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arXiv · 1707.03840

Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game -

Koji Hashimoto·Norihiro Iizuka·Sotaro Sugishita
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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 $\mathbf{Z}_N$ 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 for a generic class of diagonal Hamiltonians to achieve a large complexity $\sim \exp(\mbox{entropy})$, which is one of the conjectured criteria necessary to have a dual black hole, the Abelian gauge theory needs to be maximally nonlocal.

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Koji Hashimoto, Norihiro Iizuka, Sotaro Sugishita. 2018-04-10. Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game -. https://doi.org/10.1103/physrevd.96.126001

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