Affiliation:
1. Institute for Theoretical Physics
2. University of Amsterdam
3. Vrije Universiteit Brussel (VUB) and The International Solvay Institutes
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.
Published by the American Physical Society
2024
Funder
Universiteit van Amsterdam
Fonds Wetenschappelijk Onderzoek
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Vrije Universiteit Brussel
Delta Institute for Theoretical Physics
International Centre for Theoretical Physics
Uitvoeringsinstituut Werknemersverzekeringen
Publisher
American Physical Society (APS)
Cited by
6 articles.
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