PIRSA:17080015 Scientific Series Other

DOI10.48660/17080015

Series: Quantum Fields and Strings

Hashimoto, K. (2017). Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game . Perimeter Institute. https://pirsa.org/17080015

Hashimoto, Koji. Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game . Perimeter Institute, Aug. 11, 2017, https://pirsa.org/17080015 

@misc{ pirsa_PIRSA:17080015,
  doi = {10.48660/17080015},
  url = {https://pirsa.org/17080015},
  author = {Hashimoto, Koji},
  keywords = {Other},
  language = {en},
  title = {Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game },
  publisher = {Perimeter Institute},
  year = {2017},
  month = {aug},
  note = {PIRSA:17080015 see, \url{https://pirsa.org}}
}

Abstract

Quantum complexity is conjectured to probe inside of black hole horizons (or wormhole) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for generic Abelian pure gauge theories. For this purpose, we discretize U(1) gauge group as Z_N and also continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories, and evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ∼exp(entropy), which is one of the conjectured criteria necessary to have a dual  black hole, the Abelian gauge theory needs to be maximally nonlocal. (Based on collaboration with Norihiro Iizuka and Sotaro Sugishita, https://arxiv.org/abs/1707.03840)

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