PIRSA:20110003

Symmetry and information flow in quantum circuits with measurements

Altman, E. (2020). Symmetry and information flow in quantum circuits with measurements. Perimeter Institute. https://pirsa.org/20110003

Altman, Ehud. Symmetry and information flow in quantum circuits with measurements. Perimeter Institute, Nov. 23, 2020, https://pirsa.org/20110003 

          @misc{ pirsa_PIRSA:20110003,
            doi = {10.48660/20110003},
            url = {https://pirsa.org/20110003},
            author = {Altman, Ehud},
            keywords = {Condensed Matter},
            language = {en},
            title = {Symmetry and information flow in quantum circuits with measurements},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {nov},
            note = {PIRSA:20110003 see, \url{https://pirsa.org}}
          }

Ehud Altman University of California, Berkeley

DOI 10.48660/20110003
Talk Type Scientific Series
Subject

Abstract

Quantum circuits, relevant for quantum computing applications, present a new kind of many-body problem. Recently it was discovered that the quantum state evolved by random unitary gates, interrupted by occasional local measurements undergoes a phase transition from a highly entangled (volume law) state at small measurement rate to an area law state above a critical rate. I will review the current understanding of this transition from the statistical mechanics and the information perspectives. I will then argue that a circuit with intrinsic symmetries admits more phases, which represent distinct patterns of protection and flow of quantum information. These states can be studied and classified by mapping to an effective ground state problem of a Hamiltonian with enlarged effective symmetry. I will give two simple examples to illustrate these ideas: (i) a circuit with intrinsic Z2 spin symmetry; (ii) A circuit with Gaussian Majorana fermion gates showing a surprising Kosterlitz-Thouless transition in the entanglement content.