Krylov complexity is not a measure of distance between states or operators
High Energy Physics - Theory
2024-03-20 v2 Quantum Physics
Abstract
We ask whether Krylov complexity is mutually compatible with the circuit and Nielsen definitions of complexity. We show that the Krylov complexities between three states fail to satisfy the triangle inequality and so cannot be a measure of distance: there is no possible metric for which Krylov complexity is the length of the shortest path to the target state or operator. We show this explicitly in the simplest example, a single qubit, and in general.
Keywords
Cite
@article{arxiv.2311.04093,
title = {Krylov complexity is not a measure of distance between states or operators},
author = {Sergio E. Aguilar-Gutierrez and Andrew Rolph},
journal= {arXiv preprint arXiv:2311.04093},
year = {2024}
}
Comments
6 pages, 1 figure. Version to appear in PRD