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  • Letter
  • Open Access

Spread complexity rate as proper momentum

Pawel Caputa1,2,3, Bowen Chen4,2, Ross W. McDonald5, Joan Simón5, and Benjamin Strittmatter5

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Phys. Rev. D 113, L041901 – Published 11 February, 2026

DOI: https://doi.org/10.1103/7zs8-9zpg

Abstract

We demonstrate a precise relation between the rate of complexity of quantum states excited by local operators in two-dimensional conformal field theories and the radial momentum of particles in three-dimensional anti–de Sitter spacetimes. Similar relations have been anticipated based on qualitative models for operator growth. Here, we make this correspondence sharp with two key ingredients: the precise definition of quantum complexity given by the spread complexity of states, and the match of its growth rate to the bulk momentum measured in the proper radial distance coordinate.

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Phys. Rev. D 113, L041901– Published 11 February, 2026
  • Received 19 November 2024
  • Accepted 14 January 2026
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