Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe

Abstract

We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume duality in a geodesic causal ball in the framework of Fermi normal coordinates and derive the full non-linear Einstein equation. Using insights from the complexity/action duality, we argue that the accelerated expansion of the universe could be driven by the quantum complexity and free from coincidence and fine-tunning problems.

1+20 pages, 2 figures, references added

References in corpus (6)

• Complexity and Shock Wave Geometries
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• Einstein's Equations from Varying Complexity
• Entanglement equilibrium for higher order gravity
• Quantum Entanglement and Teleportation in Higher Dimensional Black Hole Spacetimes
• Equivalent Equations of Motion for Gravity and Entropy

Cited by in corpus (9)

• Chaos of Particle Motion near the Black Hole with Quasi-topological Electromagnetism
• Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity
• Complexity growth of rotating black holes with a probe string
• Emergent Dark Matter in Late Time Universe on Holographic Screen
• Subregion complexity and confinement-deconfinement transition in a holographic QCD model
• Complexity growth for topological black holes by holographic method
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity
• Complexity growth rate, grand potential and partition function
• Linearized Einstein's Equation around pure BTZ from Entanglement Thermodynamics