Quantum complexity and negative curvature

Type: Article

Publication Date: 2017-02-22

Citations: 148

DOI: https://doi.org/10.1103/physrevd.95.045010

Abstract

As time passes, once simple quantum states tend to become more complex. For strongly coupled $k$-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we show that the same pattern is exhibited by a much simpler system---classical geodesics on a compact two-dimensional geometry of uniform negative curvature. This striking parallel persists whether the system is allowed to evolve naturally or is perturbed from the outside.

Locations

  • Physical review. D/Physical review. D. - View - PDF
  • arXiv (Cornell University) - View - PDF
  • DataCite API - View

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