PIRSA:24050089

Replica topological order in quantum mixed states and quantum error correction

Mong, R. (2024). Replica topological order in quantum mixed states and quantum error correction. Perimeter Institute. https://pirsa.org/24050089

Mong, Roger. Replica topological order in quantum mixed states and quantum error correction. Perimeter Institute, May. 22, 2024, https://pirsa.org/24050089 

          @misc{ pirsa_PIRSA:24050089,
            doi = {10.48660/24050089},
            url = {https://pirsa.org/24050089},
            author = {Mong, Roger},
            keywords = {Condensed Matter},
            language = {en},
            title = {Replica topological order in quantum mixed states and quantum error correction},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050089 see, \url{https://pirsa.org}}
          }

Roger Mong

University of Pittsburgh

Talk number
PIRSA:24050089
Collection
Talk Type
Subject
Abstract

 

Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively under-explored. We will give various definitions for replica topological order in mixed states. Similar to the replica trick, our definitions also involve n copies of density matrix of the mixed state. Within this framework, we categorize topological orders in mixed states as either quantum, classical, or trivial, depending on the type of information they encode.

For the case of the toric code model in the presence of decoherence, we associate for each phase a quantum channel and describes the structure of the code space. We show that in the quantum-topological phase, there exists a postselection-based error correction protocol that recovers the quantum information, while in the classical-topological phase, the quantum information has decohere and cannot be fully recovered. We accomplish this by describing the mixed state as a projected entangled pairs state (PEPS) and identifying the symmetry-protected topological order of its boundary state to the bulk topology.

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