Towards universal topological quantum computation in the ν = 5 2 fractional quantum Hall state

@article{Freedman2006TowardsUT,
  title={Towards universal topological quantum computation in the $\nu$ = 5 2 fractional quantum Hall state},
  author={Michael H. Freedman and C. Nayak and Kevin Walker},
  journal={Physical Review B},
  year={2006},
  volume={73},
  pages={245307}
}
The Pfaffian state, which may describe the quantized Hall plateau observed at Landau level filling fraction $\ensuremath{\nu}=\frac{5}{2}$, can support topologically-protected qubits with extremely low error rates. Braiding operations also allow perfect implementation of certain unitary transformations of these qubits. However, in the case of the Pfaffian state, this set of unitary operations is not quite sufficient for universal quantum computation (i.e. is not dense in the unitary group). If… 
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
Braid matrices and quantum gates for Ising anyons topological quantum computation
Abstract We study various aspects of the topological quantum computation scheme based on the non-Abelian anyons corresponding to fractional quantum hall effect states at filling fraction 5/2 using
Quantum origami: Transversal gates for quantum computation and measurement of topological order
TLDR
It is demonstrated that multi-layer topological states with appropriate boundary conditions and twist defects allow modular transformations to be effectively implemented by a finite sequence of local SWAP gates between the layers, and methods to directly measure the modular matrices, and thus the fractional statistics of anyonic excitations are provided, providing a novel way to directlyMeasure topological order.
Parafermions in a Kagome lattice of qubits for topological quantum computation
Engineering complex non-Abelian anyon models with simple physical systems is crucial for topological quantum computation. Unfortunately, the simplest systems are typically restricted to Majorana zero
Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors
Measurement-only quantum computation with Floquet Majorana corner modes
Majorana modes, typically arising at the edges of one-dimensional topological superconductors, are considered to be a promising candidate for encoding nonlocal qubits in fault-tolerant quantum
A Blueprint for a Topologically Fault-tolerant Quantum Computer
TLDR
A schematic blueprint for a fully topologically-protected Ising based quantum computer is provided, which may serve as a starting point for attempts to construct a fault-tolerant quantum computer, which will have applications to cryptanalysis, drug design, efficient simulation of quantum many-body systems, searching large databases, engineering future quantum computers, and -- most importantly -- those applications which no one in the authors' classical era has the prescience to foresee.
Adiabatic topological quantum computing
TLDR
This work develops protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions.
Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
TLDR
This work analytically prove the existence of a fault-tolerant threshold for a certain class of non-Abelian anyon models, and numerically simulate the procedure for the specific example of Ising anyons.
...
1
2
3
4
5
...

References

On Witten’s 3-manifold Invariants
I distributed a preliminary version of some notes on Witten's recently discovered 3-manifold invariants. For various reasons the paper was never completed and published. Nevertheless, many people