Einstein's Equations from Varying Complexity

Abstract

A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by varying complexity. I present such a derivation for vacuum solutions of pure Einstein gravity in three-dimensional asymptotically anti-de Sitter space. The argument relies on known facts about holography and on properties of Tensor Network Renormalization, an algorithm for coarse-graining (and optimizing) tensor networks.

4 pages, 2 figures

References in corpus (2)

• A class of quantum many-body states that can be efficiently simulated
• From Path Integrals to Tensor Networks for AdS/CFT

Cited by in corpus (4)

• Path integral optimization as circuit complexity
• On complexity growth in massive gravity theories, the effects of chirality and more
• Investigating two counting methods of the holographic complexity
• To be unitary-invariant or not?: a simple but non-trivial proposal for the complexity between states in quantum mechanics/field theory