Holographic fluctuations and the principle of minimal complexity

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.

10 pages, 4 figures

References in corpus (3)

• Simulating Hamiltonian dynamics with a truncated Taylor series
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• Optimal control, geometry, and quantum computing

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• Complexity Functionals and Complexity Growth Limits in Continuous MERA Circuits
• Complexity growth of rotating black holes with a probe string
• Towards the Web of Quantum Chaos Diagnostics
• Properties of Krylov state complexity in qubit dynamics
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity