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Know your anyons
They started out as a quantum flight of fancy, but these strange particles could usher in a computing revolution, says Don Monroe
Know your anyons ●
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” 40 | NewScientist | 4 October 2008
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 www.newscientist.com
SIMON DANAHER
“When Wilczek dreamed anyons up,
he considered them to be nothing more than a theoretical notion” 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 www.newscientist.com
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, page 42). 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 4 October 2008 | NewScientist | 41
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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.
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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
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-
“After decades of slow
progress, this year’s results are causing quite a bit of buzz ”
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 42 | NewScientist | 4 October 2008
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
particles to within a fraction of a micrometre of one another (see diagram, right). 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 www.newscientist.com
SIMON DANAHER
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
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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.” ● Don Monroe is a writer based in New Jersey
www.newscientist.com
4 October 2008 | NewScientist | 43
Know your anyons ●
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” 40 | NewScientist | 4 October 2008
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 www.newscientist.com
SIMON DANAHER
“When Wilczek dreamed anyons up,
he considered them to be nothing more than a theoretical notion” 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 www.newscientist.com
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, page 42). 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 4 October 2008 | NewScientist | 41
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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.
8
9 9
I[gk[dY[(
9
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8 7
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
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-
“After decades of slow
progress, this year’s results are causing quite a bit of buzz ”
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 42 | NewScientist | 4 October 2008
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
particles to within a fraction of a micrometre of one another (see diagram, right). 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 www.newscientist.com
SIMON DANAHER
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
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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.” ● Don Monroe is a writer based in New Jersey
www.newscientist.com
4 October 2008 | NewScientist | 43