Quantum Complexity and Negative Curvature

Aug 8, 2016
19 pages
Published in:
  • Phys.Rev.D 95 (2017) 4, 045010
  • Published: Feb 22, 2017
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Abstract: (APS)
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.
Note:
  • 43 pages
  • dimension: 2
  • curvature
  • strong coupling
  • Hamiltonian
  • geometry