Landscape of Measurement-Prepared Tensor Networks and Decohered Non-Abelian Topological Order

          @misc{ pirsa_PIRSA:24050042,
            doi = {10.48660/24050042},
            url = {https://pirsa.org/24050042},
            author = {Verresen, Ruben},
            keywords = {Quantum Information},
            language = {en},
            title = {Landscape of Measurement-Prepared Tensor Networks and Decohered Non-Abelian Topological Order},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050042 see, \url{https://pirsa.org}}
          }
          

Abstract

What is the structure of many-body quantum phases and transitions in the presence of non-unitary elements, such as decoherence or measurements? In this talk we explore two new directions. First, recent works have shown that even if one starts with an ideal preparation of topological order such as the toric code, decoherence can lead to interesting mixed states with subtle phase transitions [e.g., Fan et al, arXiv:2301.05689]. Motivated by a recent experimental realization of non-Abelian topological order [Iqbal et al, Nature 626 (2024)], we generalize this to decohered non-Abelian states, based on work with Pablo Sala and Jason Alicea [to appear]. Second, we study whether and how one can prepare pure states which are already detuned from ideal fixed-point cases---with tunable correlation lengths. This turns out to be possible for large classes of tensor network states which can be deterministically prepared using finite-depth measurement protocols. This is based on two recent works with Rahul Sahay [arXiv:2404.17087; arXiv:2404.16753].