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21 April 2008


First steps to topological quantum computer on GaAs?

A quantum state, like ignorance, is a delicate exotic fruit; “touch it and the bloom is gone” (Lady Bracknell in [Wilde, Importance of Being Earnest, Act 1, 1895]). There have been many proposals but fewer demonstrations of computing devices based on quantum principles. One of the main practical difficulties has been in maintaining the quantum states needed to perform error-free computations.

However, a proposal in 1997 [preprint date; peer-reviewed publication in Kitaev, Ann. Phys., vol.303, p2, 2003] to use topological properties of quantum states that can only be realized in two dimensions to create error-free quantum computation may now be closer, with quantum Hall effect experiments showing quarter-electron-charge (e/4) states in gallium arsenide (GaAs) quantum point contact systems (QPCs). Topological properties are often more robust against deformation (cf the ‘topological equivalence’ between a coffee mug and a donut).

Picture: Schematic of experimental set-up of [Dolev et al, Nature, p.829, 17 April 2008] used to make shot-noise measurements.

Why e/4? As might be expected, the reasoning is rather involved, but Kitaev’s proposal needs a system that satisfies what is called ‘non-Abelian statistics’. The usual statistics of Fermi-Dirac (fermions: electrons, nucleons, neutrinos, quarks, bound systems consisting of odd numbers of fermions) and Bose-Einstein (bosons: photons, weak interaction bosons, Higgs particles, bound systems consisting of even numbers of fermions) are Abelian. The quantum spin-statistics theorem would seem to restrict particles and quasi-particles to such states, but it only strictly applies above two dimensions, such as the three-dimensional world we seem to inhabit.

Enter the two-dimensional electron gases (2DEGs) routinely created in compound semiconductor heterostructures. In two dimensions, it is theoretically possible to create states that are between fermion and boson; ‘anyons’, as they have been dubbed. Furthermore, it is theoretically possible for some anyons to be non-Abelian. While Abelian systems are blind to the order in which interactions take place, this is not the case with non-Abelian systems and, from this, topological properties can emerge and be manipulated.

One candidate for a non-Abelian anyon in a quantum Hall system has e/4. The first experiment suggesting a particle-like state (quasi-particle) of charge e/4 has just been published in Nature [Dolev et al, p.829, 17 April 2008]. Another experimental report is in preprint form, no doubt somewhere on the road to peer-reviewed publication [Radu et al,, 2008]. The latter (involving researchers from MIT, Harvard University and Bell Labs) compares experimental tunneling conductance data with various models and finds that they are most consistent with a non-Abelian e/4 state. The Nature paper (Weizmann Institute of Science) uses shot-noise measurements to find that the charge state is consistent with charge e/4 but inconsistent with e or e/2.

Both groups use AlGaAs/GaAs layers with silicon delta-doping to produce 2DEGs at depths of the order of hundreds of nanometers that are controlled by electrodes to produce the quantum point contact restriction. The experiments were carried out with the QPCs at tens of milli-Kelvin, although some of the measurement electronics were at higher temperatures (e.g. preamplifiers at 4.2K). Being a Hall experiment, there is a magnetic field of the order of 5 tesla.

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The author Mike Cooke is a freelance technology journalist who has worked in the semiconductor and advanced technology sectors since 1997.