PIRSA:14040136

A non-commuting stabilizer formalism

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

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

          @misc{ pirsa_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},
            year = {2014},
            month = {apr},
            note = {PIRSA:14040136 see, \url{https://pirsa.org}}
          }

Xiaotong Ni

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

Talk number
PIRSA:14040136
Collection
Talk Type
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.