First steps to topological quantum computer
on GaAs?
April
23 2008
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
errorfree computations.
However, a proposal in 1997 [preprint date;
peerreviewed 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 errorfree quantum
computation may now be closer, with quantum Hall
effect experiments showing
quarterelectroncharge (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 setup of
[Dolev et al, Nature, p.829, 17 April 2008]
used
to make shotnoise 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 ‘nonAbelian statistics’.
The usual statistics of
FermiDirac (fermions:
electrons, nucleons, neutrinos,
quarks, bound systems consisting
of odd numbers of fermions) and
BoseEinstein (bosons: photons,
weak interaction bosons, Higgs
particles, bound systems
consisting of even numbers of
fermions) are Abelian. The
quantum spinstatistics theorem
would seem to restrict particles
and quasiparticles to such
states, but it only strictly
applies above two dimensions,
such as the threedimensional
world we seem to inhabit.
Enter the twodimensional
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 nonAbelian.
While Abelian systems are blind
to the order in which
interactions take place, this is
not the case with nonAbelian
systems and, from this,
topological properties can
emerge and be manipulated.
One candidate for a nonAbelian
anyon in a quantum Hall system
has e/4. The first experiment
suggesting a particlelike state
(quasiparticle) 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
peerreviewed publication [Radu
et al, http://arxiv.org/abs/0803.3530,
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
nonAbelian e/4 state. The
Nature paper (Weizmann Institute
of Science) uses shotnoise
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 deltadoping
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 milliKelvin,
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.
Source
http://www.semiconductortoday.com/news_items/2008/APRIL/QUANTCOMP_210408.htm
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