Spacetime as a quantum circuit

• URL: http://arxiv.org/abs/2101.01185v2
• Date: Sun, 25 Apr 2021 11:24:20 GMT
• Title: Spacetime as a quantum circuit
• Authors: A. Ramesh Chandra, Jan de Boer, Mario Flory, Michal P. Heller, Sergio H\"ortner, Andrew Rolph
• Abstract summary: We find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the "complexity equals volume" conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $T\bar T$, we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

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