Video URL

https://pirsa.org/14040136

A non-commuting stabilizer formalism

Ni, X. (2014). A non-commuting stabilizer formalism. Perimeter Institute for Theoretical Physics. https://pirsa.org/14040136

Ni, Xiaotong. A non-commuting stabilizer formalism. Perimeter Institute for Theoretical Physics, Apr. 09, 2014, https://pirsa.org/14040136 

          @misc{ scivideos_PIRSA:14040136,
            doi = {10.48660/14040136},
            url = {https://pirsa.org/14040136},
            author = {Ni, Xiaotong},
            keywords = {Quantum Foundations, Quantum Gravity},
            language = {en},
            title = {A non-commuting stabilizer formalism},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2014},
            month = {apr},
            note = {PIRSA:14040136 see, \url{https://scivideos.org/pirsa/14040136}}
          }

Xiaotong Ni Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)

DOI 10.48660/14040136
Source Repository PIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are tensor products of single-qubit operators drawn from the group {\alpha I, X,S}, where \alpha=e^{i\pi/4} and S=diag(1,i). We provide techniques to efficiently compute various properties, related to e.g. bipartite entanglement, expectation values of local observables, preparation by means of quantum circuits, parent Hamiltonians etc. We also highlight significant differences compared to the Pauli stabilizer formalism. In particular we give examples of states in our formalism which cannot arise in the Pauli stabilizer formalism, such as topological models that supports non-abelian anyons. This is a joint work with O. Buerschaper and M. van den Nest.