On page 829 of this issue, Dolev et al.1 report the detection of vortices in a fluid of electrons confined to two dimensions within a semiconductor structure that carry just 1/4 of the electron's charge. These 'quasiparticles' are an exciting find: according to theoretical predictions, their collective behaviour should be described by an unusual type of particle statistics known as non-abelian statistics. Above all, that could make them useful in an exotic, but highly promising, brand of quantum computer — the topological quantum computer (see News Feature on page 803)2.

It is an established fact that, if a large magnetic field is applied perpendicular to the plane confining a soup of mobile electrons in a gallium arsenide semiconductor structure, the confined electrons can be made to enter correlated states with very unusual properties. When an electric field is applied in the plane, and at certain values of the 'filling fraction' ν (defined as the ratio of the number of electrons in the fluid to the number of magnetic field quanta penetrating through the sample), the electrons will flow without encountering any resistance. In such states, the conductivity transverse to the electric field, the Hall conductivity, takes on the universal value νe2/h, where e is the electron charge, h is Planck's constant and ν = 1/m; m is an odd integer.

This 'fractional quantum Hall effect' was discovered3 in 1982, and explained theoretically4 a year later — achievements that were rewarded with a Nobel prize in 1998. In the theoretical treatment, a quantum Hall state at filling fraction 1/m will involve quasiparticles of fractional electric charge e/m. Such quasiparticles were first detected in 1997 through measurements of the statistical fluctuations of electrical current ('shot noise') on a single point contact in a quantum Hall device5,6.

As well as having a charge somewhere between 0 and 1, these quasiparticles obey an intermediate form of quantum statistics that lies somewhere between the two established forms, Fermi–Dirac statistics and Bose–Einstein statistics. Fermi–Dirac statistics applies to systems of spin-1/2 'fermions', which obey the Pauli exclusion principle; particles covered include electrons, protons, neutrons, quarks, neutrinos and atoms with an odd number of constituent particles. Bose–Einstein statistics governs the behaviour of collections of integer-spin 'bosons': atoms with an even number of constituents such as photons, gluons and the yet-to-be-found Higgs particle.

A crucial difference between fermions and bosons is that a wavefunction describing two bosons is symmetrical when the two particles are swapped around in space: it does not change sign, and the wavefunctions before and after the particle exchange are said to have a phase factor of 0. The wavefunction describing two fermions, on the other hand, is antisymmetrical, flipping sign when particles are exchanged (phase factor π). But the phase of the wavefunction representing two quasiparticles in a two-dimensional system such as a quantum Hall fluid can change by an arbitrary phase factor, not just 0 or π. The precise value of this phase depends on both the nature of the two quasiparticles and how their paths through space-time intertwine or 'braid' — a latitude that led to these quasiparticles being dubbed 'anyons' (see also 'Braiding anyons'2 on page 804). Anyons in a fractional quantum Hall fluid with filling factor 1/m are predicted to have fractional statistical phase π/m.

And indeed, the fractional quantum Hall states observed so far do largely follow that prediction. But remember that m is supposed to be an odd number; thus, the discovery some 20 years ago7 of a no-resistance quantum Hall state with an even denominator, at a filling factor of 5/2, was initially puzzling. This state was soon realized to have very special properties8,9: the associated quasiparticles would also have fractional charge, but would obey non-abelian statistics.

The definition of non-abelian statistics is complex, but one facet is that the state of a system of many quasiparticles obeying non-abelian statistics cannot be completely determined by knowing the quasiparticles' spatial coordinates. Several linearly independent wavefunctions are possible: a system with four quasiparticles, for instance, can have two different states. In this situation, the final state of an exchange interaction is a linear combination of the two initial states, and the braiding process as particles interact and their trajectories intertwine is encoded in a two-by-two matrix. More generally, for a system with 2n quasiparticles, there are 2n−1 states. In general, because any pair of quasiparticles in the quantum fluid can become intertwined, these states do not commute with each other — in other words, the order in which the exchange interactions between quasiparticles occur will determine the system's final state. This order-dependence of the state is crucial to the proposed use of non-abelian quasiparticles as the basic 'qubits' of information in a topological quantum computer2,10,11.

Dolev and colleagues' detection1 of a quasiparticle of charge e/4 is a first step in that direction. The discovery was made in a shot-noise experiment similar to those in which the original quasiparticle states were found5,6. But the new measurement was much harder to make than those pioneering experiments: the 5/2 state is so delicate that to study it requires a sample quality such that the mean free path of electrons before they collide with impurities in the semiconductor structure is very long (about 0.5 millimetres). It also requires low temperatures so that thermal fluctuations do not obscure the state.

Naively, one would have expected that the quasiparticle in the 5/2 state, with its denominator of 2, would have a charge of e/2 (the multiplier of 5 in the numerator is not relevant to these considerations). But through a series of non-trivial consistency checks, Dolev et al. show that the charge at filling fraction 5/2 is consistent with e/4, but not with e/2 (at integer filling fraction, the measured charge is just e and at a filling fraction 1/3 it is e/3). For that reason, this quasiparticle is also called a 'half-vortex' state.

Measuring the charge to be e/4 is a necessary, but not sufficient proof of a non-abelian state: there is a conceivable (but very unlikely) possible 'strongly paired' abelian state with the same filling fraction and charge. But an independent (and as-yet unpublished)12 direct-current transport measurement at a point contact has not only measured the same value of the fractional charge, but also a tunnelling probability consistent with the predictions for a non-abelian state.

Further tests of the statistics of these intriguing quasiparticles at single point contacts will be the next step. They will be the key to the development of well-controlled, multi-contact quantum inteferometers that are needed to test the properties of these intriguing quasiparticles, and thus to construct the qubits of a topological computer.