Quantum complexity and negative curvature

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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.

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