Complexity Equals Action

Understand

We conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that we call a Wheeler-DeWitt patch.

• We illustrate and test the conjecture in the context of neutral, charged, and rotating black holes in AdS, as well as black holes perturbed with static shells and with shock waves.
• This conjecture evolved from a previous conjecture that complexity is dual to spatial volume, but appears to be a major improvement over the original.
• In light of our results, we discuss the hypothesis that black holes are the fastest computers in nature.