摘要
Quantum complexity is conjectured to probe inside of black hole horizons (or wormholes) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for Abelian pure gauge theories. For this purpose, we discretize the U(1) gauge group as Z(N) and also the continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories and to evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity similar to 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.