[quantum-info] PIQuDos seminar Wed Sept 10: Jeongwan Haah

[Gus Gutoski]

Please join us on Wednesday, September 10 at 4pm in the Time room for
a quantum information seminar by Jeongwan Haah.

Title:  An invariant of topologically ordered states under local
unitary transformations
Speaker: Jeongwan Haah

Abstract: For an anyon model in two spatial dimensions described by a
modular tensor category, the topological S-matrix encodes the mutual
braiding statistics, the quantum dimensions, and the fusion rules of
anyons. It is nontrivial whether one can compute the topological
S-matrix from a single ground state wave function. In this talk, I
will show that, for a class of Hamiltonians, it is possible to define
the S-matrix regardless of the degeneracy of the ground state. The
definition manifests invariance of the S-matrix under local unitary
transformations (quantum circuits). The defined S-matrix depends only
on the ground state, in the sense that it can be computed by any
Hamiltonian in the class of which the state is a ground state. This
property, together with the local unitary invariance implies that any
quantum circuit that connects two ground states of distinct
topological S-matrices must have depth that is at least linear in the
diameter of the system. A higher dimensional analog is
straightforward. [arXiv:1407.2926]

Date: Wednesday, September 10, 2014.
Time: 16:00
Location: Time Room