Computing spacetime

TL;DR

This paper proposes a principle where gravity and spacetime emerge from the optimization of quantum computational complexity, linking spacetime dynamics with quantum information theory within the AdS/CFT framework.

Contribution

It introduces a novel principle of spacetime complexity, connecting gravity to quantum computation, and visualizes spacetime evolution through Lorentzian threads representing quantum operations.

Findings

Einstein's equations emerge from quantum complexity laws.

Spacetime evolution can be visualized via Lorentzian threads.

Complexity optimization underpins gravitational dynamics.

Abstract

Inspired by the universality of computation, we advocate for a principle of spacetime complexity, where gravity arises as a consequence of spacetime optimizing the computational cost of its own quantum dynamics. This principle is explicitly realized in the context of the Anti-de Sitter/Conformal Field Theory correspondence, where complexity is naturally understood in terms of state preparation via Euclidean path integrals, and Einstein's equations emerge from the laws of quantum complexity. We visualize spacetime complexity using Lorentzian threads which, conceptually, represent the operations needed to prepare a quantum state in a tensor network discretizing spacetime. Thus, spacetime itself evolves via optimized computation.