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The topology of four-dimensional manifolds
0. Introduction Manifold topology enjoyed a golden age in the late 1950's and 1960's. Of the mysteries still remaining after that period of great success the most compelling seemed to lie in
Non-Abelian Anyons and Topological Quantum Computation
Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of
Topology of 4-manifolds
One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological
Least area incompressible surfaces in 3-manifolds
Let M be a Riemannian manifold and let F be a closed surface. A map f: F---,M is called least area if the area of f is less than the area of any homotopic map from F to M. Note that least area maps
Interacting anyons in topological quantum liquids: the golden chain.
Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional (2D) conformal field theory with central charge c=7/10.
Topological Quantum Computation
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones poly-
A Modular Functor Which is Universal¶for Quantum Computation
Abstract:We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently
Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes
We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that