Holographic fluctuations and the principle of minimal complexity

TL;DR

This paper explores how minimal quantum circuit complexity can determine the emergent holographic spacetime and relate bulk geometric fluctuations to boundary quantum fluctuations, proposing an Einstein-like equation for dual gravity systems.

Contribution

It introduces a novel approach linking minimal quantum complexity to holographic spacetime and derives an Einstein-like equation for bulk-boundary fluctuation relations.

Findings

Minimal complexity determines holographic bulk geometry.

Bulk fluctuations relate to boundary quantum fluctuations.

Derived Einstein-like equations for dual gravity systems.

Abstract

We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. We describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system.