Measurement-induced criticality in random quantum circuits

A new class of quantum entanglement transitions separating phases with different entanglement entropy scaling has been observed in recent numerical studies. Despite the numerical efforts, an analytical understanding of such transitions has remained elusive. Here, the authors propose a theory for the area-law to volume-law entanglement transition in many-body systems that undergo both random unitary evolutions and projective measurements. Using the replica method, the authors map analytically this entanglement transition to an ordering transition in a classical statistical mechanics model. They derive the general entanglement scaling properties at the transition and show a solvable limit where this transition…

• NS
  National Science Foundation

  Awards: DMR-1309667, 1309667, 1748958
• UD
  U.S. Department of Energy

  Award: DE-SC0019168
• AP
  Alfred P. Sloan Foundation
• GA
  Gordon and Betty Moore Foundation

  Awards: PHY-1748958, GBMF4304
• OO
  Office of Science

  Award: DE-SC0019168
• DO
  Division of Materials Research

  Award: DMR-1309667
• KI
  Kavli Institute for Theoretical Physics, University of California, Santa Barbara

  Awards: 1748958, PHY-1748958
• BE
  Basic Energy Sciences

  Award: DE-SC0019168