摘要
Phys. Rev. D 96, 126001 (2017) 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.