# Majorana

Fermions are fundamental particles, or elementary particles, which means that they have no constituent particles. They have half-integer intrinsic spins, such as +1/2 and -1/2, and are classified as either quarks or leptons. They can contribute to composite fermions, such as protons, neutrons, atoms, and molecules, and with assistance from force-carrying bosons they comprise all matter in the universe. The stability of matter is owed to fermions never occupying identical quantum states simultaneously, which is known as the Pauli exclusion principle.

All known fermions, with the possible exception of neutrinos, are Dirac fermions. These particles all have distinct antiparticles. A Majorana fermion, or Majorana particle, is a hypothesized fermion that is both a particle and its own antiparticle; it has the same properties either way. It is also inherently resilient to noise, which makes the theoretical Majorana qubit highly sought after for fault-tolerant quantum computing (FTQC). In regard to neutrinos, it remains unconfirmed whether they are Dirac fermions or Majorana fermions.

For more information, “Topology And Physics” by Chen Ning Yang, Mo-lin Ge, and Yang-hui He is a 232-page book published by World Scientific. It includes a chapter titled “Majorana Fermions and representations of the braid group.” For a relatively-quick visual explainer, QuTech Academy offers a free 6:27-minute video titled “Majorana fermions and where to find them.” The explanation includes some mathematics, but it also includes illustrations and some simplified descriptions.

## What is Majorana

Dirac fermions are like a traditional pair of gloves, with one glove comfortably fitting the left hand and one glove comfortably fitting the right hand, or a traditional pair of slippers, with one slipper comfortably fitting the left foot and one slipper comfortably fitting the right foot. The particles and antiparticles can be thought of as mirror images of each other, similar but not identical. In contrast, Majorana fermions would be the type of wool gloves or hotel slippers that can fit either the left or the right comfortably. In a mirror, the particles and antiparticles are identical.

## Theoretical Foundations of Majorana Particles

The Italian theoretical physicist Ettore Majorana laid the theoretical foundations for Majorana fermions back in 1937. Some of the key points today include:

- A majorana particle is a self-antiparticle, which means that it is identical to its own antiparticle.
- The Majorana equation describes the wave functions of particles that are their own antiparticles; it is the counterpart to the Dirac equation for Dirac fermions.
- In contrast to Dirac fermions, the creation and annihilation operators of Majorana fermions are identical.
- Some of the theoretical neutralinos in theoretical supersymmetry (SUSY) models are Majorana fermions that are the superpartners of gauge and Higgs bosons.
- If proven to exist, and if proven to be Majorana fermions, sterile neutrinos would be the first example of such within the Standard Model.
- In condensed matter physics, Majorana quasiparticles are collective quasiparticle excitations that appear to be a single Majorana fermion.

Research continues into understanding and discovering Majorana fermions. Some of this research has already extended beyond theory and into attempts to experimentally confirm their existence.

## Hunting for Majorana Particles: Experimental Pursuits

Experimentation has not yet confirmed the existence of Majorana fermions. However, the following are some of the leading experiments and initiatives toward achieving that aim:

- A 2017 experiment involving a superconductor, a topological insulator, and a magnet
- Further development of indium-antimonide nanowires, which might lead to detection
- Development of quantum materials and devices in which observations may be made
- Development of topological superconducting phases, from which particles may emerge

The controversy over Majorana particles is eroding confidence in the field. More accountability and openness are needed — from authors, reviewers and journal editors.

A paper titled “Quantum computing’s reproducibility crisis: Majorana fermions,” published in Nature, notes that there is considerable controversy in the field. Claims of Majorana particle detection have been heralded as breakthroughs upon their announcements, only to end up not being reproducible experimentally. Their existence, unfortunately, remains unconfirmed.

## Majorana Fermions in Condensed Matter Physics

In condensed matter physics, quasiparticles condense and some can exhibit the behaviors of Majorana particles. There are several areas from which Majorana fermions are predicted to emerge:

- Topological superconductors
- Between topological superconductors and topological insulators
- Indium-antimonide (InSb), indium-arsenide (InAs), and other semiconductor nanowires
- Superconductor midgap states
- One-dimensional superconducting nanowire systems

Although each of these areas are not without challenges, the confirmation of Majorana particles could lead to breakthroughs in:

- Fault-tolerant quantum computing (FTQC)
- Other topological quantum technologies
- Understanding quantum matter
- New areas of physics

In other words, the confirmation of Majorana particles would be a breakthrough both technologically and scientifically. The resultant applications and advancements could be far-reaching. Just thinking about quantum technologies, potential benefits include:

- The realization of a Majorana qubit that requires less quantum error correction (QEC) overhead, thus accelerating the arrival of FTQC
- The simulation of other quantum systems, which could accelerate discoveries in other areas of physics, chemistry, and material science
- Ultra-high-precision quantum sensors
- The development of topologically-protected quantum materials

The most exciting prospects of all might just be the ones that remain unforeseen.