They started out as a quantum flight of fancy, but these strange
particles may just bring quantum computing into the real world,
says Don Monroe
Don Monroe
WE SHOULD have known there was something in it when Microsoft got
involved. Back in 2003, the software giant began sponsoring a small
research effort with an interest in an abstruse area of physics known
as the fractional quantum Hall effect. The effect, which has been the
subject of two Nobel prizes, involves the delicate manipulation of
electrons inside semiconductor crystals. What could a software company
like Microsoft hope to gain from funding this research?
The answer is now clear. This year, we have seen the first indications
that this strange and abstract phenomenon could bring us a revolution
in computing. "We have good reason to believe that, if we can do
anything [with this], we can do a lot," says Michael Freedman of
Microsoft-sponsored Station Q research group in Santa Barbara,
California.
Microsoft is interested because an ability to manipulate the
fractional quantum Hall effect promises a unique and powerful way to
process information using the resources of the subatomic world. Down
at the level of photons, electrons, protons and atoms, matter behaves
very differently from what we are used to. These quantum objects can
be in two places at once, for example, or spin clockwise and
anticlockwise at the same time. This phenomenon, known as
superposition, is entirely foreign to the way things work in the
ordinary "classical" world.
It was realised years ago that superposition provides an opportunity
for information processing, and researchers have been working for
decades to build a "quantum computer" that exploits it. Encode a 0 as
the clockwise spin of an electron and 1 as the anticlockwise spin, for
example, and superposition gives you a kind of "buy one, get one free"
special offer, with both of these binary digits appearing on the same
particle. Process one of these quantum bits, or "qubits", and you get
two answers. If you could create an array of electrons in
superposition, it would be possible to use this phenomenon for
superfast processing. In principle, qubits enable huge sequences of
binary digits to be encoded and processed with much less computational
effort than would be needed in the classical world.
The thing is, while theorists drew up the blueprint for a quantum
computer more than two decades ago, we still don't have one. That is
largely because of a problem called decoherence. Quantum
superpositions are notoriously delicate. If the electron in a
superposition state is disturbed - by something in its environment
such as a little heat or a stray electromagnetic field, say - the
superposition will collapse and lose the double helping of information
it was carrying.
Follow the trail
This is where the fractional quantum Hall effect can help. Quantum
particles are conventionally divided into two types: fermions, such as
the electron; and bosons, such as the photon. Then, about 25 years
ago, researchers such as Frank Wilczek of the Massachusetts
Institute of Technology began to realise there might be a third type.
The idea came from considering whether you can tell two identical
particles apart from each other. Imagine a quantum version of the
magic cup game much beloved by dodgy street magicians. Two photons,
marked A and B, are hidden under two cups sitting on a table. The
magician swaps the cups around on the table top at a furious pace.
When the swaps are finished, would there be any way to tell, without
lifting the cups, which was which?
For photons, the answer is no: swapping their positions does not leave
a record on their quantum states. The same trick done with electrons
might leave a mark, but only after an odd number of swaps. With one
swap, the quantum state of the electrons gains a "topological charge",
rather in the way a balloon dragged along a carpet gains an
electrostatic charge, but if it is followed by a second swap that
topological charge is lost.
Wilczek realised, though, that quantum laws allow another possibility
- as long as there are only two dimensions. That restriction arises
because swapping positions is equivalent to rotating the particles
clockwise or anticlockwise. If you have three dimensions, shifting
your perspective - looking from under the table, for instance - can
make opposite rotations look identical; only in 2D would they always
be distinguishable.
Wilczek reasoned that if you could confine the game - including the
watchers - to two dimensions, perhaps a new class of particle, neither
fermions nor bosons, but something in between, could retain a
topological charge. In the highly artificial scenario of strange new
particles that exist only in 2D - Wilczek called them anyons - a
quantum trace of the particles' relative motions would remain.
This is the key to "topological quantum computing". We have known for
a very long time that knots and braids - which are the result of
swapping the relative positions of threads - offer a way to encode
numbers: that is how the ancient Incas kept records. Likewise,
swapping the relative positions of quantum particles can encode
numbers for quantum processing.
Consider three anyons in a row, denoted A, B and C. Swapping the left
two, then the right two, then the left two again yields first BAC,
then BCA and finally CBA. Swapping right, left, right yields ACB, CAB
and, as before, CBA. Though they appear identical, the two different
ways of swapping or "braiding" these anyons leaves them with different
topological charges. This means different numbers can be encoded in
the two knots that result in CBA (see diagram).
That's a good start, but there is a bonus that comes with anyons: they
are highly resistant to decoherence. That's because the numbers are a
result of the anyons' braiding, and cannot be shaken out. The kinds of
vibration or radiation that affect quantum states such as spin will
have no effect on the topological charge: it is, effectively, set in
stone.
It is a neat idea, but there seemed little chance of ever putting it
to practical use. After all, when he dreamed them up, Wilczek
considered his anyons to be nothing more than a theoretical notion. It
wasn't long before an unexpected development changed all that. In the
mid-1980s, researchers began to see the signatures of Wilczek's
anyons. The revelation that the entities he had conjured up can exist
in the real world still sends his eyebrows heading for the ceiling.
"It's something that we realised was actually allowed by quantum
mechanics a long time ago, but finding realisations is sort of a
surprise," Wilczek says.
That surprise has now led researchers to the threshold of creating a
quantum computer. The anyons researchers had been seeing were cropping
up on the surfaces of semiconductor crystals cooled close to absolute
zero. The quantum physics of semiconductors dictates that in the
presence of an electric field, the electrons can only move
perpendicular to the surface if they have enough energy to make the
leap to a new quantum energy level. At very low temperatures, the
electrons are starved of energy and so they can only move in 2D.
Dancing charges
When the researchers applied high magnetic fields to the crystal, a
new phenomenon emerged: the quantum Hall effect. The space available
to the electrons on the 2D semiconductor surface is divided into
"orbits", much like 2D versions of the fuzzy electron orbitals in
atoms. Quantum rules mean that the electrons' 2D orbits cannot overlap
and so, to avoid each other, the billions of electrons in the surface
coordinate their motions in an intricate dance. The precise nature of
the dance changes, depending on how many electrons there are compared
with the number of available orbits - a parameter known as the filling
factor. Experiments have revealed dozens of these complex, dynamic
patterns, known as quantum Hall states.
Once the electrons form a quantum Hall state, any latecomers have a
hard time cutting in, since the ones already there must alter their
steps to make room. Only when the newcomers are given a certain energy
will the rearrangement take place. Klaus von Klitzing won a Nobel
prize in 1985 for the discovery that there are a variety of such
quantum Hall states corresponding to integer filling factors.
Subsequent experiments have found similar states at a host of other
filling factors that are fractions of an integer, such as 1/3, 3/7,
6/11 and so on - the source of another Nobel prize.
Much as the collective movement of air molecules gives rise to a still
region that we call the eye of a storm, the coordinated motion of
electrons in the quantum Hall state creates a ghostly quasi-particle.
Each state has its own characteristic quasi-particles, which move
along the edge of the crystal. In many quantum Hall states, the
properties of these quasi-particles turn out to match those of
Wilczek's hypothetical anyons.
Unfortunately, it's not just any old anyon that will allow us to build
a quantum computer. Though all anyons gain topological charge when
swapped, or braided, for most of them the final charge does not depend
on the order in which the swaps are made, an essential property for
topological quantum computing. Anyons that "remember" the order of
swaps are known as "non-abelian" and, wouldn't you know it,
non-abelian anyons seem to be the hardest type to make. In fact, until
recently, it was not clear whether they could be made at all. Happily,
though, researchers are now closing in on these particles.
The key is picking the right filling factor. Experiments have revealed
dozens of complex quantum Hall states, each corresponding to
particular properties for the quasi-particles that emerge from it.
Hopes for non-abelian anyons hang on the quasi-particles for the
filling factor 5/2 state, which was discovered in 1988 by Bob Willett
and co-workers at Bell Labs in New Jersey. Theorists have proposed
several models for the properties of the quasi-particle associated
with this state and, tantalisingly, some of them are non-abelian.
So how do we find out for sure whether we have a non-abelian
candidate? Among all the theoretical possibilities set out for the 5/2
state, the correct description will be the one with the lowest total
mutual repulsion of the electrons in the 2D sheet, and thus the
minimum energy. Theorists can't calculate that energy accurately
enough to determine which theory is right, so the final verdict will
be found by experiment.
Clues to the winning theory are already beginning to emerge, and the
news is good. In April, a team led by Moty Heiblum at the Weizmann
Institute of Science in Rehovot, Israel, applied voltages to the
semiconductor, causing quasi-particle currents to flow around the
edges. They steered those currents by putting metallic electrodes over
the semiconductor and applying electric fields that nudge the streams
of charged quasi-particles to within a fraction of a micrometre of one
another (see diagram).
With such a tiny gap between the currents, a few quasi-particles sneak
from one edge to the other by a quantum-mechanical process called
tunnelling. By studying the current that tunnels across the
constriction, the researchers can isolate the properties of the
quasi-particles. One particularly useful indicator is the "shot noise"
in the tunnelling current. This electrical noise, which results from
statistical fluctuations in the number of particles over time, is
smaller if the current consists of more numerous, smaller charges. The
Weizmann researchers found that the current varied less in the 5/2
state than for ordinary electrons (Nature, vol 452, p 829), and
the size of this reduction implied that the quasi-particles have only
a quarter of the electron's charge, e.
This is good news, as it is exactly what theorists predicted the
charge to be. However, a frustrating gap in our knowledge remains.
"Every state anybody has proposed for 5/2 - abelian or non-abelian -
actually has e/4 charge," says Sankar Das Sarma of the University
of Maryland, College Park. "This really doesn't make any statement on
the non-abelian nature of the state."
The task of distinguishing possible descriptions of the 5/2 state has
fallen to another team, led by Charles Marcus of Harvard
University and Marc Kastner at MIT. To do this, they measured how
the tunnelling varies with both temperature and the total current.
This variation is thought to be related to a parameter known as the
coupling constant, which reflects how drastically the electrons must
rearrange themselves to accommodate an extra quasi-particle that
tunnels into it from the other side. Different models for the 5/2
state have well-defined values for this coupling constant, so this
provides a good experimental tool for determining whether the state is
non-abelian. Waiting for the result has had the quantum computing
researchers on tenterhooks. "It's a disaster if it's abelian,"
Freedman says.
Happily, it seems that disaster has been averted. When the Harvard and
MIT teams fixed the charge in the theory at the expected one-quarter
value, only a narrow range of coupling constants fitted their current
and temperature data. Of the existing tunnelling models, the two with
a coupling constant of 1/2 match best - and both are non-abelian. "It
really points very strongly in this direction, which is a very
exciting thing," Kastner says.
The implications are not yet set in stone - the measurements do not
quite rule out a state that has a coupling constant of 3/8, and which
is abelian - but most researchers are optimistic that the first step
towards a computing revolution is complete. It seems we really can
create the non-abelian anyons that could lead us into the new era of
information processing. Even more exciting, Kastner says, is the
demonstration that the flow of tunnelling quasi-particles can be
manipulated - an ability that will be critical if we are going to be
able to decode the information held in the particles' quantum states.
Measuring interference effects between tunnelling quasi-particles is
one way to do this, and several teams are racing to demonstrate
interference of 5/2 quasi-particles, with some promising early
results.
After decades of slow progress, this year's results are causing "quite
a bit of buzz", says theorist Nick Read at Yale University. Of course,
they are only the beginning. Building a technology based around anyon
computing will be challenging, to say the least. But it seems that
anyons have gone from hypothetical to high potential within a very
short period, and computing with quantum particles might be about to
hit the big time. "I expected zero experimental progress by now," says
Das Sarma. "We are all very pleased."
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