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A Short Introduction to Topological Quantum Computation

by Ville Lahtinen, Jiannis K. Pachos

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Submission summary

As Contributors: Ville Lahtinen · Jiannis Pachos
Arxiv Link: (pdf)
Date accepted: 2017-08-24
Date submitted: 2017-08-15 02:00
Submitted by: Lahtinen, Ville
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


This review presents an entry-level introduction to topological quantum computation -- quantum computing with anyons. We introduce anyons at the system-independent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. Both the encoding and the processing are inherently resilient against errors due to their topological nature, thus promising to overcome one of the main obstacles for the realisation of quantum computers. We outline the general steps of topological quantum computation, as well as discuss various challenges faced it. We also review the literature on condensed matter systems where anyons can emerge. Finally, the appearance of anyons and employing them for quantum computation is demonstrated in the context of a simple microscopic model -- the topological superconducting nanowire -- that describes the low-energy physics of several experimentally relevant settings. This model supports localised Majorana zero modes that are the simplest and the experimentally most tractable types of anyons that are needed to perform topological quantum computation.

Ontology / Topics

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Anyons Majorana zero modes Nanowires Quantum information Topological quantum computation

Published as SciPost Phys. 3, 021 (2017)

Author comments upon resubmission

Thank you very much again for the high quality reviewing process with our first submission to SciPost. We have addressed the final remark by the referee (details in the list of changes) and hope that the manuscript is now ready for publication. We also added few more references to recent works that were brought to our attention.

Best regards,
Ville Lahtinen and Jiannis K. Pachos.

List of changes

Last paragraph of Sec 2.1:
We have split the paragraph into two paragraphs, where the first deals with simulations of actual topologically ordered systems, while the second deals with those that are only unitarily equivalent. As suggested by the referee, we now explicitly mention that unitary equivalence does not imply topological protection and mention that the aim of this approach is to simulate and test control operations in an encoding that parallels that of a genuine topological encoding.

We also added references [91,92,93] on simplified ways to construct braids for topological quantum computation, as well as reference on contemporary review on Majorana modes in solid-state systems [75] and reference [165] on a recent blueprint for a measurement-only topological quantum computer.

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