# Topological Quantum Computer¶

## Introduction¶

*Background:*

*Topological Defects and Phase Transitions*, Nobel Lecture 2016 [L3]*Topological Phase Transitions and Topological Phases of Matter*[M14]

*To investigate and summarize:*

*A Short Introduction to Topological Quantum Computation*[74].*Topological Quantum Computation*in Preskill’s lecture notes [L4].*Non-Abelian Anyons and Topological Quantum Computation*[97]*Introduction to topological superconductivity and Majorana*1*fermions*[78]*Computing with Quantum Knots*[M9], more accessible but the topic remains very abstract

## Advances and setbacks¶

*More recently, about a retracted paper and further concerns:*

*Quantized Majorana conductance*[140]Retraction Note - 08 March 2021: “We can therefore no longer claim the observation of a quantized Majorana conductance, and wish to retract this Letter.”

*Flux-induced topological superconductivity in full-shell nanowires*[125]Editorial Expression of Concern - 30 July 2021: “After the release of the additional data, two readers expressed a joint concern that the tunneling spectroscopy data published in the original paper are not representative of the entirety of the data released in association with this project.”

*Evidence of elusive Majorana particle dies — but computing hope lives on*[25]“The retraction is a setback for this approach to quantum computing, but scientists say it should still be possible to create and study the exotic states, known as Majorana fermions, that were the subject of the research. And researchers at Microsoft and elsewhere are still optimistic about the company’s plans to employ the phenomenon in a future quantum computer.”

“The theory says that these collective quantum states would be topological, meaning that they would ‘remember’ how they moved around with respect to one another, in the same way that strings in a braid ‘remember’ how they were intertwined (topology is a branch of mathematics that studies knots and braids, among other things). This should make the Majorana states robust carriers of information, suitable for building a quantum computer that can do certain calculations faster than any ordinary classical computer can.”

**Further learning:**

Online course Topology in Condensed Matter: Tying Quantum Knots on edX by the Delft University of Technology (TU Delft).