Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence

We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of…

• NS
  National Science Foundation

  Awards: 1125565, 0803371, PHY-0803371
• GA
  Gordon and Betty Moore Foundation

  Awards: PHY-1125565, PHY-0803371
• IF
  Institute for Quantum Information and Matter, California Institute of Technology

  Award: PHY-1125565