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arXiv · 2507.13226

Krylov complexity, path integrals, and instantons

Cameron Beetar·Eric L Graef·Jeff Murugan·Horatiu Nastase·Hendrik J R Van Zyl
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Abstract

Krylov complexity has emerged as an important tool in the description of quantum information and, in particular, quantum chaos. Here we formulate Krylov complexity $K(t)$ for quantum mechanical systems as a path integral, and argue that at large times, for classical chaotic systems with at least two minima of the potential, that have a plateau for $K(t)$, the value of the plateau is described by quantum mechanical instantons, as is the case for standard transition amplitudes. We explain and test these ideas in a simple toy model.

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Cameron Beetar, Eric L Graef, Jeff Murugan, Horatiu Nastase, Hendrik J R Van Zyl. 2025-07-17. Krylov complexity, path integrals, and instantons. https://arxiv.org/abs/2507.13226

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