nLab
topological quantum computation

Contents

Context

Constructivism, Realizability, Computability

Topological physics

Contents

Idea

In topological quantum computation one aims to make use of quantum systems described by topological quantum field theory for quantum computation, the idea being that the defining invariance of TQFTs under small deformations implements a robust form of quantum error correction.

One approach to potentially realizing topological quantum computation in practice is via anyons in the quantum Hall effect and effectively described by some kind of Chern-Simons theory.

For the time being see at quantum computation for more.

References

Topological quantum computation with anyons

The idea of topological quantum computation via the Chern-Simons theory of anyons in the quantum Hall effect is due to:

Further discussion:

Review:

Anyons in the quantum Hall liquids

References on anyon-excitations (satisfying braid group statistics) in the quantum Hall effect (for more on the application to topological quantum computation see the references there):

The prediction of abelian anyon-excitations in the quantum Hall effect (i.e. satisfying braid group statistics in 1-dimensional linear representations of the braid group):

The original discussion of non-abelian anyon-excitations in the quantum Hall effect (i.e. satisfying braid group statistics in higher dimensional linear representations of the braid group, related to modular tensor categories):

Review:

Anyons in topological superconductors

On anyon-excitations in topological superconductors.

via Majorana zero modes:

Original proposal:

  • Nicholas Read, Dmitry Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect, Phys. Rev. B61:10267, 2000 (arXiv:cond-mat/9906453)

Review:

Further development:

  • Meng Cheng, Victor Galitski, Sankar Das Sarma, Non-adiabatic Effects in the Braiding of Non-Abelian Anyons in Topological Superconductors, Phys. Rev. B 84, 104529 (2011) (arXiv:1106.2549)

via Majorana zero modes restricted to edges of topological insulators:

  • Biao Lian, Xiao-Qi Sun, Abolhassan Vaezi, Xiao-Liang Qi, and Shou-Cheng Zhang, Topological quantum computation based on chiral Majorana fermions, PNAS October 23, 2018 115 (43) 10938-10942; first published October 8, 2018 (doi:10.1073/pnas.1810003115)

Last revised on February 17, 2021 at 00:53:52. See the history of this page for a list of all contributions to it.