Bad science articles often make the very misleading claim that nobody really understands quantum mechanics. Maybe the foundations of quantum mechanics are not understood well (i.e., whether there is a more basic theory underlying quantum mechanics). However, quantum mechanics itself is understood so well that physicists have enough mathematical machinery, understanding, and hubris to conjecture with confidence a new kind of quantum particle, and to tailor design a new solid state material that will generate it! The new particle, called the Majorana fermion (MF), has never been seen before by man.

Elbowing the competition: Unlike the less useful new particles observed with the multi-billion dollar Large Hadron Collider (LHC), quantum computerists expect their solid state MFs to have many practical applications and to be cheap to generate. They plan to use solid state MFs to make quantum computers. If we can build them, QCs will perform certain calculations faster (i.e., with a more favorable time complexity) than current non-quantum computers, plus QCs may elucidate the very foundations of quantum mechanics.

The story of MFs is a real-life detective story filled with challenging puzzles and “what will happen next?” suspense.

(Ettore means Hector in Italian. In Homer’s Iliad, Hector was the bravest warrior on the Trojan side. He was killed by Achilles.) Ettore Majorana was born in 1906 and went missing in 1938. In those 32 years, he wrote just 9 papers, but they were good enough to make him famous. Enrico Fermi (a Nobel prize winner who worked with some of the greatest physicists of his time, like von Neumann, Feynman, etc.) was one of Majorana’s mentors and considered Majorana’s talent for physics equal to that of a Newton or a Galileo. Majorana was probably the first to hypothesize neutral protons (what we now call neutrons) before they were discovered in the lab. He also hypothesized massive neutrinos, something that took more than half a century to be taken seriously. More importantly for quantum computing, in 1932, he wrote down an equation, now called “the” Majorana equation, very similar to “the” Dirac equation.

The Dirac equation predicts two different types (electrons and positrons) of fermion particles that are anti-particles of each other and can annihilate each other. On the other hand, the Majorana equation predicts only one type of fermion particle (Majorana fermion) which is its own anti-particle and can annihilate a copy of itself. (The Dirac equation has complex-value field solutions whereas the Majorana equation has real-valued field solutions. According to Majorana, this is analogous to a Dirac particle requiring 4 wheels to move through space-time, like a car, versus a Majorana particle requiring only 2 wheels, like a bicycle or motorcycle).

Majorana disappeared under mysterious circumstances during a fairly short boat trip from Palermo to Naples. Many claim that he didn’t commit suicide or drowned accidentally, but that instead he faked his own death. Some say that he fled to a monastery or to Argentina and lived there anonymously for the rest of his life.

Another major Majorana mystery is where are the MFs? Scientists have neither found nor manufactured any MFs yet, almost 80 years after Majorana hypothesized their existence.

None of the “elementary” particles that have been observed so far by High Energy physicists are MFs. MFs occur in supersymmetric theories, but there is no evidence for such theories yet. It’s possible that neutrinos are MFs, but they could also be Dirac fermions. We still don’t know which one for sure.

MFs are expected to occur as “quasi-particles” in certain solid state systems, but even there, they are just a hypothesis. We still haven’t proven their existence experimentally or measured or harnessed their properties.

Anyons are particles that obey “any” statistics; i.e., statistics that are different from those obeyed by particles with half-integral spin (fermions) or integral spin (bosons). Scientists believe that nonabelian anyons could be used to make **embarrassingly long-lived qubits**. The reason for this expectation is that nonabelian anyons are protected by topology, and have no easy means of decohering by interacting with the environment.

Free MFs moving in 3D space obey spin 1/2 statistics. However, if MFs are confined to a 2 dimensional surface, they will instead obey nonabelian anyon statistics. To make a good qubit, it is also desirable that an MF remain close to a point (i.e., be localized) as occurs if it’s in a bound state.

Many labs are currently racing with each other to be the first to produce 2D bound MFs that are usable as qubits. They are looking for such MFs, for example, on the surface of a 3D topological insulator that is in close proximity to a superconductor. The MFs occur where the superconductor vortices intersect the surface of the topological insulator.

If you want to read a little more about the exciting race to build solid state MFs, check out the following introductory articles:

- Race for Majorana fermions, by Marcel Franz, March 15, 2010 (Physics 3, 24 (2010))
- Majorana fermions inch closer to reality, by Taylor L. Hughes, August 22, 2011 (Physics 4, 67 (2011))
- Topological insulators, by Charles Kane, Joel Moore. Physics World 24:32

## Leave a Reply