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Tilted Interferometry Realizes Universal Quantum Computation in the Ising TQFT without Overpasses
Michael Freedman, Chetan Nayak, Kevin Walker
We show how a universal gate set for topological quantum computation in the Ising TQFT, the non-Abelian sector of the putative effective field theory of the fractional quan…
Towards Universal Topological Quantum Computation in the Fractional Quantum Hall State
Michael Freedman, Chetan Nayak, Kevin Walker
The Pfaffian state, which may describe the quantized Hall plateau observed at Landau level filling fraction , can support topologically-protected qubits with extremely low…
Distortion in transformation groups
Danny Calegari, Michael H Freedman
We exhibit rigid rotations of spheres as distortion elements in groups of diffeomorphisms, thereby answering a question of J Franks and M Handel. We also show that every homeomorph…
Lieb-Schultz-Mattis theorem for quasi-topological systems
Michael Freedman, Chetan Nayak, Kirill Shtengel
In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are…