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Krylov complexity is not a measure of distance between states or operators
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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.
Forward citations
Cited by 3 Pith papers
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A family of SU(2) and SU(3) Lipkin-Meshkov-Glick-type Hamiltonians reproduces de Sitter quasinormal-mode densities of states, and late-time probes reveal integrability beneath saddle-dominated scrambling.
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