Quantum Complexity has emerged in the past few years as a candidate for quantum chaos diagnostic. This talk is based on a work that appeared last year, in which we show that a notion of quantum complexity (spread complexity / Krylov state complexity) is sensitive to Topological Phase Transitions – at least for the prototypical Kitaev chain. I’ll give a brief overview of what we mean when we say “quantum” chaos, make connections with classical chaos and proceed to discuss our results by introducing the Krylov subspace methods.

*Nitin Gupta, University of Cape Town