broad spectrum of spin-half models hosting local andsymmetry protected topological order. Furthermore, an implementation of thequench dynamics featuring a topological phase transition on a digital quantumcomputer is proposed to quantify the associated criticality.

Kibble-Zurek mechanism and errors of gapped quantum phases