Anyons

Anyons are quasiparticles in two-dimensional systems whose exchange can produce phases or transformations beyond the bosonic and fermionic possibilities.

Particle statistics: Rules describing how identical particles behave when their labels are exchanged. Anyons extend the boson–fermion alternatives allowed in three dimensions.
Two-dimensional electron gas: Electrons confined so their motion is effectively restricted to a plane. Such systems provide the setting in which fractional quantum Hall anyons emerge.
Topological quantum computation: A model of quantum computation that encodes information in topological degrees of freedom. Non-Abelian anyon braids can implement quantum gates through particle exchanges.
Leinaas–Myrheim statistics: A formulation of particle statistics based on configuration spaces, published by Jon Leinaas and Jan Myrheim in 1977. It established that two-dimensional exchanges need not reduce to bosons or fermions.
Anyon detection: Experimental methods for determining whether excitations obey fractional exchange statistics. Distinguishing anyons requires signatures beyond measuring fractional charge alone.
Braid group: The mathematical group describing how strands can be intertwined without being cut. In two dimensions, particle exchanges follow braid-group paths rather than only permutations.
Quantum Hall effect: Quantized electrical transport observed in two-dimensional systems under strong magnetic fields. Its fractional regimes host the best-known candidate anyonic excitations.
Topological qubit: A quantum bit encoded in global properties of a topologically ordered system. Non-Abelian anyon states can store information across spatially separated excitations.
Frank Wilczek: A theoretical physicist who introduced the term anyon and developed models of fractional statistics. His work named and clarified the broader class of two-dimensional statistics.
Moore–Read state: A proposed fractional quantum Hall state associated with non-Abelian quasiholes. Its predicted non-Abelian excitations remain a major target for experimental tests.

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