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A Topological Phase in a Quantum Gravity Model
Michael H. Freedman
I would claim that we do not have a suitably general definition of what a topological phase is, or more importantly, any robust understanding of how to enter one even in the world…
Complexity Classes as Mathematical Axioms
M. Freedman
Treating a conjecture, P^#P != NP, on the separation of complexity classes as an axiom, an implication is found in three manifold topology with little obvious connection to complex…
Measurement-Only Topological Quantum Computation via Anyonic Interferometry
Parsa Bonderson, Michael Freedman, Chetan Nayak
We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation…
Positivity of the universal pairing in 3 dimensions
Danny Calegari, Michael Freedman, Kevin Walker
Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3-manifolds which it bounds. Gluing along S defines a Hermitian p…
Measurement-Only Topological Quantum Computation
Parsa Bonderson, Michael Freedman, Chetan Nayak
We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyon…