1. The quantum world is lumpy

The quantum world has a lot in common with shoes. You cant just go to a shop and pick out sneakers that are an exact match for your feet. Instead, youre forced to choose between pairs that come in predetermined sizes.

The subatomic world is similar. Albert Einstein won a Nobel Prize for proving that energy is quantized. Just as you can only buy shoes in multiples of half a size, so energy only comes in multiples of the same "quanta" hence the name quantum physics.

The quanta here is the Planck constant, named after Max Planck, the godfather of quantum physics. He was trying to solve a problem with our understanding of hot objects like the sun. Our best theories couldnt match the observations of the energy they kick out. By proposing that energy is quantized, he was able to bring theory neatly into line with experiment.

J. J. Thomson won the Nobel Prize in 1906 for his discovery that electrons are particles. Yet his son George won the Nobel Prize in 1937 for showing that electrons are waves. Who was right? The answer is both of them. This so-called wave-particle duality is a cornerstone of quantum physics. It applies to light as well as electrons. Sometimes it pays to think about light as an electromagnetic wave, but at other times its more useful to picture it in the form of particles called photons.

A telescope can focus light waves from distant stars, and also acts as a giant light bucket for collecting photons. It also means that light can exert pressure as photons slam into an object. This is something we already use to propel spacecraft with solar sails, and it may be possible to exploit it in order to maneuver a dangerous asteroid off a collision course with Earth, according to Rusty Schweickart, chairman of the B612 Foundation.

Wave-particle duality is an example of superposition. That is, a quantum object existing in multiple states at once. An electron, for example, is both here and there simultaneously. Its only once we do an experiment to find out where it is that it settles down into one or the other.

This makes quantum physics all about probabilities. We can only say which state an object is most likely to be in once we look. These odds are encapsulated into a mathematical entity called the wave function. Making an observation is said to collapse the wave function, destroying the superposition and forcing the object into just one of its many possible states.

This idea is behind the famous Schrdingers cat thought experiment. A cat in a sealed box has its fate linked to a quantum device. As the device exists in both states until a measurement is made, the cat is simultaneously alive and dead until we look.

The idea that observation collapses the wave function and forces a quantum choice is known as the Copenhagen interpretation of quantum physics. However, its not the only option on the table. Advocates of the many worlds interpretation argue that there is no choice involved at all. Instead, at the moment the measurement is made, reality fractures into two copies of itself: one in which we experience outcome A, and another where we see outcome B unfold. It gets around the thorny issue of needing an observer to make stuff happen does a dog count as an observer, or a robot?

Instead, as far as a quantum particle is concerned, theres just one very weird reality consisting of many tangled-up layers. As we zoom out towards the larger scales that we experience day to day, those layers untangle into the worlds of the many worlds theory. Physicists call this process decoherence.

Danish physicist Niels Bohr showed us that the orbits of electrons inside atoms are also quantized. They come in predetermined sizes called energy levels. When an electron drops from a higher energy level to a lower energy level, it spits out a photon with an energy equal to the size of the gap. Equally, an electron can absorb a particle of light and use its energy to leap up to a higher energy level.

Astronomers use this effect all the time. We know what stars are made of because when we break up their light into a rainbow-like spectrum, we see colors that are missing. Different chemical elements have different energy level spacings, so we can work out the constituents of the sun and other stars from the precise colors that are absent.

The sun makes its energy through a process called nuclear fusion. It involves two protons the positively charged particles in an atom sticking together. However, their identical charges make them repel each other, just like two north poles of a magnet. Physicists call this the Coulomb barrier, and its like a wall between the two protons.

Think of protons as particles and they just collide with the wall and move apart: No fusion, no sunlight. Yet think of them as waves, and its a different story. When the waves crest reaches the wall, the leading edge has already made it through. The waves height represents where the proton is most likely to be. So although it is unlikely to be where the leading edge is, it is there sometimes. Its as if the proton has burrowed through the barrier, and fusion occurs. Physicists call this effect "quantum tunneling".

Eventually fusion in the sun will stop and our star will die. Gravity will win and the sun will collapse, but not indefinitely. The smaller it gets, the more material is crammed together. Eventually a rule of quantum physics called the Pauli exclusion principle comes into play. This says that it is forbidden for certain kinds of particles such as electrons to exist in the same quantum state. As gravity tries to do just that, it encounters a resistance that astronomers call degeneracy pressure. The collapse stops, and a new Earth-sized object called a white dwarf forms.

Degeneracy pressure can only put up so much resistance, however. If a white dwarf grows and approaches a mass equal to 1.4 suns, it triggers a wave of fusion that blasts it to bits. Astronomers call this explosion a Type Ia supernova, and its bright enough to outshine an entire galaxy.

A quantum rule called the Heisenberg uncertainty principle says that its impossible to perfectly know two properties of a system simultaneously. The more accurately you know one, the less precisely you know the other. This applies to momentum and position, and separately to energy and time.

Its a bit like taking out a loan. You can borrow a lot of money for a short amount of time, or a little cash for longer. This leads us to virtual particles. If enough energy is borrowed from nature then a pair of particles can fleetingly pop into existence, before rapidly disappearing so as not to default on the loan.

Stephen Hawking imagined this process occurring at the boundary of a black hole, where one particle escapes (as Hawking radiation), but the other is swallowed. Over time the black hole slowly evaporates, as its not paying back the full amount it has borrowed.

Our best theory of the universes origin is the Big Bang. Yet it was modified in the 1980s to include another theory called inflation. In the first trillionth of a trillionth of a trillionth of a second, the cosmos ballooned from smaller than an atom to about the size of a grapefruit. Thats a whopping 10^78 times bigger. Inflating a red blood cell by the same amount would make it larger than the entire observable universe today.

As it was initially smaller than an atom, the infant universe would have been dominated by quantum fluctuations linked to the Heisenberg uncertainty principle. Inflation caused the universe to grow rapidly before these fluctuations had a chance to fade away. This concentrated energy into some areas rather than others something astronomers believe acted as seeds around which material could gather to form the clusters of galaxies we observe now.

As well as helping to prove that light is quantum, Einstein argued in favor of another effect that he dubbed spooky action at distance. Today we know that this quantum entanglement is real, but we still dont fully understand whats going on. Lets say that we bring two particles together in such a way that their quantum states are inexorably bound, or entangled. One is in state A, and the other in state B.

The Pauli exclusion principle says that they cant both be in the same state. If we change one, the other instantly changes to compensate. This happens even if we separate the two particles from each other on opposite sides of the universe. Its as if information about the change weve made has traveled between them faster than the speed of light, something Einstein said was impossible.

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10 mind-boggling things you should know about quantum physics

The development of an ultrathin magnet that operates at room temperature could lead to new applications in computing and electronics such as high-density, compact spintronic memory devices and new tools for the study of quantum physics.

The ultrathinmagnet,which was recentlyreported in the journal Nature Communications, could make big advances in next-gen memory devices, computing, spintronicsand quantum physics. It was discovered by scientists at the Department of Energys Lawrence Berkeley National Laboratory (Berkeley Lab) and UC Berkeley.

Were the first to make a room-temperature 2D magnet that is chemically stable under ambient conditions, said senior authorJie Yao, afaculty scientist in Berkeley Labs Materials Sciences Division and associate professor ofmaterials science and engineering at UC Berkeley.

This discovery is exciting because it not only makes 2D magnetism possible at room temperature, but it also uncovers a new mechanism to realize 2Dmagneticmaterials, added Rui Chen, a UC Berkeley graduate student in theYao Research Groupand lead author on the study.

The magnetic component of todays memory devices is typically made of magnetic thin films. But at the atomic level, these materials are still three-dimensional hundreds or thousands of atoms thick. For decades, researchers have searched for ways to make thinner and smaller 2D magnets and thus enable data to be stored at a much higher density.

Previous achievements in the field of 2D magnetic materials have brought promising results. But these early 2D magnets lose their magnetism and become chemically unstable at room temperature.

State-of-the-art 2D magnets need very low temperatures to function. But for practical reasons, a data center needs to run at room temperature, Yao said. Our 2D magnet is not only the first that operates at room temperature or higher, but it is also the first magnet to reach the true 2D limit: Its as thin as a single atom!

The researchers say that their discovery will also enable new opportunities to study quantum physics. It opens up every single atom for examination, which may reveal how quantum physics governs each single magnetic atom and the interactions between them, Yao said.

The researchers synthesized the new 2D magnet called a cobalt-doped van der Waals zinc-oxide magnet from a solution of graphene oxide, zinc, and cobalt.

Just a few hours of baking in a conventional lab oven transformed the mixture into a single atomic layer of zinc-oxide with a smattering of cobalt atoms sandwiched between layers of graphene.

In a final step, the graphene is burned away, leaving behind just a single atomic layer of cobalt-doped zinc-oxide.

With our material, there are no major obstacles for industry to adopt our solution-based method, said Yao. Its potentially scalable for mass production at lower costs.

To confirm that the resulting 2D film is just one atom thick, Yao and his team conducted scanning electron microscopy experiments at Berkeley LabsMolecular Foundryto identify the materials morphology, and transmission electron microscopy (TEM) imaging to probe the material atom by atom.

X-ray experiments at Berkeley LabsAdvanced Light Sourcecharacterized the 2D materials magnetic parameters under high temperature.

Additional X-ray experiments at SLAC National Accelerator Laboratorys Stanford Synchrotron Radiation Lightsource verified the electronic and crystal structures of the synthesized 2D magnets. And at Argonne National Laboratorys Center for Nanoscale Materials, the researchers employed TEM to image the 2D materials crystal structure and chemical composition.

The researchers found that the graphene-zinc-oxide system becomes weakly magnetic with a 5-6 percentconcentration of cobalt atoms. Increasing the concentration of cobalt atoms to about 12 percentresults in a very strong magnet.

To their surprise, a concentration of cobalt atoms exceeding 15 percentshifts the 2D magnet into an exotic quantum state of frustration, whereby different magnetic states within the 2D system are in competition with each other.

And unlike previous 2D magnets, which lose their magnetism at room temperature or above, the researchers found that the new 2D magnet not only works at room temperature but also at 100 degrees Celsius (212 degrees Fahrenheit).

Our 2D magnetic system shows a distinct mechanism compared to previous 2D magnets, said Chen. And we think this unique mechanism is due to the free electrons in zinc oxide.

When you command your computer to save a file, that information is stored as a series of ones and zeroes in the computers magnetic memory, such as the magnetic hard drive or a flash memory.

And like all magnets, magnetic memory devices contain microscopic magnets with two poles north and south, the orientations of which follow the direction of an external magnetic field. Data is written or encoded when these tiny magnets are flipped to the desired directions.

According to Chen, zinc oxides free electrons could act as an intermediary that ensures the magnetic cobalt atoms in the new 2D device continue pointing in the same direction and thus stay magnetic even when the host, in this case the semiconductor zinc oxide, is a nonmagnetic material.

Free electrons are constituents of electric currents. They move in the same direction to conduct electricity, Yao added, comparing the movement of free electrons in metals and semiconductors to the flow of water molecules in a stream of water.

The new material which can be bent into almost any shape without breaking, and is a million times thinner than a sheet of paper could help advance the application of spin electronics or spintronics, a new technology that uses the orientation of an electrons spin rather than its charge to encode data. Our 2D magnet may enable the formation of ultra-compact spintronic devices to engineer the spins of the electrons, Chen said.

I believe that the discovery of this new, robust, truly two-dimensional magnet at room temperature is a genuine breakthrough, said co-author Robert Birgeneau, a faculty senior scientist in Berkeley Labs Materials Sciences Division and professor of physics at UC Berkeley who co-led the study.

Our results are even better than what we expected, which is really exciting. Most of the time in science, experiments can be very challenging, Yao said. But when you finally realize something new, its always very fulfilling.

Co-authors on the paper include researchers from Berkeley Lab, including Alpha NDiaye and Padraic Shafer of the Advanced Light Source; UC Berkeley; UC Riverside; Argonne National Laboratory; and Nanjing University and the University of Electronic Science and Technology of China.

The Advanced Light Source and Molecular Foundry are DOE national user facilities at Berkeley Lab.

The Stanford Synchrotron Radiation Lightsource is a DOE national user facility at SLAC National Accelerator Laboratory.

The Center for Nanoscale Materials is a DOE national user facility at Argonne National Laboratory.

This work was funded by the DOE Office of Science, the Intel Corporation, and the Bakar Fellows Program at UC Berkeley.

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News Scientists create the world's thinnest magnet - University of California

Strange ideas can come from ordinary places. This one came from Texas. In 1981, John A. Wheeler, the father of the black hole and a theoretical physicist at the University of Texas in Austin, threw a party. The guests were all young physicists with a common interest in the foundations of computing, a topic that Wheeler believed--correctly--would become increasingly important in the years to come.

It was at this party that a conversation with Charles Bennett, an IBM physicist, sparked an idea in the mind of Oxford University researcher David Deutsch. It struck him that computer theory was based on Newton's laws, not the more fundamental description of the universe provided by quantum theory.

At the time, the computer industry was beginning to fret over the future of microchips. How many calculations per second would be ultimately possible, how much heat would this produce, and could silicon survive the constant baking? To help them, computer scientists turned to the theory developed in the 1930s by the pioneer of their field, Alan Turing. But at Wheeler's party, said Deutsch, "I could see immediately that using the laws [of quantum mechanics] would give a different answer."

Deutsch began work on a paper that is now generally regarded as a classic in the field. Published in 1985, it describes how a computer might run using the strange rules of quantum mechanics and why such a computer differs fundamentally from ordinary computers.

Fifteen years later, the revolution that Deutsch started has reached global proportions. Quantum computers are no longer seen as weird curiosities but as the powerful future of the computer industry, and the debate is shifting from whether they will ever become a reality to when they will do so. The excitement is not due to their power, although they undoubtedly will be more powerful than today's models. Their big selling point, the killer app if you like, is that they can solve problems and carry out simulations that are basically impossible on conventional computers.

Such is the potential of these devices that the list of companies funding research programs sounds like a roll call of the world's biggest telecommunications and computer businesses. They include IBM, Hewlett-Packard, Lucent Technologies, AT&T, and Microsoft. There is even a New York Citybased start-up called MagiQ Technologies that hopes to make money by developing intellectual property in this field.

One of the strongest forces driving the development of quantum computers is the fear they will crack with ease secret codes that are impervious to other computers. The alarm bells started ringing in 1994, when Peter Shor of AT&T's Bell Laboratories in New Jersey showed that quantum computers were far faster than their ordinary brethren at factoring numbers.

Finding the factors of large numbers is so difficult for conventional computers that code-makers rely on this weakness of theirs to protect sensitive data. With the development of quantum computers, these codes will be obsolete. As soon as the first modest-sized quantum computer is switched on, governments and their militaries will be forced to concede that many of their codes are unsafe. Understandably, they are keen to find out just what quantum computers can do, and various national laboratories have begun substantial programs, in particular the U.S. National Institute of Standards and Technology in Boulder, Colo.; Los Alamos National Laboratory in New Mexico; and the United Kingdom equivalent, the Defence Evaluation and Research Agency in Malvern.

Aside from its promise for espionage there is the new physics unveiled almost daily by scientists trying to understand quantum information and how to control it. Quantum computers are becoming tiny laboratories in which scientists can test the theories of quantum mechanics with greater precision than ever before. Arguably the strongest team in the world making such discoveries is at the University of Oxford. Smaller groups exist at places such as MIT, Caltech, and a group of Australian universities, with influential individuals scattered throughout the United States, Europe, and Israel. After a late start, Japan has begun a concerted effort to catch up.

ILLUSTRATION: STEVE STANKIEWICZ

How Spin States Can Make Qubits: The spin of a particle in a dc magnetic field is analogous to a spinning top that is precessing around the axis of the field. In such a field, the particle assumes one of two states, spin up or spin down, which can represent 0 and 1 in digital logic. A particle in one spin state can be pushed toward another by a radio frequency pulse perpendicular to the magnetic field. A pulse of the right frequency and duration will flip the spin completely [top]. A shorter RF pulse will tip the spin into a superposition of the up and down state [bottom], allowing simultaneous calculations on both states.

Quantum information

Digital information appears mundane stuff. The 0s and 1s of binary code can be easily measured, copied, and moved around. But assign a piece of information to a quantum particle, and it takes on the bizarre characteristics of the quantum world. This fundamental unit of quantum information is called a quantum bit, or qubit (pronounced cue bit), and it is quite different from its classical counterpart.

For a start, a qubit can be both a 0 and 1 at the same time. Take the spin of an electron--a property that can be imagined as the spin of a top with its axis pointing either up or down [see figure, above}. The up or down spin can correspond to a 0 or 1. But the electron can also be placed in a ghostly dual existence, known as a superposition of states, in which it is both up and down, a 0 and a 1, at the same time. Carry out a calculation using the electron, and you perform it simultaneously on both the 0 and the 1, two calculations for the price of one.

At first glance, this may not seem impressive, but add more qubits and the numbers become much more persuasive. While 1 qubit can be in a superposition of two states, 0 and 1, two qubits can be in a superposition of four states--00, 01, 10, and 11--representing four numbers at once. The increase is exponential: with m qubits, it is possible to carry out a single calculation on 2m numbers in parallel. With only a few hundred qubits, it is possible to represent simultaneously more numbers than there are atoms in the universe.

Algorithms, entanglement, and error correction

Of course, once the calculation has finished, the answer must be obtained. A simple measurement destroys the superposition, leaving the system in one state or another. Unfortunately, it is rarely possible to determine in advance which state this will be, and that is a problem. The goal is to ensure that the measurement produces the answer of interest, and it can be reached by exploiting the phenomenon of quantum interference. Each of the superposed states has a probability associated with it that has a wavelike behavior--it can interfere with the probabilities of other states destructively or constructively. Getting the desired answer to a calculation means processing the information in such a way that undesired solutions interfere destructively, leaving only the wanted state, or a few more or less wanted states, at the end. The process is known as a quantum algorithm, and its design challenges physicists, mathematicians, and computer scientists. A final measurement then gives the desired answer, or in the case of a few final states, a series of measurements gives their probability distribution from which the desired answer can be calculated.

Quantum algorithms have the potential to be dramatically faster than their conventional counterparts. A good example is an algorithm for searching through lists that was developed by Lov Grover at Lucent Technologies' Bell Laboratories, in Murray Hill, N.J. The problem is to find a person's name in a telephone directory, given his or her phone number. If the directory contains N entries, then on average, you would have to search through N/2 entries before you find it. Grover's quantum algorithm does better. It finds the name after searching through only (check)N entries, on average. So for a directory of 10 000 names, the task would require (check)(10 000) = 100 steps, rather than 5000. The algorithm works by first creating a superposition of all 10 000 entries in which each entry has the same likelihood of appearing in response to a measurement made on the system. Then, to increase the probability of a measurement producing the required entry, the superposition is subjected to a series of quantum operations that recognize the required entry and increase its chances of appearing. (Remember that the recognition is possible because you have the phone number but not the name.)

ILLUSTRATION: STEVE STANKIEWICZ

Entangled Particles: If two particles, both in states of superposition, are entangled, measuring one forces both to assume complementary states.

Coherence/Decoherence: the ability of a quantum system to maintain a superposition of states. Decoherence is the process by which interactions with the environment destroy superposition, forcing a system into one state or another.

Entanglement: the state in which two quantum systems in indeterminate states are linked so that measuring or manipulating one system instantaneously manipulates the second.

Qubit: a unit of information used in quantum computing. It is distinct from an ordinary bit in that it can encode a superposition of values.

Spin: a quantum mechanical property of particles that in certain cases can take only two mutually exclusive values. It is used widely in nuclear magnetic resonance.

Superposition: if a physical system such as a particle can be found in more than one state and its state is unknown, it exists in a superposition of those states. That is, if there are two possible states, the system can be said to exist in both at once until its state is actually measured. Such a measurement collapses the system onto one state or another.

Teleportation: communication between two parties using entangled particles. Through the entanglement the state of one particle can be transferred to another distant particle with which it is entangled.

Vibrational State: the quantized state of the collective motion of ions in a linear ion trap. The vibrational state can encode a qubit and is used to link the ions during calculations.

As if superposed values and probability waves were not counterintuitive enough, another strange phenomenon is prominent in the new science of quantum information. In the '30s, scientists fiercely debated whether what quantum mechanics predicted had a real existence or whether its strangeness was due to some deficiency in the theory. In particular, Albert Einstein could not believe that the universe was built as quantum mechanics claimed. So, together with his colleagues Boris Podolsky and Nathan Rosen, he devised a thought experiment to find holes in the new theory.

The thought experiment centers on the behavior of pairs of particles that, according to quantum theory, are joined together--entangled--in a profound way that has no analog in the classical world. Prod one, and it seems the other instantly feels the influence, no matter how far away it might be [see figure, above]. The three scientists pointed out that this process would have to involve a faster-than-light signal passing between the particles--an impossibility. Their conclusion became known as the EPR (Einstein-Podolsky-Rosen) paradox and the entangled particles as EPR pairs.

The debate was resolved by John Bell, a theorist at CERN, the European laboratory for particle physics near Geneva, and the French physicist Alain Aspect. They proved that the Siamese twins of the quantum world, EPR pairs, indeed behave in the way predicted by quantum mechanics. However, the experiment also showed that there is no faster-than-light signal and that entanglement cannot be used for superluminal communication. Rather than communicating, EPR pairs share the same existence, the same destiny, if you like. Entanglement is now one of the key phenomena exploited in quantum information processing. Today the EPR experiment is performed almost daily around the world.

If creating entanglement and superposition has become a commonplace event compared with 10 years ago, quantum information remains fragile stuff. Ordinary interactions with the environment destroy qubits and the information they contain, a process known as decoherence. (Its opposite, coherence, is the ability of a qubit to maintain such quantum characteristics as superposition.) If quantum information is to pass into the world of computer science, a process of error correction is needed to protect against decoherence [see Defining Terms, left].

Initially, physicists believed that such a technique was impossible, because detecting and correcting errors would mean measuring the state of a quantum system and so destroying the information it contained. Still, by the early '90s Deutsch had shown this need not be the case. And in 1994 Andrew Steane at the University of Oxford and Peter Shor at AT&T's Bell Laboratories in New Jersey independently discovered practical quantum error-correction algorithms.

The problem is similar to reproducing in one place a message that has been constructed in another. If the message is sent over a channel or stored in a place noisy enough to distort some of the bits in the sequence, how can the receiver recognize the message? By adding redundancy to the message so that the sender can correct bits that have been distorted.

Shor and Steane came up with the quantum equivalent of sending the same bit three times. The extra qubits are known as ancillas. Measuring these qubits tells the receiver what errors have occurred and how to correct the qubits that are part of the message.

NMR leads the charge

The first big breakthrough for scientists building actual quantum computers came in the mid-'90s, when they discovered how to carry out calculations using the techniques of nuclear magnetic resonance (NMR). The key idea was that a single molecule can act like a tiny computer. Information is stored in the orientation of nuclear spins in the molecule, each nucleus holding one qubit. And the interaction between the nuclear spins, known as spin-spin coupling, serves to mediate logic operations. In a strong magnetic field, these nuclei precess around the direction of the magnetic field at frequencies that depend on their chemical environment.

For instance, in a 9.3-tesla field, a carbon-13 nucleus in a chloroform molecule precesses at about 100 MHz. By zapping the molecule with radio waves tuned to these resonant frequencies, it is possible to manipulate each nucleus individually to carry out logic operations. The manipulation might involve flipping a nucleus from a 1 to a 0, a so-called one-qubit operation or single-bit rotation; or it might involve two linked nuclei in a two-qubit operation, in which the value of one nucleus is flipped in a way that depends on the value of the other.

Chloroform made with the carbon-13 isotope is a good example of a molecule that can act as a two-qubit quantum computer, because its hydrogen and carbon-13 nuclei can be addressed individually by the radio waves. A quantum calculation is then carried out by encoding a program--a sequence of one- and two-qubit operations--as a series of RF pulses. The results are then read out by listening for the magnetic induction signal generated by the precessing nuclei at the end of the calculation. That signal indicates the orientation of the nuclear spin.

Nuclear magnetic resonance sounds like the dream solution to a thorny problem. Nuclei are naturally isolated from the noise of the outside world and so can maintain coherence for many seconds, enough time to perform hundreds of logic operations. In addition, NMR is a mature technology, having been used over many years for imaging and chemical analysis.

But the technique has some severe limitations. Single molecules do not produce a signal strong enough to be observed. Instead, NMR experiments must involve huge numbers of molecules (of the order of 1023) so that their combined magnetic induction signal is large enough to be picked up. (These molecules are usually distributed in a solvent, so the first quantum computers actually have liquid hearts.)

To begin a calculation, the initial state of the computer must be known. But in a material at room temperature, the spin up and spin down states are distributed almost equally and at random. In other words, the state of each of the many computers in solution cannot be known, rendering any subsequent calculation meaningless.

ILLUSTRATION: STEVE STANKIEWICZ

Quantum Logic: One of the most important logic elements in quantum computing is the controlled-NOT gate, similar to a controllable inverter circuit. In such an element, the state of one qubit, the control qubit, determines whether the final state of a second qubit, the input qubit, will be inverted by a series of RF pulses.

But never say die. In 1997, two groups independently came to quantum computing's rescue. Isaac Chuang, now at IBM's Almaden Laboratory near San Jose, Calif., and Neil Gershenfeld at the Massachusetts Institute of Technology (MIT), in Cambridge, found that they could turn a small natural bias--say, toward spinning up rather than down with respect to the magnetic field--in the nuclei of some molecules to advantage. They could use it to establish a kind of artificial ground state (00 for a two-qubit stystem) from which to start a calculation. At the same time, David Cory, also at MIT, and Amr Fahmy and Timothy Havel, both from Harvard University, in Cambridge, Mass., discovered that by bombarding the sample with radio pulses they could effectively "jam" the signal from all but the ground state.

To carry out useful calculations, the computer must be able to perform any logical operation. For quantum computers, there are two logic operations from which all other operations can be derived, rather like the AND and NOT gates in classical computing. One involves rotating a single qubit. The other, carried out on two qubits and called a controlled-NOT gate, flips or fails to flip one qubit depending on the state of another to which it is coupled [see figure, above]. Both these operations are straightforward: simply bombard the liquid sample with the appropriate sequence of radio pulses. Since 1997, these two groups and others, notably at Los Alamos and Oxford University, have built liquid NMR quantum computers with up to seven qubits to perform simple algorithms, one of which even belongs to the mathematical family of Shor's code-cracking formula [see "Quantum Code Cracking Creeps Closer," Spectrum, October 2000].

Unfortunately, quantum computers based on liquid NMR will never be much more powerful than this. The readout signals they produce plummet exponentially with the number of qubits involved in the calculation, because the proportion of molecules found in the appropriate starting state decreases. So scientists do not expect to be able to handle any more than a dozen qubits or so before the signal becomes indistinguishable from the background. Attempts to build machines that can handle more than 10 qubits continue, but if nontrivial quantum computing is ever to become possible, some other approach is needed.

Refrigerated ions

A technology that is less in the public eye than NMR has attracted others. In 1995 Ignacio Cirac and Peter Zoller of the University of Innsbruck, in Austria, suggested using ion traps to build quantum logic gates. The technology behind ion traps is already used for spectroscopy and to improve time and frequency standards, but huge advances are needed for quantum computation. The idea is that a number of ultra-cold ions can be trapped using a device known as a linear radio-frequency Paul trap. This device sets up a high-frequency RF field that holds the ions tightly in two dimensions but only weakly in the third dimension. Because the ions have the same charge, they repel each other and tend to arrange themselves in a straight line, equally spaced, like beads on an elastic string. The arrangement allows them to vibrate as a group in ways important for quantum computing.

The qubits are initially stored in the internal spin states of the ions relative to a background magnetic field. They are written to the ions using a pulsed, oscillating magnetic field, which flips the bits or places them in a superposition of up and down states, depending on its duration. An advantage of ion traps is that this superposition is extremely robust, lasting for at least as long as the qubits in NMR, ample time to carry out the desired logic operations.

ILLUSTRATION: STEVE STANKIEWICZ

Computing in an Ion Trap: Ions are lined up in a trap by RF energy from four electrodes, then chilled using lasers [top]. The electrostatic repulsion between the ions couples their individual motion as if they were connected by springs [middle]. The coupled motion, or vibrational state, can be used to transfer quantum information from one qubit to another. Basically, a pulse of energy equal to the difference between the quantum state of the ion and the vibrational state of the two ions (0 or 1) leads the ion to swap its internal state for the vibrational state. A similar pulse to the other ion performs another swap, transferring the original state of the first qubit to the second.

To share the qubits between the ions, scientists turn to the ion vibrations. The aim is to chill the ions until as a group they are absolutely still. This is the ground state of the system. Inject a little energy, and the ions begin to vibrate. But being quantum particles, the ions can exist in a superposition of the ground state and the vibratory state, so the vibration can be used to store a qubit. Because the ions all take part in the vibration, this qubit is shared among them. It's as if this collective motion is a kind of databus, allowing all the ions to temporarily share the information and become entangled. This sharing allows the IF and THEN type operations that are the building blocks of computer logic gates. For example, an instruction might be: IF the vibrational state is 1, THEN flip the qubit in the first ion's internal spin state. Researchers at the National Institute of Science and Technology (NIST) have already demonstrated that a string of four ions can be entangled and have said that more should be possible.

At least five groups around the world are working on ion trap quantum computers, but David Wineland's team at NIST is widely regarded as the leader. His group has built a 2-qubit logic gate using a single beryllium ion cooled to its vibrating ground state. Using a laser focused on the ion, the group superimposes on the background magnetic field a second magnetic field with a magnitude that varies with the position of the ions. The ion's vibration causes it to experience an oscillating magnetic field, and when the frequency of the oscillation matches the energy difference between the ion's two spin states, energy is transferred from the spin to the vibrational state, mapping the quantum information to the vibrational from the spin state [see figure, above]. This is the basis of a controlled-NOT gate and was realized in 1995 only a few months after Cirac and Zoller's announcement. Reading the data involves scattering light off the ion, since a spin up ion can be made to scatter strongly, while a spin down ion will scatter hardly at all.

Ion traps, too, have their limitations. One is the short decoherence time of the qubits after transfer to the vibrational "databus." Because the ions are charged, the vibrations are strongly influenced by stray electric fields, causing decoherence. Nonetheless, the group is confident that this tendency can be overcome by isolating the trap better from the environment. Ion traps also suffer from problems of scalability. The more ions there are in the trap, the greater the risk of tapping into uncontrollable vibrational states and so destroying the calculation. The next step will be to build adjacent traps, each holding only a few ions, and sending quantum information from one trap to another, either by physically moving the ions or by a phenomenon peculiar to quantum information called teleportation.

The alternatives

While liquid NMR is doomed because of the problems of working at room temperature, several groups are looking into carrying out NMR-type manipulations on single atoms in the solid state. A proposal from Bruce Kane at the University of Maryland in particular has attracted attention. His idea is to bury an array of phosphorus atoms in silicon and overlay it with an insulating layer, on top of which sits a like array of electrodes, each of which can apply a voltage to the atom beneath it. The ingenious aspect of this setup is how Kane proposes to control the spin of each nucleus.

Just as in NMR, the spin of the nuclei can be flipped by being zapped with radio waves of just the right energy--but, of course, these radio waves would flip every nucleus. Now phosphorus atoms have a single electron in their outer shell that interacts with the nuclear spin in a complex way. Applying a voltage to the atom changes the energy required to address both the nuclear and the electronic spin, and therefore it changes the frequency of the radio waves needed to flip the nucleus. So by applying a voltage to a specific electrode and zapping the array with the new frequency, it is possible to address a single nucleus.

But to perform a controlled-NOT logic operation, two qubits have to become entangled. Kane also has a way of doing this. Voltages applied between adjacent phosphorus atoms in the array can turn on and off the interactions between the outer electrons in each atom, allowing two-qubit operations.

Of course, the theory is all very well. The difficulty is actually building such a device, and Kane's collaborators are already working on it. At the Centre for Quantum Computer Technology at the University of New South Wales, in Australia, Robert Clark heads a team that is hoping to overcome many of the obstacles Kane's device faces. First up is the difficulty of creating the atomic array and preventing the phosphorus atoms from migrating within the silicon.

Kane is setting up a lab to study another challenging aspect of his device: the readout. Once the one- or two-qubit operation has been completed, the result has to be read out from the nuclear spins. Once again, Kane relies on the link between nuclear and electronic spins to get an answer. By very carefully measuring the spin of the electron, he said, it is possible to infer the spin of the nucleus. Measuring the spin of a single electron has never been done, but Kane said this should be possible shortly.

Kane's idea has attracted so much attention because many of these logic gates can be linked together to form a large quantum computer, though doing so may take some time. New South Wales's Clark believes that a handful of qubits might be possible in the medium term.

The quantum phenomena of superconductivity may also prove useful for building quantum computers. In 1999, at the Delft University of Technology in the Netherlands, a team designed a superconducting circuit in which superposed counter-rotating currents could prove useful for storing and manipulating qubits. The circuit consists of a loop with three or four Josephson junctions for measuring the circuit's state. The fact that it is made by conventional electron-beam lithographic techniques makes it particularly conducive to large-scale integration. However, superconducting circuits have short decoherence times, and today's techniques for measuring the states of the circuits are too invasive for useful manipulation of qubits.

A more advanced solid-state technology is the quantum dot, essentially a semiconductor trap holding a discrete number of electrons. These have been studied since the early 1990s because the trapped electrons act like artificial atoms, with their own periodic table and chemistry. Then in 1998, David DiVincenzo of IBM and Daniel Loss of the University of Basel, in Switzerland, proposed using quantum dots as the building block of a quantum computer, and a variety of ideas have since been put forward for exploiting the dots' quantum properties for computation. One idea is a two-qubit system consisting of two electrons shared by four quantum dots in a square. The electrons, seeking to minimize their energy, occupy opposite corners of the square, and since this arrangement has two configurations, they exist as a superposition that is manipulable through electrodes at the corners of the square. A number of other techniques involve reading and writing data to the dots with laser pulses and placing a single nucleus at the center of each dot that can be addressed with NMR techniques, rather as in Kane's proposal.

A quantum Internet

The problems in scaling up many of these ideas have persuaded many scientists that if quantum computing is to become useful any time soon, it will have to involve networking small quantum computers together. But sending quantum information from one place to another is tricky. One option is to physically move the qubits, but then they would be liable to decoherence. In 1993, however, Charles Bennett, from IBM's Thomas J. Watson Laboratory in Yorktown Heights, N.Y., and a few colleagues came up with a different option: teleportation.

Teleportation utilizes the deep link that entanglement sets up between one point in the universe and another. Bennett theorized that entanglement could act as a kind of phone line down which to send quantum information--in other words, create an entangled pair of particles and send one of them to the receiver while keeping the other [see "Quantum Teleportation"]. This process links these two points in a way that allows the exchange of quantum information from one qubit to another.

Bennett and his colleagues had to wait four years to see their predictions verified. In 1997, in a small room at the University of Innsbruck, in Austria, a group of physicists led by Anton Zeilinger performed the first teleportation experiment. Zeilinger's travelers were photons and he was sending them only a meter or so, from one side of the lab to the other. Today, more than three years later, Zeilinger is working on the next step, which is to teleport photons over distances of a kilometer.

Soon after Zeilinger's breakthrough, Cirac and Zoller proposed that teleportation could become the basis of a kind of quantum Internet. And in March of 2000, Seth Lloyd and Selim Shahriar at MIT and Philip Hemmer at the U.S. Air Force Research Laboratory, in Lincoln, Mass., suggested sending entangled photons over optical fibers to nodes containing cold atoms that would absorb the photons and so store the entanglement. This entanglement could then be used for error correction, teleportation, and various other valuable applications. A number of groups are working on this idea, including Jeff Kimble at the California Institute of Technology and Eli Yablonovitch at the University of California at Los Angeles. They hope to have a three-node network running within 10 years.

Some scientists hope for even greater things from entanglement, believing it will be so useful that it will one day be traded as a currency over the quantum Internet. Considerable progress will be required before anything remotely like that becomes possible. Even so, the pace of innovation in quantum computing has already exceeded most scientists' wildest dreams. Only five years ago, many were confident that quantum computers would not be built for 20 years, yet NMR proved them wrong within a year. Only the bravest forecaster would dare to predict how the field will stand five years from now.

With only a few hundred qubits it is possible to represent simultaneously more numbers than there are atoms in the universe

Spectrum Editor: Samuel K. Moore

JUSTIN MULLINS [p. 42], a contributing editor, is a freelance science writer based in Oxford, England. He is a consulting technology editor for New Scientist.

For an overview of quantum computing techniques and the peculiarities of quantum information, try Introduction to Quantum Computing and Information, edited by Hoi-Kwong Lo, Sandu Popescu, and Tim Spiller, and published in 1998 by World Scientific (Singapore).

Some important papers in quantum computing include: "Bulk Spin-Resonance Quantum Computation," by N. Gershenfeld and I. L. Chuang, Science, Vol. 275, p. 350 (1997); "Quantum Logic Gates in Optical Lattices," by G. Brennen, C. Caves, I. Deutsch, and P. Jessen, Physics Review Letters, Vol. 82, p. 1060 (1999); "A Silicon-Based Nuclear Spin Quantum Computer," by B. E. Kane, Nature, Vol. 393, p. 133 (1998); and Teleportation and the Quantum Internet, by S. Lloyd, M. Shahriar, and P. Hemmer, available from the Los Alamos Archive (http://xxx.lanl.gov).

An informative Web site explaining quantum teleportation is http://info.uibk.ac.at/c/c7/c704/qo/ photon/_teleport/index.html.

Nuclear magnetic resonance (NMR) is explained in an on-line book at http://www.cis.rit.edu/htbooks/nmr/. The author is Joseph P. Hornak.

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The Topsy Turvy World of Quantum Computing - IEEE Spectrum

Illustration: Emily Cooper

Since the invention of paper money, counterfeiters have churned out fake bills. Some of their handiwork, created with high-tech inks, papers, and printing presses, is so good that its very difficult to distinguish from the real thing. National banks combat the counterfeiters with difficult-to-copy watermarks, holograms, and other sophisticated measures. But to give money the ultimate protection, some quantum physicists are turning to the weird quirks that govern natures fundamental particles.

At the moment, the idea of quantum money is very much on the drawing board. That hasnt stopped researchers from pondering what encryption schemes they might apply for it, or from wondering how the technologies used to create quantum states could be shrunk down to the point of fitting it in your wallet, says Scott Aaronson, an MIT computer scientist who works on quantum money. This is science fiction, but its science fiction that doesnt violate any of the known laws of physics.

The laws that govern subatomic particles differ dramatically from those governing everyday experience. The relevant quantum law here is the no-cloning theorem, which says it is impossible to copy a quantum particles state exactly. Thats because reproducing a particles state involves making measurementsand the measurements change the particles overall properties. In certain cases, where you already know something about the state in question, quantum mechanics does allow you to measure one attribute of a particle. But in doing so youve made it impossible to measure the particles other attributes.

This rule implies that if you use money that is somehow linked to a quantum particle, you could, in principle, make it impossible to copy: It would be counterfeit-proof.

The visionary physicist Stephen Wiesner came up with the idea of quantum money in 1969. He suggested that banks somehow insert a hundred or so photons, the quantum particles of light, into each banknote. He didnt have any clear idea of how to do that, nor do physicists today, but never mind. Its still an intriguing notion, because the issuing bank could then create a kind of minuscule secret watermark by polarizing the photons in a special way.

To validate the note later, the bank would check just one attribute of each photon (for example, its vertical or horizontal polarization), leaving all other attributes unmeasured. The bank could then verify the notes authenticity by checking its records for how the photons were set originally for this particular bill, which the bank could look up using the bills printed serial number.

Thanks to the no-cloning theorem, a counterfeiter couldnt measure all the attributes of each photon to produce a copy. Nor could he just measure the one attribute that mattered for each photon, because only the bank would know which attributes those were.

But beyond the daunting engineering challenge of storing photons, or any other quantum particles, theres another basic problem with this scheme: Its a private encryption. Only the issuing bank could validate the notes. The ideal is quantum money that anyone can verify, Aaronson saysjust the way every store clerk in the United States can hold a $20 bill up to the light to look for the embedded plastic strip.

That would require some form of public encryption, and every such scheme researchers have created so far is potentially crackable. But its still worth exploring how that might work. Verification between two people would involve some kind of black boxa machine that checks the status of a piece of quantum money and spits out only the answer valid or invalid. Most of the proposed public-verification schemes are built on some sort of mathematical relationship between a bank notes quantum states and its serial number, so the verification machine would use an algorithm to check the math. This verifier, and the algorithm it follows, must be designed so that even if they were to fall into the hands of a counterfeiter, he couldnt use them to create fakes.

As fast as quantum money researchers have proposed encryption schemes, their colleagues have cracked them, but its clear that everyones having a great deal of fun. Most recently, Aaronson and his MIT collaborator Paul Christiano put forth a proposal [PDF] in which each banknotes serial number is linked to a large number of quantum particles, which are bound together using a quantum trick known as entanglement.

All of this is pie in the sky, of course, until engineers can create physical systems capable of retaining quantum states within moneyand that will perhaps be the biggest challenge of all. Running a quantum economy would require people to hold information encoded in the polarization of photons or the spin of electrons, say, for as long as they required cash to sit in their pockets. But quantum states are notoriously fragile: They decohere and lose their quantum properties after frustratingly short intervals of time. Youd have to prevent it from decohering in your wallet, Aaronson says.

For many researchers, that makes quantum money even more remote than useful quantum computers. At present, its hard to imagine having practical quantum money before having a large-scale quantum computer, says Michele Mosca of the Institute for Quantum Computing at the University of Waterloo, in Canada. And these superfast computers must also overcome the decoherence problem before they become feasible.

If engineers ever do succeed in building practical quantum computersones that can send information through fiber-optic networks in the form of encoded photonsquantum money might really have its day. On this quantum Internet, financial transactions would not only be secure, they would be so ephemeral that once the photons had been measured, there would be no trace of their existence. In todays age of digital cash, we have already relieved ourselves of the age-old burden of carrying around heavy metal coins or even wads of banknotes. With quantum money, our pockets and purses might finally be truly empty.

Michael Brooks, a British science journalist, holds a Ph.D. in quantum physics from the University of Sussex, which prepared him well to tackle the article Quantum Cash and the End of Counterfeiting. He says he found the topic of quantum money absolutely fascinating, and adds, I just hope I get to use some in my lifetime. He is the author, most recently, of Free Radicals: The Secret Anarchy of Science (Profile Books, 2011).

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Quantum Cash and the End of Counterfeiting - IEEE Spectrum