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We discuss, from a quantum information perspective, recent proposals ofMaldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetimeis an emergent property of the quantum entanglement of an associated boundaryquantum system. We review the idea that the informational principle of minimalcomplexity determines a dual holographic bulk spacetime from a minimal quantumcircuit U preparing a given boundary state from a trivial reference state. Wedescribe how this idea may be extended to determine the relationship betweenthe fluctuations of the bulk holographic geometry and the fluctuations of theboundary 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 bulkgravity theory dual to the boundary system.

Holographic fluctuations and the principle of minimal complexity