Spacetime as a quantum circuit

Abstract

We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the "complexity equals volume" conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $T\bar{T}$, we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

arXiv comment26 pages, 2 figures; v2: published version, minor clarifications added

References in corpus (53)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• A class of quantum many-body states that can be efficiently simulated
• Complexity Equals Action
• Entanglement Renormalization and Holography
• Complexity and Shock Wave Geometries
• On space of integrable quantum field theories
• Complexity, action, and black holes
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Quantum Computation as Geometry
• Holographic Dual of BCFT
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• The Gravity Dual of a Density Matrix
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Aspects of AdS/BCFT
• Generalised Israel Junction Conditions for a Gauss-Bonnet Brane World
• Gravitational action with null boundaries
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• On the Time Dependence of Holographic Complexity
• Noether charge, black hole volume, and complexity
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Entanglement renormalization for quantum fields
• A Stereoscopic Look into the Bulk
• Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
• Holography at finite cutoff with a $T^2$ deformation
• cMERA as Surface/State Correspondence in AdS/CFT
• Entwinement and the emergence of spacetime
• $T\bar{T}$ and the mirage of a bulk cutoff
• Einstein's Equations from Varying Complexity
• Entanglement, Holography and Causal Diamonds
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Tensor Networks from Kinematic Space
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• $T\overline{T}$ in AdS${}_2$ and Quantum Mechanics
• Complexity and the bulk volume, a new York time story
• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• Hamiltonian deformations in quantum mechanics, $T\bar{T}$, and SYK
• Path integral optimization as circuit complexity
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• Topological Complexity in AdS3/CFT2
• Extremal Surface Barriers
• Causal structure of the entanglement renormalization ansatz
• Is the gravitational action additive?
• Bending branes for DCFT in two dimensions
• Path Integral Optimization for $T\bar{T}$ Deformation
• Gravitational path integral from the $T^2$ deformation
• Path-Integral Optimization from Hartle-Hawking Wave Function
• Cutoff Dependence and Complexity of the CFT${}_2$ Ground State
• Surface/State correspondence and $T\overline{T}$ deformation
• $T\bar{T}$ Deformation and the Complexity=Volume Conjecture
• Holographic Complexity of LST and Single Trace $T\bar{T}$

Cited by in corpus (15)

• Complexity for Conformal Field Theories in General Dimensions
• Complexity Equals Anything II
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Lorentzian threads as 'gatelines' and holographic complexity
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Exact Gravity Duals for Simple Quantum Circuits
• Holographic Path-Integral Optimization
• Path Integral Complexity and Kasner singularities
• Circuit Complexity in Topological Quantum Field Theory
• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Q-curvature and Path Integral Complexity
• Complexity of non-trivial sound speed in inflation
• Holographic and QFT Complexity with angular momentum
• Cost of holographic path integrals