In this article, we will discuss the Majorana particle and topological computation. The Majorana particle is a qubit that Microsoft has been studying as a quantum bit in quantum computers, but this year it was discovered that the paper on which it was based was wrong. Since then, the paper has been retracted and has become infamous, but the possibility of using the Majorana particle as a qubit has not disappeared. Nevertheless, the Majorana particle is a strong candidate for a topological qubit. The main points of this article are as follows
Majorana particles appear when a pair of zero-point crossings in the Fermi surface occur.
Majorana particles can be moved to perform quantum calculations.
Topological quantum computation has not yet found a quantum system directly, so various quantum computation methods have been proposed.
Although the Majorana particle is a virtual particle without mass and charge, it can be treated as a qubit, and the transport phenomena specific to it have been confirmed. The Majorana particle is a virtual particle without mass and charge, but it can be treated as a qubit, and its specific transport phenomena have been confirmed. This particle is commutative and always appears in pairs. However, the positions and distances of each pair of particles are movable and can be calculated. The system in which this particle appears is a Josephson device made of a topological superconductor and a topological insulator. They appear there in pairs, each at a different position. Another way is to produce them as vortex threads in defects in a two-dimensional system. A pair of Majorana particles can be generated there, one moving toward the other, and both observed simultaneously to complete the calculation. The above is just one example described in reference [1]. In practice, various methods have been proposed and vary depending on how the particle pair is generated.
The particles are defined by topological parameters and are therefore supposed to be robust to noise. In fact, theoretical predictions estimate that the error rate in Clifford gates other than phase gates is about 10-12 [2]. When this is completed, the performance of quantum computers will improve dramatically, and we may be able to go all the way to the third generation. I hope that Microsoft will not give up on this possibility.
[1]https://slidetodoc.com/majorana-fermions-and-topological-insulators-charles-l-kane/
[2][1501.02813] Majorana Zero Modes and Topological Quantum Computation (arxiv.org)
