Jamadagni, AmitAmitJamadagniKazemi, JavadJavadKazemiBhattacharyya, ArpanArpanBhattacharyya2025-08-222025-08-222024-01-012331-8422https://doi.org/10.48550/arXiv.2401.13625http://repository.iitgn.ac.in/handle/IITG2025/18533Kibble-Zurek mechanism relates the domain of non-equilibrium dynamics with the critical properties at equilibrium. It establishes a power law connection between non-equilibrium defects quenched through a continuous phase transition and the quench rate via the scaling exponent. We present a novel numerical scheme to estimate the scaling exponent wherein the notion of defects is mapped to errors, previously introduced to quantify a variety of gapped quantum phases. To demonstrate the versatility of our method we conduct numerical experiments across a broad spectrum of spin-half models hosting local and symmetry protected topological order. Furthermore, an implementation of the quench dynamics featuring a topological phase transition on a digital quantum computer is proposed to quantify the associated criticality.en-USe-Printe-Print123456789/615