arXiv:1608.02612hep-th
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.
a lot at stake this year with a discussion of the foundations. Leonard Susskind, Adam R. Brown, Ying Zhao Quantum Complexity and Negative Curvature https://arxiv.org/abs/1608.02612 The Second Law of Quantum Complexity https://arxiv.org/abs/1701.01107
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