SSL, or Secure Socket Layer, was first developed by Netscape in the mid-1990's to address the growing need to be able to securely transmit data. It protects data, verifies legitimacy of a website, and is supported by all major browsers. When you log into a banking website, your computer is sent a file called an "SSL certificate" which contains the following data:
Based on the certificate's info, your browser decides whether or not to trust the certificate. This is possible because it uses third-party data, already in your browser, to confirm the certificate wasn't sent by a hacker. Once the certificate is received, the browser checks that the certificate was issued by a trusted third party known as a certificate authority. The browser then uses the public key to encrypt a random, symmetric encryption key and sends it to the server. The web server then decrypts the symmetric encryption key using its private key and uses the symmetric key to decrypt the URL and the HTTP data. Finally, the browser decrypts a response from the server using the symmetric key and displays the information.
Due to the nature of the Internet, the path the content follows between a server and a web browser is not secure. There is always the possibility someone is using a "packet sniffer" to capture data as it passes through a network or, if you're wireless, right out of the air. This is where encryption comes in. Originally, SSL used 40-bit encryption, meaning the value of the key used to decrypt data was selected from 1 out of 1,099,511,627,776 possible values. Today, that level of encryption can be broken almost instantly; so, a 128-bit encryption is commonly used which means 340,282,366,920,938,463,463,374,607,431,768,211,456 possible values; increase it to 256 bits for more security and you have the theoretical number of atoms in the universe. Even with millions of today's top-of-the-line computers working together, brute-force decryption simply takes too long if data is encrypted properly. That said, it's always best to be paranoid because future technologies like quantum computing may render conventional encryption obsolete.
If a brute-force attack won't work, how else can SSL be compromised? No matter how air-tight a security system is, all that work is pointless if users trusted with access have weak passwords or can be tricked into providing their passwords. Although not SSL-specific, it's vital best practices are used to prevent non-technical, "social engineering" attacks.
There is also the possibility that browser and/or server flaws could be exploited. A good way to minimize the risk of a hacker taking advantage of exploits is to subscribe to twitter feeds or blogs related to web security. This way, vulnerabilities can be fixed shortly after they're made public. Another approach would be to establish a list of supported browsers so that you can block or redirect users whose browsers aren't secure.
Flaws in SSL itself could potentially be identified and exploited. SSL supports multiple types of encryption and, in 2008, researchers were able to spoof a certificates by exploiting md5 encryption. This was done with an array of 200 PlayStation 3's and it was made possible because some certificate authorities relied on md5 alone. So, the reliability of an SSL certificate is directly related to the reliability of its certificate authority. If a certificate authority issues an SSL to a hacker's site, users could be fooled into thinking they are on a legitimate site due to successful SSL authentication. Furthermore, some authorities use better encryption methods than others. You can get a certificate from GoDaddy for $70/year or you can spend at least $695 at Symantec. Guess which business takes security more seriously!
First, there's a yearly cost associated with SSL which must be weighed against the security benefit. Is there any data on the site that any hackers might use or is there any motivation for your site to be hacked more than another site? If you're doing financial transactions then you pretty much have to use SSL or users will not feel secure, not to mention it would be an obvious target for hackers. That said, if your site only contains openly shared data and is backed up regularly, the biggest risks might be that an admin's password could be captured or that users might use the same password on other sites that do contain sensitive data.
SSL also uses additional server resources encrypting and decrypting content. Although the difference is minor due to processing power of today's servers, it can be noticeable on high-traffic sites. If you want to mix secure and non-secure content on the same page then users may get a browser warnings, so this limits the ability to host some content elsewhere; for example, a content distribution network. Finally, extra time is needed to purchase the certificate, set up the server, configure the website, and test.
Sometimes SSL is a given, but it can be more of a qualitative question based on the balance between practicality and ideology. Yes, any unencrypted login is vulnerable to attack, but what are the chances? The best thing do is weigh the overall cost of SSL against how sensitive your content is and what might happen, worst case,if it is compromised. If you're not sure whether or not to use SSL but you have the money and don't see any major technical obstacles then go ahead and use it.
A less expensive alternative might be to integrate a service like PayPal that handles authentication outside your website. On the other hand, if SSL's authentication and encryption aren't enough, consider using physical tokens. A physical token is a device that assists with authentication. For example, the device may periodically display a different value used to log in based on the current time. This approach removes the reliance in the certificate authority and allows more control over who has access. It can even be used to establish a VPN connection to the server before the website can be accessed.
When configuring Drupal to use SSL, a good place to start is the Secure Pages modules which lets you define which pages are secure and handles redirects from or to secure pages as needed. If you're using Secure Pages with Drupal 6 then the Secure Pages Prevent Hijack module should be installed to prevent hijacked sessions from access SSL pages. Also, the Auth SSL Redirect module can be used to redirect authenticated users to SSL and it will work in conjunction with Secure Pages. If you're using Ubercart and want to either secure the whole site or just Ubercart pages then another option is Ubercart SSL and it can be extended to secure additional pages. In general, these modules help manage transitions between secure and insecure pages.
[Updated based on comment feedback.]
What do you think, what approaches do you recommend, and what do you recommend against?


Quantum computers should be much easier to build than previously thought, because they can still work with a large number of faulty or even missing components, according to a study published today in Physical Review Letters. This surprising discovery brings scientists one step closer to designing and building real-life quantum computing systems – devices that could have enormous potential across a wide range of fields, from drug design, electronics, and even code-breaking.
Scientists have long been fascinated with building computers that work at a quantum level – so small that the parts are made of just single atoms or electrons. Instead of 'bits', the building blocks normally used to store electronic information, quantum systems use quantum bits or 'qubits', made up of an arrangement of entangled atoms.
Materials behave very differently at this tiny scale compared to what we are used to in our everyday lives – quantum particles, for example, can exist in two places at the same time. "Quantum computers can exploit this weirdness to perform powerful calculations, and in theory, they could be designed to break public key encryption or simulate complex systems much faster than conventional computers," said Dr Sean Barrett, the lead author of the study, who is a Royal Society University Research Fellow in the Department of Physics at Imperial College London.
The machines have been notoriously hard to build, however, and were thought to be very fragile to errors. In spite of considerable buzz in the field in the last 20 years, useful quantum computers remain elusive.
Barrett and his colleague Dr. Thomas Stace, from the University of Queensland in Brisbane, Australia, have now found a way to correct for a particular sort of error, in which the qubits are lost from the computer altogether. They used a system of 'error-correcting' code, which involved looking at the context provided by the remaining qubits to decipher the missing information correctly.
"Just as you can often tell what a word says when there are a few missing letters, or you can get the gist of a conversation on a badly-connected phone line, we used this idea in our design for a quantum computer," said Dr Barrett. They discovered that the computers have a much higher threshold for error than previously thought – up to a quarter of the qubits can be lost – but the computer can still be made to work. "It's surprising, because you wouldn't expect that if you lost a quarter of the beads from an abacus that it would still be useful," he added.
The findings indicate that quantum computers may be much easier to build than previously thought, but as the results are still based on theoretical calculations, the next step is to actually demonstrate these ideas in the lab. Scientists will need to devise a way for scaling the computers to a sufficiently large number of qubits to be viable, says Barrett. At the moment the biggest quantum computers scientists have built are limited to just two or three qubits.
"We are still some way off from knowing what the true potential of a quantum computer might be, says Barrett. "At the moment quantum computers are good at particular tasks, but we have no idea what these systems could be used for in the future," he said. "They may not necessarily be better for everything, but we just don't know. They may be better for very specific things that we find impossible now."
For further information please contact:
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Telephone: +44 (0)207 594 8432 or ext. 48432
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Notes to editors:
1. All are welcome to attend the lecture by Professor Alain Aspect of CNRS at Imperial College London from 17.30 – 18.30 on Thursday 11 November, "From Einstein's intuition to quantum bits: a new quantum age?"
The lecture will be held in the Great Hall in the Sherfield Building on Imperial College London's South Kensington campus. Please email firstname.lastname@example.org for further information or to register to attend.
2 "Fault tolerant quantum computation with very high threshold for loss errors"
Physical Review Letters 09 November 2010, to be published online at:
1500 London time (GMT) / 1000 US Eastern time Tuesday 9th November (no embargo)
Link to paper on pre-print server: http://arxiv.org/abs/1005.2456
Corresponding author: Sean Barrett, Institute for Mathematical Sciences, Imperial College London.
3. Contact for Australian media:
Dr Thomas Stace, Co-author (University of Queensland, Brisbane, Australia)
Tel: +61 40 441 3069
4. Images are available for the media at:
Credit: Sean Barrett and Thomas Stace.
Caption: Illustration of the error correcting code used to demonstrate robustness to loss errors. Each dot represents a single qubit. The qubits are arranged on a lattice in such a way that the encoded information is robust to losing up to 25 percent of the qubits
5. The Royal Society is an independent academy promoting the natural and applied sciences. Founded in 1660, the Society has three roles, as the UK academy of science, as a learned Society, and as a funding agency. It responds to individual demand with selection by merit, not by field. As we celebrate our 350th anniversary in 2010, we are working to achieve five strategic priorities, to:
6. About Imperial College London: Consistently rated amongst the world's best universities, Imperial College London is a science-based institution with a reputation for excellence in teaching and research that attracts 14,000 students and 6,000 staff of the highest international quality. Innovative research at the College explores the interface between science, medicine, engineering and business, delivering practical solutions that improve quality of life and the environment - underpinned by a dynamic enterprise culture.
Since its foundation in 1907, Imperial's contributions to society have included the discovery of penicillin, the development of holography and the foundations of fibre optics. This commitment to the application of research for the benefit of all continues today, with current focuses including interdisciplinary collaborations to improve global health, tackle climate change, develop sustainable sources of energy and address security challenges. In 2007, Imperial College London and Imperial College Healthcare NHS Trust formed the UK's first Academic Health Science Centre. This unique partnership aims to improve the quality of life of patients and populations by taking new discoveries and translating them into new therapies as quickly as possible. Website: www.imperial.ac.uk
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Scientists Split Atom, Then Put It Back Together
"Now that we have gained control of single neutral atoms trapped in laser fields, we would like to use atoms to perform a novel kind of information processing -- namely, the so-called quantum information processing," explained research team leader Andrea Alberti. "In essence, our atoms behave as a quantum bit, a qubit."
06/15/12 5:00 AM PT
Mention the words, "splitting the atom," and most people will automatically think of nuclear fission, bombs and radioactivity.
Recently, however, physicists at Germany's University of Bonn not only managed to "split" an atom in a different way -- using quantum mechanics -- but also put it back together again.
"The fact that atoms, photons and molecules can be split at different locations is something already known," Andrea Alberti, team lead for the Bonn experiment and Alexander von Humboldt fellow at the Institut für Angewandte Physik, told TechNewsWorld. "What is really exciting is the level of quantum control and precision to which we pushed our system."
The results of the experiment -- which has potential ramifications for quantum computing and beyond -- were published recently in the journal Proceedings of the National Academy of Sciences.
Two Places at Once
As part of this new experiment, which amounts to what's known as an "atom interferometer," scientists managed to keep a single atom simultaneously in two places at once separated by more than 10 micrometers, or one hundredth of a millimeter. Then, they were able to put it back together undamaged.
"We are capable of trapping a single atom in a tiny box -- a box which is 0.020 micrometers in size and created by laser fields -- and subsequently split the atom into two boxes to reach separations up to 10 micrometers," Alberti explained.
For an atom, 10 micrometers is an enormous distance. To put it in perspective, if the box were a glass of about 5 centimeters in diameter, say, then the atom's two parts would have been separated in two glasses 25 meters apart, he pointed out.
The split was not directly visible, however. If you tried to take a picture, the atom would be seen in several images -- sometimes on the left, sometimes on the right, but never in both places.
Nevertheless, it can be proven by putting the atom back together, the scientists noted. In addition, differences between the magnetic fields of the two positions or accelerations of the atom are discernible, since they become imprinted in the atom's quantum mechanical state.
'A Split Personality'
Such quantum effects can only take place at the lowest temperatures and with careful handling. Specifically, the scientists involved used lasers to cool a cesium atom to a temperature of a tenth of a million degrees above absolute zero and then held it using another laser.
Next, they took advantage of the fact that atoms have a spin that can go in two directions simultaneously. Essentially, if the atom is moved by the second laser to the right and the left at the same time, it will split.
"The atom has kind of a split personality: half of it is to the right, and half to the left, and yet, it is still whole," explained Andreas Steffen, lead author on the publication describing the experiment.
'More Like a Cloud Than a Marble'
Brain hurting yet? You're not alone.
"If you think of an atom as being like a very small, very hard, very tough version of a marble or a ball bearing, then your thinking is trapped in a pre-1925 misconception," Daniel Styer, Schiffer Professor of physics at Oberlin College, told TechNewsWorld. "An atom can behave more like a cloud than a marble, although it doesn't behave exactly like either."
Many people are familiar with the famous Schrödinger's cat thought experiment, in which a hypothetical cat exists both "alive" and "dead" at the same time. That experiment illustrates the difficulty of applying quantum mechanics to everyday objects.
"In quantum mechanics, an atom doesn't have to have a position," Styer explained. "So if there are two routes to go from A to B, it is entirely possible for the atom to take both."
What's known as the classic "double slit experiment" in physics gets at much the same notion.
"Imagine a wall containing two small slits that are separated by a short distance," explained Jeanie Lau, an associate professor in the department of physics at the University of California at Riverside.
"A particle in our everyday experience can go through only one of the slits, or bounce back," Lau told TechNewsWorld.
A wave hitting the wall, however, will go through both slits, she pointed out.
"In quantum mechanics, if the particle is small enough -- i.e., as small as an atom -- it can go through both slits and form interference patterns on the other side, just like a wave," Lau added. "Atoms, like waves, can interfere with each other, due to the particle-wave duality, a fundamental property of matter and a consequence of quantum mechanics."
So, the Bonn experiment doesn't so much "split" the atom as it "uses the quantum mechanical nature of the particle -- that it can also behave like a wave -- to create interference by directing it to go through both slits," she explained.
'A Big Step Forward'
It should be noted that atom interferometry -- or the process of "splitting" atoms and reassembling them -- "has been an active field of research since the 1930s, when it was first demonstrated," Andrew Cleland, professor of physics at the University of California at Santa Barbara, told TechNewsWorld.
Indeed, "the ability to split a system into separate states and then bring them back together has long been one of the key aspects of quantum mechanics, and it has been shown experimentally in many circumstances," agreed Gary Felder, associate professor of physics at Smith College.
"However, larger objects are harder to split and recombine in this way than smaller ones, and larger distances are harder than short ones," Felder told TechNewsWorld. "To split and recombine something as large as an atom over distances as great as tens of micrometers is a big step forward."
Indeed, "only now, with this work from Bonn, have we had precise control over a single atom starting at one place with a position, then spreading out so as not to have a position, and finally ending with a single position again," Styer said.
So where is all this leading?
The Bonn scientists hope eventually it could help simulate complex quantum systems. Plant photosynthesis, for example, is a phenomenon that's hard to capture with modern supercomputers, but small quantum systems based on technology like this could be just what's needed.
Then, too, there are the possibilities for quantum computing.
"Now that we have gained control of single neutral atoms trapped in laser fields, we would like to use atoms to perform a novel kind of information processing -- namely, the so-called quantum information processing," Alberti explained.
"In essence, our atoms behave as a quantum bit, a qubit," he noted. "Each atom can encode information in its spin state, up and down, but all possible superpositions of these two states are possible, exactly as we could split the atom at far apart locations."
Computational speeds could be increased enormously as a result, Alberti added.
An Exciting Era
In some ways, however, the experiment's practical applications are almost less important, Styer opined.
"Perhaps it can be used for precision measurements, perhaps it can be used to help build a quantal computer, or perhaps it will prove useful for nothing," he concluded. "But regardless of potential applications, it is great to be alive during an era when our understanding and control of nature is becoming so subtle and nuanced."


Chips measure electron spin
Technology Research News
Practical quantum computers are at least a decade away, and some researchers are betting that they will never be built.
This is because controlling individual particles like atoms, electrons and photons is extraordinarily challenging. Information carried in particles always comes in shades of gray and can be corrupted or wiped out by the slightest wisp of energy from the environment.
A pair of experiments has brightened prospects for quantum computing, however, by making it more likely that a practical means of reading electron-based quantum bits, or qubits, can be developed. Research teams from the University of California at Los Angeles and from Delft University of Technology in the Netherlands have developed electronic methods of detecting the spins of individual electrons.
Spin is a property of electrons that is akin to the rotation of a top. The two spin directions, spin up and spin down, are magnetically opposite, like the two poles of a kitchen magnet. The spins can represent the 1s and 0s and digital information.
Particles that are isolated from their environment are in the weird quantum state of superposition, meaning they are in some mix of the two spin directions. This means a qubit can be in some mix of 1 and 0, which allows a string of qubits to represent every binary number at once.
This gives a quantum computer the ability to check every possible answer to a problem with a single set of operations, promising speedy solutions to problems that classical computers have to churn through one answer at a time. These include factoring large numbers, a problem whose difficulty is the foundation of most of today's security codes.
Electronic equipment has become sensitive enough that it is no longer difficult to detect the presence of a single electron. But detecting an electron's spin orientation is another matter.
In recent years, researchers have succeeded in detecting electron spin optically using specialized laser setups. The key to using electron spin in quantum computers whose architecture is similar to today's computer chips is being able to detect the spin orientation electronically.
The UCLA team's method of electron spin detection uses devices that are already mass-produced. The researchers flipped a single electron spin in a commercial transistor chip, and detected the spin flip by measuring changes in current flowing through the device.
Several proposed quantum computer architectures call for circuits that can be manufactured using today's chipmaking techniques. "The transistor structure used for our experiment [closely] resembles some proposed spin-based qubit architectures," said Hong-Wen Jiang, a professor of physics at the University of California at Los Angeles. "We believe that our read-out scheme can be readily adapted in a scalable quantum information processor," he said.
Electrons travel through a transistor via a semiconductor channel that is electrically insulated. The transistor is controlled by a gate electrode, which produces an electric field that penetrates the insulator and increases the conductivity of the channel, allowing electrons to flow. Occasionally defects occur, producing one or more spots in the insulator that can draw individual electrons from the channel and trap them.
The researchers sought out transistors that contained single defect traps, set the gate voltage so that the trap had an equal chance of attracting an electron or not, and applied a large magnetic field to the trap.
A high magnetic field causes electrons in the spin-down state to have slightly more energy than spin-up electrons. The researchers flipped the electron's spin with a microwave pulse. An electron that is spin-up fills the trap but a higher-energy spin-down electron leaves room, electrically speaking, for a second, spin-up electron from the channel to join it in the trap.
The difference between having one and having two electrons in the trap is measurable as a change in the current flowing through the transistor. Two electrons decrease the amount of current. The researchers can observe a microwave pulse flipping the spin of an electron in the trap by measuring the current.
In its present form, the UCLA device uses a randomly-positioned defect as its electron trap, and electrons cycle through the trap rapidly enough that the spin measurement is an average of a few thousand electrons. The researchers are conducting similar experiments in specially designed semiconductor structures that promise greater control over electron spin, the ability to entangle two spins, and to eventually build a scalable quantum processor, said Jiang.
Properties of entangled particles, including spin, remain in lockstep regardless of the distance between them. Entanglement is a basic requirement of quantum algorithms, and entangled electrons would enable information to be teleported between circuits within a quantum computer.
Meanwhile, the Delft team devised a way to measure the spin of an electron trapped in a quantum dot -- a tiny semiconductor device that produces electric fields capable of confining one or a few electrons. "The technique works fully electrically, and is therefore... suitable for integration with existing solid-state technologies," said Jeroen Elzerman, a researcher at Delft University of Technology.
The researchers applied a large magnetic field to the trapped electron, which caused the spin-down state to have slightly more energy than the spin-up state. They tuned the quantum dot's electric field so that the energy of a spin-down electron was just high enough for it to escape, but the energy of a spin-up electron was below the threshold. Therefore, if an electron is present it is spin-up, and if the quantum dot is empty, the electron that escapes is spin-down.
The researchers next step is to to use pulsed microwaves to control the exact quantum superposition of the spin, said Elzerman. They then plan to entangle two spins. "When this is done, all the basic ingredients for a quantum computer are in place," he said.
Coupling many spins and controlling their interactions accurately
enough to perform a quantum algorithm is a matter of improving control
over the fabrication process, said Elzerman. "We need cleaner and purer
materials and more reproducible electron beam lithography so that all
dots on a single chip are really identical," he said.
Jiang's research colleagues were Ming Xiao and Eli Yablonovitch
of UCLA, and Ivar Martin of Los Alamos National Laboratory. They published
the research in the July 22, 2004 issue of Nature. The research
was funded by the Defense Advanced Research Projects Agency (DARPA) and
the Defense Microelectronics Activity (DMEA).
Elzerman's research colleagues were Ronald Hanson, Laurens Willems
van Beveren, Benoit Witkamp, Lieven Vandersypen and Leo Kouwenhoven. They
published the research in the July 22, 2004 issue of Nature. The
research was funded by DARPA, the Office of Naval Research, the European
Union and the Dutch Organization for Fundamental Research on Matter (FOM).
Timeline: 10 years; 10-20 years
TRN Categories: Physics; Quantum Computing and Communications
Story Type: News
Related Elements: Technical papers, "Electrical detection of the spin resonance of a single electron in a silicon field-effect transistor," Nature, July 22, 2004; "Single-shot read-out of an individual electron spin in a quantum dot," Nature, July 22, 2004
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Quantum Computer Passes Math Test, But Doesn’t Answer the Big Question
- 12:34 pm |
Is the world’s first commercial quantum computer the real deal or not? No one is quite sure.
The most recent experiment adding fodder to this debate used the quantum computer made by the Canadian company D-Wave Systems to determine hard-to-calculate solutions in a mathematical field known as Ramsey theory. Despite the machine’s success, many scientists are still skeptical of this quantum computer’s legitimacy.
“At the moment, it’s not clear to my eyes that D-Wave device is what we would call a quantum computer,” said computer scientist Wim van Dam from the University of California, Santa Barbara, who was not involved in the recent work.
Quantum computers harness the weird quirks of the subatomic world to run algorithms at extremely quick speeds and solve problems that stymie our current electronic devices. That’s because classical computers rely on transistors that hold memory in the form of zeros and ones. A quantum computer, by contrast, uses subatomic particles (called qubits) that can be a one, a zero, or a simultaneous superposition of these two states.
Since the early 2000s, researchers have been able to build rudimentary quantum computers but it wasn’t until 2011 that D-Wave announced a commercial product with a 128-qubit processor. If it were truly a quantum computer, it would be leaps and bounds ahead of any other product, but the company’s statements have been met with raised eyebrows from the computer science community. Still, D-Wave sold its first products to companies such as Lockheed Martin while their second-generation device was bought up by Google and NASA.
The latest experiment used the D-Wave machine to find solutions to optimization problems in what is known as Ramsey theory, after British mathematician Frank Ramsey. This field deals with situations in which a certain kind of order appears within a disordered system.
A well-known problem called the “party problem” asks what the minimum number of guests you would need to invite to a gathering to ensure that a small subset is made of people who all know each other and another who all don’t. Solutions to this problem are given in what’s known as Ramsey numbers. Calculating the minimum number of guests to ensure groups of three strangers and three friends is fairly easy (the answer is six). But increasing the number of people makes the solution increasingly hard to calculate, with most Ramsey numbers being beyond the capability of our current computers.
D-Wave’s device was able to implement an algorithm to calculate Ramsey numbers for different configurations, though none that weren’t already known from previous work. The findings appeared Sept. 25 in Physical Review Letters.
While noting that the D-Wave experiment’s calculations were correct, the authors of a commentary piece in the same issue wrote that “many more tests would be needed to conclude that the logical elements are functioning as qubits and that the device is a real quantum computer.”
Graeme Smith and John Smolin from IBM’s Watson Research Center, the authors of the commentary, question just how coherent the qubits of D-Wave’s computer are. Coherence refers to how long the particles are able to remain in a state of superposition (where they are both zero and one simultaneously), which is notoriously tricky to maintain. Even small amounts of noise can cause the qubits’ quantum mechanical wavefunction to collapse, turning them into classical objects that don’t work like a true quantum computer.
But the algorithms used to calculate these Ramsey numbers “don’t need as much coherence as a full-blown quantum computer,” said physicist Frank Gaitan of the University of Maryland, who worked on the D-Wave experiment.
Gaitan adds that D-Wave’s machine is not necessarily a universal quantum computer, which could run any algorithm given to it. Instead, it is designed to be particularly good at solving optimization problems, such as those in Ramsey theory, and the evidence from his research shows that the device “uses some kind of quantum effect that solves some kind of problems.”
Even then, there is still some question as to whether D-Wave’s system is truly a quantum computer. Van Dam noted that Ramsey number problems aren’t a good choice for proving anything about quantum computers. That’s because “it’s a really easy problem,” he said.
He gave an analogy. Imagine a company says they built a self-driving car and then placed it on top of a hill. They start the car and it rolls to the bottom of the hill. You could say the car drove itself down or you could say it was carried downhill by gravity, and it might be hard to determine which one it is.
Gaitan hopes that future work will help clear up these problems. The current generation of D-Wave’s system can’t calculate any unknown Ramsey numbers. But their third-gen device, expected to come out in 2015, should have 2048 qubits, which might be enough to figure out new Ramsey numbers that are beyond the capability of current computers.


Simple optics make quantum relay
Technology Research News
If it weren't for repeaters, the light pulses that carry information over fiber-optic long distance lines would fade before they got much further than 100 kilometers.
Quantum cryptography devices and networks, which transport photons whose properties can be used to represent the 1s and 0s of digital information, could also benefit from repeaters. Today's prototype quantum cryptography systems provide theoretically perfect security, but these systems can't carry information over long distances.
Researchers from the NASA-Caltech Jet Propulsion Laboratory have found a way to make a quantum repeater using ordinary optical equipment. Practical quantum repeaters could boost the reach of quantum cryptography systems, and eventually enable quantum networks. The device would allow for an exponential improvement in the distance quantum bits can be transmitted, said Jonathan Dowling, a principal scientist at at the Jet Propulsion Laboratory.
The challenge was finding a way to preserve entanglement.
Particle properties like polarization can become entangled when two or more particles come into contact with each other or simultaneously interact with a third entity like another particle or a laser beam. Entanglement keeps properties like polarization linked, regardless of the distance between entangled particles. A photon's electric field can be polarized, or oriented, in one of four directions. Pairs of directions can represent binary numbers.
Entanglement is the basic ingredient of many quantum computing, quantum cryptography and quantum communications schemes. Sharing entangled particles between locations makes theoretically perfectly secure communications possible because the traits of a series of particles can form a random string of bits that can be used to encrypt messages. It is impossible for an eavesdropper to copy or intercept the particles without disrupting the entanglement, which would reveal the security breach.
Shared entanglement would also make it possible to network quantum computers. "Many quantum communication protocols rely on shared entanglement between two distant parties," said Pieter Kok, one of the Jet Propulsion Laboratory researchers who is now at Hewlett-Packard Laboratories.
But because photons must be in the same place when they are initially entangled, using entangled particles for communication means finding a way to transport them, he said. This is difficult because particles can't be copied without destroying their quantum information, which means ordinary repeaters, which produce copies of fading signals, can't be used for quantum communications.
The researchers' linear optical quantum repeater uses optical elements like mirrors, beam splitters and photodetectors to purify and transfer entanglement among photon pairs. Entanglement purification makes two or more partially entangled states into one fully entangled state. Entanglement swapping converts entanglement: entanglements between particles A and B and particles C and D can be converted to an entanglement between A and D.
Beam splitters direct photons in one of two directions based on the photons' polarization, and photodetectors at each output of a beam splitter determine a photon's polarization. The repeater is made up of a network of beam splitters and photodetectors that route photons based on whether specific photodetectors detect other photons. The combination of the right paths and detection-triggered routing is enough to carry out entanglement purification and swapping.
To use the system to initiate quantum communications, a sender, Alice, would entangle photons A and B, keep A, and send B to a receiver, Bob. A repeater in the network between Alice and Bob would generate a new pair of entangled photons, C and D, and bring together B and C. This would destroy B and C and in the process leave A entangled with D. The device would then send photon D on to Bob, giving Alice and Bob a shared pair of entangled photons. Rather than copying photons, the quantum repeater transfers entanglement.
In practice, there are degrees of entanglement, and in order to transmit entangled states of high enough purity, quantum communications schemes typically distill multiple entangled pairs down to a single pair of fully entangled photons. In the researchers' repeater, the purification step takes place before the entanglement swapping.
The linear optical quantum repeater was inspired by the landmark theoretical demonstration of linear optical quantum computing by Emanuel Knill, Raymond Laflamme and Gerard Milburn in 2001, said Dowling. "Since a repeater is just a very simple type of quantum computer, logic dictated it would be possible, but the devil was in the details," he said.
Other research teams have devised quantum repeaters that tap the interactions of photons with gas atoms. In these schemes, fading photons that enter a repeater transfer their quantum states to atoms, which can briefly store the state information until it can be transferred to fresh photons that are transmitted over the next leg of the network. Light-matter interactions are difficult to carry out, however, especially with equipment that could be used in practical communications networks.
A third approach uses nonlinear optical quantum repeaters that use complicated equipment to cause photons to interact with each other; these may be harder to make than the linear design, said Dowling.
The researchers' goal is to develop simple devices that prove the utility of their linear optical approach, and eventually use the approach to build a full-scale quantum computer, said Dowling.
A reliable source of entangled photons is a top priority, said Kok. "It not only has to be able to make high-quality entanglement, it also needs to do this reproducibly," he said. "Two sources must produce almost indistinguishable photon pairs in order for the interference to work." Another key component that needs to be developed is quantum memory so that, for instance, Alice can hold onto her half of the original entangled photon pair.
And the system eventually has to be miniaturized into a quantum optoelectronic chip, according to Dowling.
Such systems could eventually be used in quantum cryptography
systems, for quantum telecommunications, and for distributed quantum computing,
said Dowling. It will be 20 years before the method can be used practically,
Dowling and Kok 's research colleague was Colin P. Williams. The
work appeared in the August 1, 2003 issue of Physical Review A.
The research was funded by the National Aeronautics and Space Administration
(NASA), and The Advanced Research and Development Activity (ARDA), the
National Security Agency (NSA), the Office of Naval Research (ONR), and
the Defense Advanced Research Projects Agency (DARPA).
Timeline: 20 years
TRN Categories: Quantum Computing and Communications; Physics; Cryptography and Security; Optical Computing, Optoelectronics and Photonics
Story Type: News
Related Elements: Technical paper, "Construction of a Quantum Repeater with Linear Optics," Physical Review A, August 1, 2003.
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Tiny device is first complete 'quantum computer'
Aug 11, 2009
Researchers in the US claim to have demonstrated the first small-scale device to perform all the functions required in large-scale ion-based quantum processing. Although the individual stages or groups of stages in quantum computing have been demonstrated previously, this new device is said to perform a complete set of quantum logic operations without significant amounts of information being lost in transit. As a result, the device represents an important step in the quest for a practical quantum computer, say the researchers based at the US National Institute of Standards and Technology (NIST) in Boulder, Colorado.
Researchers in the field have already hailed this as an important breakthrough in quantum computing. However, they also warn of the practical challenges that still lie ahead if we are to develop large-scale quantum computers.
Where conventional computers store data as “bits” with value 1 or 0, in quantum computing data is stored as “qubits” which can hold more than one value at the same time. The upshot of this phenomenon, known as superposition, is that quantum computers could potentially store and process unprecedented amounts of data. What’s more, quantum particles can become “entangled”, allowing them to share a much closer relationship than classical mechanics allows in which data is transferred instantaneously between entangled particles regardless of their separation distance.
The quantum path
The concept of quantum computing gathered significant momentum in 1994 when the mathematician Peter Shor invented an algorithm to show that quantum computation could factor numbers significantly faster than in classical computation. The implication was that quantum computers could operate at ultra-high speeds, which could be applied to solving complex problems like cracking some of today’s most widely used encryption codes. However, it quickly became apparent that researchers would have a very difficult task of putting this into practice due to the delicate nature of quantum information, particularly when quantum data is being transferred between locations.
Despite this limitation, some simple quantum algorithms have been executed in the past few years. Perhaps most notable was the first and only demonstration of Shor's factoring algorithm, using nuclear magnetic resonance, by Lieven Vandersypen and his colleagues at the IBM Almaden Research Center in California.
"Home and his team have shown the individual pieces of the puzzle to work separately in a series of beautiful experiments in recent years. Now, in this tour-de-force, they put the pieces of the puzzle together and made them all work in one experiment," Boris Blinov, University of Washington
One promising approach to realizing quantum algorithms is the storage and transfer of quantum data in ultracold ions. This is the approach taken by the group at NIST, led by Jonathan Home, which, over the past few years, has demonstrated all of the steps needed for quantum computation: (1) "initialize" qubits to the desired starting state (0 or 1); (2) store qubit data in ions; (3) perform logic operations on one or two qubits; (4) transfer information between different locations in the processor; and (5) read out qubit results individually.
Caught in a trap
In this latest research, Home’s group have now managed to combine all of these separate stages for the first time. The team held two beryllium atoms in a trap before manipulating the energy states of each ion using an applied ultraviolet laser pulse in order to store quantum data. Electric fields were then used to move the ions across macroscopic distances — up to 960 micrometres — between different zones in the trap. The researchers repeated a sequence of 15 logical operations 3,150 times on each of 16 different starting states and found that the processor worked with an overall accuracy of 94 per cent.
One of the key innovations employed by the NIST researchers was to use two partner magnesium ions as “refrigerants” for cooling the beryllium ions as they are being transported. This “sympathetic cooling” enabled logic operations to continue without any additional error due to heating incurred during transport. “We have incorporated transport, and explicitly shown that it does not impede our ability to do further computation — this is a crucial step for building a large-scale device,” Home told physicsworld.com.
Early response to this development from the research community is positive. “Home and his team have shown the individual pieces of the puzzle to work separately in a series of beautiful experiments in recent years. Now, in this tour-de-force, they put the pieces of the puzzle together and made them all work in one experiment,” said Boris Blinov, a quantum computing researcher at the University of Washington.
The road ahead
Hans Bachor, a quantum optics specialist at the Australian National University is also impressed. “The work is indeed a great step forward and most impressive — it demonstrates all the key steps required in the computing cycle.” Bachor, however, also warns of technical challenges that lie ahead. “The question is whether they can keep the ion in the ground state. I am not aware of any in principle problems, but it will require more tricks to invented,” he added.
Home told physicsworld.com that his team are continuing to develop their trapped ion system with a focus on two specific problems. The first area is to improve the logic operation accuracy: the accuracies required for a large scale device are 0.9999, where the accuracy in this device is 0.95. “Here we are limited by the control we have over our laser beams, and the power of these beams,” he said. The second area is to build larger devices. “Crosstalk between different parts of the processor may be a problem which only exists in larger devices. The classical computer control, and the need for precision control of large numbers of electrodes and laser beams, represents a major technical challenge,” he said.
Markus Aspelmeyer, a quantum optics researcher at the University of Vienna recognizes another of the challenges involved in scaling up. “It will be a challenge to minimize the individual gate errors and to gain control over a large number of ions on a single chip,” he said. Adding, “This is however essential to perform lengthy calculations on a future quantum computer. It is an exciting challenge to both engineering and quantum information science and it is not clear yet where the exact limitations will be.”
This research was reported in Science Express.
About the author
James Dacey is a reporter for physicsworld.com


Everywhere in a Flash: The Quantum Physics of Photosynthesis
- 2:40 pm |
By hitting single molecules with quadrillionth-of-a-second laser pulses, scientists have revealed the quantum physics underlying photosynthesis, the process used by plants and bacteria to capture light’s energy at efficiencies unapproached by human engineers.
The quantum wizardry appears to occur in each of a photosynthetic cell’s millions of antenna proteins. These route energy from electrons spinning in photon-sensitive molecules to nearby reaction-center proteins, which convert it to cell-driving charges.
Almost no energy is lost in between. That’s because it exists in multiple places at once, and always finds the shortest path.
“The analogy I like is if you have three ways of driving home through rush hour traffic. On any given day, you take only one. You don’t know if the other routes would be quicker or slower. But in quantum mechanics, you can take all three of these routes simultaneously. You don’t specify where you are until you arrive, so you always choose the quickest route,” said Greg Scholes, a University of Toronto biophysicist.
Scholes’ findings, published Wednesday in Nature, are the strongest evidence yet for coherence — the technical name for multiple-state existence — in photosynthesis.
Two years ago, researchers led by then-University of California at Berkeley chemist Greg Engel found coherence in the antenna proteins of green sulfur bacteria. But their observations were made at temperatures below minus 300 degrees Fahrenheit, useful for slowing ultrafast quantum activities but leaving open the question of whether coherence operates in everyday conditions.
The Nature findings, made at room temperature in common marine algae, show that it does. Moreover, similar results from an experiment on another, simpler light-harvesting structure, announced by Engel’s group last Thursday on the pre-publication online arXiv, suggest that photosynthetic coherence is routine.
The findings are wondrous in themselves, adding a new dimension to something taught — incompletely, it now seems — to every high school biology student. They also have important implications for designers of solar cells and computers, who could benefit from quantum physics conducted in nonfrigid conditions.
“There’s every reason to believe this is a general phenomenon,” said Engel, now at the University of Chicago. He called Scholes’ finding “an extraordinary result” that “shows us a new way to use quantum effects at high temperatures.”
Scholes’ team experimented on an antenna protein called PC645, already imaged at the atomic scale in earlier studies. That precise characterization allowed them to target molecules with laser pulses lasting for one-quadrillionth of a second, or just long enough to set single electrons spinning.
By analyzing changes to a laser beam sent through the protein immediately afterwards, the researchers were able to extrapolate what was happening inside — an ultra-high-tech version of shadows on a screen. They found that energy patterns in distant molecules fluctuated in ways that betrayed a connection to each other, something only possible through quantum coherence.
“It’s the same as when you hit two tuning forks at the same time, and hear a low-pitched oscillation in the background. That’s the interference of sound waves from the forks. That’s exactly what we see,” said Scholes.
According to Scholes, the physics of photosynthetic proteins will be further studied and used to improve solar cell design. Engel suggested their use in long-promised but still-unworkable quantum computing. “This allows us to think about photosynthesis as non-unitary quantum computation,” he said.
Quantum-physical processes have been observed elsewhere in the biological realm, most notably in compass cells that allow birds to navigate by Earth’s geomagnetic fields. Researchers have also proposed roles for quantum physics in the animal sense of smell and even in the brain. Engel predicts the emergence of an entire field of quantum biology.
“There are going to be some surprises,” said Scholes. “Who knows what else there is to discover?”
Images: 1. Bùi Linh Ngân/Flickr
2. Antenna protein: Light-harvesting molecules are red./Greg Scholes
3. Graph of energy wave interference inside the antenna protein/Nature
- Reverse-Engineering the Quantum Compass of Birds
- Quantum Entanglement Visible to the Naked Eye
- “Sudden Death” Threatens Quantum Computing
- Green Sea Slug Is Part Animal, Part Plant
Citations: “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature.” By Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer & Gregory D. Scholes. Nature, Vol. 463 No. 7281, Feb. 4, 2010.
“Long-lived quantum coherence in photosynthetic complexes at physiological temperature.” By Gitt Panitchayangkoon, Dugan Hayes, Kelly A. Fransted, Justin R. Caram, Elad Harel, Jianzhong Wen, Robert E. Blankenship, Gregory S. Engel. arXiv, Jan. 28, 2010.


In life, most people try to avoid entanglement, be it with unsavory characters or alarmingly large balls of twine. In the quantum world, entanglement is a necessary step for the super-fast quantum computers of the future.
According to a study published by Nature today, physicists have successfully entangled 10 billion quantum bits, otherwise known qubits. But the most significant part of the research is where the entanglement happened–in silicon–because, given that most of modern-day computing is forged in the smithy of silicon technology, this means that researchers may have an easier time incorporating quantum computers into our current gadgets.
Quantum entanglement occurs when the quantum state of one particle is linked to the quantum state of another particle, so that you can’t measure one particle without also influencing the other. With this particular study, led by John Morton at the University of Oxford, UK, the researchers aligned the spins of electrons and phosphorus nuclei–that is, the particles were entangled.
“The key to generating entanglement was to first align all the spins by using high magnetic fields and low temperatures,” said Oxford’s Stephanie Simmons, who also worked on the team…. “Once this has been achieved, the spins can be made to interact with each other using carefully timed microwave and radiofrequency pulses in order to create the entanglement, and then prove that it has been made.” [Reuters]
If the current entanglement experiment were a cooking recipe, it would go something like this: First, embed a silicon crystal with 10 billion phosphorous atoms, cool it to close to absolute zero, and then apply a sequence of radio and microwave pulses. These pulses essentially toy with the spins of the phosphorus nuclei and their electrons until the spin of each nucleus matched the spin of one of its electrons. You end up with 10 billion entangled pairs that form a two-qubit system. It’s a major breakthrough, but the researchers aren’t stopping there:
“Creating 10 billion entangled pairs in silicon with high fidelity is an important step forward for us,” said John Morton of Britain’s Oxford University, who led the team…. We now need to deal with the challenge of coupling these pairs together to build a scalable quantum computer in silicon.” [Reuters]
Spinning particles are all well and nice, but what do they have to do with computing? How does a quantum computer actually compute?
To turn this into a silicon quantum computer, the team must create a “huge 2D grid of entanglement”, in which nuclei are entangled with other phosphorus nuclei, as well as electrons, says Morton. To achieve this, electrons will be shuttled through the structure, stitching entangled states together like a thread, he says. By measuring the electron spins in a certain order, computations could be performed. [New Scientist]
Such a quantum computer would run silicon circles around conventional ones. Unlike the device sitting on your desk, quantum computers aren’t limited by the 0′s and 1′s of binary bits. In the weird world of quantum mechanics, particles can exist in more that one state at a time–they can be placed in a “superposition” of several possible states. That means that the qubits in a quantum computer could hold several different values simultaneously.
It has been shown theoretically that by running calculations in parallel, using many quantum states in superposition, a quantum computer could solve problems that would take a classical computer an infinite amount of time, for example, running Shor’s algorithm, which factors large numbers into primes and could be used, for example, to crack the most powerful encryption algorithms on the Internet. [Nature News]
In short, a quantum computer would generate a computing power the likes of which the world has never seen, capable of running–as well as cracking–evermore complex algorithms.
While impressed by the quantum leaps made by this research, scientists are already considering the next hurdles in the quantum computing story.
“It’s nice, impressive work,” says Jeremy O’Brien, a quantum-computing specialist at the University of Bristol, UK. But what is really needed, he says, is the ability to do the additional nanofabrication to put electrodes on the silicon chip to address each individual nucleus and electron pair, a technology that will be needed to get more than two spins entangled together in silicon. “That would be really impressive,” he says. [Nature News]
Even though quantum computers have a ways to go before they wind up in your living room and in your every-day gadgets, thanks to successful silicon entanglement that day is getting closer.
80beats: Can Physicists Make Quantum Entanglement Visible to the Naked Eye?
80beats: Tiny LEDs Pump out Quantum-Entangled Photons
Science Not Fiction: Quantum Quest – Potentially Awesome?
DISCOVER: Computers Go Quantum
DISCOVER: Quantum Leap
Image: Stephanie Simmons


101010: That's the number 42 represented in binary, which is the mathematical way today's binary computers see every single piece of information flowing through them, whether it's a stock price, the latest Adele track, or a calculation to generate an MRI of a tumor. But now IBM believes it's made progress in developing quantum computers, which don't use binary coding. It is not overstating the matter to say this really may be the ultimate answer in computing machines. Quick, mop your brow and don't worry: The science isn't too hard to grasp and the revolution, when it comes, could rock the world. In a very good way.
First, a little background: Computers today, everything from the chip controlling your washing machine cycle to the screen you're reading this on, rely on binary math to work. This reduces the information in problems you ask a computer to a counting system based on just "1"s and "0"s. That translates beautifully into the electronics of a computer circuit: A "1" matches up with a little burst of electricity, a "0" means none. By shuttling trillions upon trillions of these pulses, called bits, through tiny silicon circuits and transistor gates that flip their direction or trigger an ongoing signal, the chip does math with these ones and zeros. It's a mind-bogglingly complex and very swift dance that ultimately results in Angry Birds playing on the screen of your iPad. Or, after kajillions of calculations more in a supercomputer, it results in a model predicting climate change.
Now, what if instead of simply being able to do math with ones and zeros, a computer chip could work with bits that included other numbers? You'd have to design more complex circuitry, for sure, but it means every single one of those tiny electronic calculations that's happening every millisecond could tackle more information at once, and would ultimately mean a more powerful computer that may calculate faster. Got that? Good. Now how about if instead of a one or a zero, your computer's "bits" could have any one of an infinite number of values?
That's quantum computing. Essentially this moves way beyond the well-known physics of electronics, and on into the weird and wonderful world of quantum physics—where bizarre twists of the laws of the universe mean a "bit" in a quantum computer could hold both a "1" and a "0" and any other value at the same time. That means the circuits of a quantum computer could carry out an incredibly huge number of calculations at the same time, handling more information at once than you can possibly imagine.
By using some other very strange physics (superconducting materials cooled to hundreds of degrees below freezing) IBM's research team is trying to build some of the core components of a quantum computer, and has made big progress. They're now saying they've made the quantum "bits" of information, also called qubits, live a lot longer before they essentially get scrambled. They've also worked out how to speed up the actual quantum computing circuit. IBM's progress is so impressive that they're now confident a quantum computer could be made sooner rather than later, perhaps as close as 15 years away.
Whenever it arrives, the world will change.
On a very simple level, this is because instead of asking a supercomputer to work with endless strings of "1"s and "0"s to calculate all the variables in, say, a global warming simulation (performing trillions of small math calculations one after the other to work out the dynamics of the climate over a period of hours or days) a quantum computer would be able to process much of the math at the same instant instead of sequentially. Which could reduce the compute time to a second or less. Which ultimately means better and more accurate models of the climate. Similar processing tricks could improve medical imaging, or maybe even simulations of your own particular disease's spread, which may improve treatment.
And there are many ways this tech would touch your life on an everyday basis, as well. Tasks like image recognition in Google Goggles or voice recognition in Apple's Siri rely on whisking your data off to a powerful computer, running it through a process, and sending you the results back (identifying that photo of a building as the Eiffel tower, or answering your question about the rain in Spain). These recognition problems are partly based on how good the recognition algorithm is, but also on how much time the computer can afford to spend on your problem. A quantum computer would work so swiftly that there would be no issues with spending more time trying to accurately understand your query, meaning we could reach near-perfect image and voice recognition. Perhaps even in real time, from a video feed. Imagine the sort of augmented reality tech that that would enable, with a head-up display on your view of the world constantly delivering relevant info about everything you see.
Then think about security—most encryption systems nowadays rely on clever math that means they couldn't be cracked even by a supercomputer running for years. A quantum computer could try every single combination of passwords to crack the security in a single second, which is pretty terrible news. That's going to force all sorts of changes with how we protect information, and yet it could also lead to more secure encryption, made by a quantum computer. There's also the matter of surveillance: Recognizing every word of every phone conversation on the planet and identifying every single face on every CCTV image would defeat all of today's supercomputer power...but maybe a quantum computer could do it. George Orwell would've loved that. Also on the dark side, ponder how insurance firms would use or abuse this phenomenal power ("our simulation says it's 75% more plausible the accident was your fault"), or how worried nations could simulate social dynamics to try to predict crime.
Next, on the lighter side, consider art. Or at least the movies. Look at computer graphics in films: The computers in render farms that companies like Pixar use to make Brave take hours to put together a single frame, and that limits how truly amazing the image can be made. A quantum computer could tackle a render of today's Pixar movies in a blink of an eye. And that has all sorts of implications, maybe meaning CGI actors could be even more realistic.
Which leads on to artificial intelligence—a sci-fi promise that's so far been very difficult to make real, although IBM's Watson has recently wowed everyone. What if quantum computing suddenly enabled such swift, complex calculations that a system like Watson or Siri could talk back to you convincingly, reading the nuances in your voice enough to ask, as a friend might, if you're a little stressed today and wondering if they could help?
Quantum computers won't necessarily be able to speed up solving every class of problem you throw at them, but it's undeniable that they'll change modern life in many ways, at times small, at others great. As for questions on life, the universe, and everything? Those still require the human element to try to answer.


Introduced in Alan Turing
's 1936 paper On computable numbers, with an application to the Entscheidungsproblem
, a universal Turing machine is a mathematical idealisation of a general purpose computer
. Able to act, with appropriate input, as literally any
other possible Turing Machine
, Turing's invention, essentially the concept of a general purpose cpu
executing a stored program
, was probably the largest single step taken in the development of the computer, and is often regarded as the start of computer science
A Turing machine (TM) consists of a tape, a head which can mark and erase the tape, and a set of states. Depending on whether the tape is currently marked, and which state is occupied, the TM will erase or mark the tape or not, and move it one square left or right, at which point the next state kicks in.
Additionally, there is a state which causes the TM to halt, if it is reached.
The tape is considered to be of arbitrary length and composed of discrete units which are accessible to the head in strict order, singly and wholly - that is the tape is an idealised one-bit erasable paper tape which never stretches, breaks, folds, runs out, or breaks other rules which are harder to think of.
The critical thing is that though the tape may be arbitrarily large, each step of the operation of a TM is completely determined by a finite number of simple and unambiguous rules. It is completely mechanical in its operation, and always behaves in the same way for any particular state and input.
These rules defining a TM (the set of states) can be written out in a standard form as marks on a tape. The interpretation of such an on-tape representation of a TM is then a mechanical procedure which can be realised by some TM with a suitable set of states.
A universal Turing machine (UTM) is a particular TM so constructed that its tape can encode any TM whatsoever, with the guarantee that the UTM will then do just what the encoded TM would do.
Suppose we have a machine M, then its output with initial tape t can be written M(t). Then a UTM U is a TM such that:
for all outputs Mi(tj) there's some ei,j such that U(ei,j) = Mi(tj)
We'd call ei,j the encoding of Mi(tj).
It's also required that the UTM can recognise input that is not a valid encoding of a TM and produce a predetermined response when this occurs.
Turing proved the existence of such UTM's by specifying one in his paper - it turned out not to be very complex - and showing it had the characteristic required, of replicating the behaviour of an arbitrary TM which is encoded on its tape. This is the essence of the modern computer, that given sufficient storage it can carry out an arbitrary program, encoded into some specific "language". The choice of a particular UTM defines a particular language.
Turing's insight was that an algorithm, when encoded, is just so much data that can then be operated on by another algorithm. The idea of encoding a TM as input for execution by a UTM is pretty much all you need for the general idea of a computer program.
The fact that a UTM can emulate any TM at all makes it easy to establish fundamental equivalences between various computational methods. If a particular method can produce a UTM, then it's obvious it can compute anything computable by an arbitrary TM. Such a formalism or language is said to be Turing complete. Specifications for UTM's have been written in formalisms as diverse as XSLT, sendmail.cf and cellular automata such as Conway's game of life.
This property of universality shifts the competition from what can be computed to the number of steps and amount of input required. No matter how featureful, elegant and concise the programming language you construct, whatever computations it can perform can be done in sendmail.cf or brainfuck.
Universality has been of interest to some heterodox physicists, such as Ed Fredkin and Steven Wolfram. Fredkin, on a suggestion of Feynman's, has been investigating the possibility of using cellular automata as a physics model and suggests suitable automata must be both universal (i.e. Turing complete) and reversible. Wolfram (also big on CA) sees in the UTM an upper bound to the complexity of the makeup of the universe. David Deutsch has proposed that "every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means", and has attempted to extend the idea of a UTM to quantum computing.
Mathematician Gregory Chaitin has used the UTM as a building block in his algorithmic information theory, refining the notion by specifying that the encoding for the TM's must instruct the UTM how long they are (Chaitin says they are 'self-delimiting') and using them to define the algorithmic complexity of a string relative to a given UTM - the length of the shortest input that will cause the UTM to output that string - and to formulate his bizarre constant Omega - the probability, for some self-delimiting UTM, that it will halt with random input. Chaitin imagines flipping a coin to determine the state of each successive bit of the unread tape, as the UTM reads in its program. It's required to be self-delimiting so that the UTM knows when to stop reading and Chaitin knows when to stop flipping coins.
Gregory Chaitin, Foundations of Mathematics at:
For Fredkin, see:


In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number represents the number of times that each curve winds around the other. The linking number is always an integer, but may be positive or negative depending on the orientation of the two curves.
The linking number was introduced by Gauss in the form of the linking integral. It is an important object of study in knot theory, algebraic topology, and differential geometry, and has numerous applications in mathematics and science, including quantum mechanics, electromagnetism, and the study of DNA supercoiling.
Any two closed curves in space, if allowed to pass through themselves but not each other, can be moved into exactly one of the following standard positions. This determines the linking number:
|linking number −2||linking number −1||linking number 0|
|linking number 1||linking number 2||linking number 3|
Each curve may pass through itself during this motion, but the two curves must remain separated throughout. This is formalized as regular homotopy, which further requires that each curve be an immersion, not just any map. However, this added condition does not change the definition of linking number (it does not matter if the curves are required to always be immersions or not), which is an example of an h-principle (homotopy-principle), meaning that geometry reduces to topology.
This fact (that the linking number is the only invariant) is most easily proven by placing one circle in standard position, and then showing that linking number is the only invariant of the other circle. In detail:
- A single curve is regular homotopic to a standard circle (any knot can be unknotted if the curve is allowed to pass through itself). The fact that it is homotopic is clear, since 3-space is contractible and thus all maps into it are homotopic, though the fact that this can be done through immersions requires some geometric argument.
- The complement of a standard circle is homeomorphic to a solid torus with a point removed (this can be seen by interpreting 3-space as the 3-sphere with the point at infinity removed, and the 3-sphere as two solid tori glued along the boundary), or the complement can be analyzed directly.
- The fundamental group of 3-space minus a circle is the integers, corresponding to linking number. This can be seen via the Seifert–Van Kampen theorem (either adding the point at infinity to get a solid torus, or adding the circle to get 3-space, allows one to compute the fundamental group of the desired space).
- Thus homotopy classes of a curve in 3-space minus a circle are determined by linking number.
- It is also true that regular homotopy classes are determined by linking number, which requires additional geometric argument.
The total number of positive crossings minus the total number of negative crossings is equal to twice the linking number. That is:
where n1, n2, n3, n4 represent the number of crossings of each of the four types. The two sums and are always equal, which leads to the following alternative formula
Note that involves only the undercrossings of the blue curve by the red, while involves only the overcrossings.
Properties and examples
- Any two unlinked curves have linking number zero. However, two curves with linking number zero may still be linked (e.g. the Whitehead link).
- Reversing the orientation of either of the curves negates the linking number, while reversing the orientation of both curves leaves it unchanged.
- The linking number is chiral: taking the mirror image of link negates the linking number. The convention for positive linking number is based on a right-hand rule.
- The winding number of an oriented curve in the x-y plane is equal to its linking number with the z-axis (thinking of the z-axis as a closed curve in the 3-sphere).
- More generally, if either of the curves is simple, then the first homology group of its complement is isomorphic to Z. In this case, the linking number is determined by the homology class of the other curve.
- In physics, the linking number is an example of a topological quantum number. It is related to quantum entanglement.
Gauss's integral definition
Pick a point in the unit sphere, v, so that orthogonal projection of the link to the plane perpendicular to v gives a link diagram. Observe that a point (s,t) that goes to v under the Gauss map corresponds to a crossing in the link diagram where is over . Also, a neighborhood of (s,t) is mapped under the Gauss map to a neighborhood of v preserving or reversing orientation depending on the sign of the crossing. Thus in order to compute the linking number of the diagram corresponding to v it suffices to count the signed number of times the Gauss map covers v. Since v is a regular value, this is precisely the degree of the Gauss map (i.e. the signed number of times that the image of Γ covers the sphere). Isotopy invariance of the linking number is automatically obtained as the degree is invariant under homotopic maps. Any other regular value would give the same number, so the linking number doesn't depend on any particular link diagram.
This formulation of the linking number of γ1 and γ2 enables an explicit formula as a double line integral, the Gauss linking integral:
This integral computes the total signed area of the image of the Gauss map (the integrand being the Jacobian of Γ) and then divides by the area of the sphere (which is 4π).
- Just as closed curves can be linked in three dimensions, any two closed manifolds of dimensions m and n may be linked in a Euclidean space of dimension . Any such link has an associated Gauss map, whose degree is a generalization of the linking number.
- Any framed knot has a self-linking number obtained by computing the linking number of the knot C with a new curve obtained by slightly moving the points of C along the framing vectors. The self-linking number obtained by moving vertically (along the blackboard framing) is known as Kauffman's self-linking number.
- The linking number is defined for two linked circles; given three or more circles, one can define the Milnor invariants, which are a numerical invariant generalizing linking number.
- In algebraic topology, the cup product is a far-reaching algebraic generalization of the linking number, with the Massey products being the algebraic analogs for the Milnor invariants.
- A linkless embedding of an undirected graph is an embedding into three-dimensional space such that every two cycles have zero linking number. The graphs that have a linkless embedding have a forbidden minor characterization as the graphs with no Petersen family minor.
- This is the same labeling used to compute the writhe of a knot, though in this case we only label crossings that involve both curves of the link.
- This follows from the Jordan curve theorem if either curve is simple. For example, if the blue curve is simple, then n1 + n3 and n2 + n4 represent the number of times that the red curve crosses in and out of the region bounded by the blue curve.
- − (2001), "Writhing number", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4


In the world of computers, silicon is king. The semiconducting element forms regular, near-perfect crystals into which chipmakers can carve the hundreds of millions of features that make the microchips that power the processors. Technological improvements let chipmakers cut the size of those features in half every 18 months-a feat known as Moore’s law, after Intel cofounder Gordon Moore. Today, that size hovers around 180 nanometers (180 billionths of a meter), and researchers expect to push below 50 nanometers within a decade. But that’s about as far as silicon can go: below that quantum physics makes electrons too unruly to stay inside the lines. If computers are to keep up with Moore’s law, they will have to move beyond silicon. After a couple of decades of theorizing, computer scientists, bioengineers and chemists in the mid-1990s began lab experiments seeking alternative materials for future CPUs and memory chips. Today, their research falls into three broad categories: quantum, molecular and biological computing.In the field of quantum computing, researchers seek to harness the quantum effects that will be silicon’s undoing. Scientists succeeded in making rudimentary logic gates out of molecules, atoms and sub-atomic particles such as electrons. And incredibly, other teams have discovered ways to perform simple calculations using DNA strands or microorganisms that group and modify themselves.
Molecular Building Blocks
In one type of molecular computing (or nanocomputing), joint teams at Hewlett Packard Co. and UCLA sandwich complex organic molecules between metal electrodes coursing through a silicon substrate. The molecules orient themselves on the wires and act as switches. Another team at Rice and Yale universities has identified other molecules with similar properties.
Normally, the molecules won’t let electrons pass through to the electrodes, so a quantum property called tunneling, long used in electronics, is manipulated with an electric current to force the electrons through at the proper rate. If researchers can figure out how to lay down billions of these communicating molecules, they’ll be able to build programmable memory and CPU logic that is potentially millions of times more powerful than in today’s computers.
Molecular researchers like the HP/UCLA team, however, face a challenge in miniaturizing their current wiring technology-nanowires made from silicon strands-from several hundred to approximately 10 nanometers. Carbon nanotubes are promising substitutes. The rigid pipes make excellent conductors, but scientists must figure out how to wrangle them into the latticework needed for complex circuitry. “We’ve shown that the switching works,” says HP computer architect Philip Kuekes. “But there is still not as good an understanding of the basic mechanism so that an engineer can design with it.” Hewlett Packard and UCLA have jointly patented several techniques for manufacturing of molecular computers, most recently in January of 2002.
Although molecular circuits employ some quantum effects, a separate but related community of scientists is exploring the possibilities of quantum computing-computing with atoms and their component parts. It works from the notion that some aspect of a sub-atomic particle-say, the location of an electron’s orbit around a nucleus-can be used to represent the 1s and 0s of computers. As with molecules, these states can be manipulated-programmed, in effect.
One approach pursued by members of a national consortium involving Berkeley, Harvard, IBM, MIT and others, involves flipping the direction of a spinning electron to turn switches on or off. By applying electromagnetic radiation in a process called nuclear magnetic resonance (NMR) like that used in medical imaging, researchers can control the spin of the carbon and hydrogen nuclei in chloroform. Alternatively, filters and mirrors show promise for controlling photons’ light as a switching mechanism. Other researchers work with materials such as quantum “dots” (electrons in silicon crystal), and “ion traps” (ionized atoms suspended in an electrical field).
Quantum bits (qubits) have an unusual quality that makes them a double-edge sword for computing purposes, though. Due to the lack of determinism inherent in quantum mechanics, qubits can be on or off simultaneously, a phenomenon called superposition. This makes it harder to force qubits into digital lockstep, but it also multiplies exponentially the amount of information groups of qubits can store. It theoretically allows massively parallel computation to solve problems previously thought uncomputable, such as factoring large prime numbers. One implication: today’s encryption techniques depend on the unfeasibility of computing the two multipliers (factors) of certain numbers, so quantum computers may one day be able to crack most encrypted files that exist today. This possibility has given the research a boost from government agencies, including the National Security Agency.
To be manufacturable, quantum computers will require billions of such sub-atomic switches working together and interacting with their environments without falling into a disorganized state called decoherence. A quantum state called entanglement-where many atoms are made to behave exactly alike-provides one possible solution. Researchers also hope to fight decoherence by harnessing a phenomenon called interference, that is, the overlapping of quantum particles’ wavelike energy.
Getting Down to the Biology
In addition to molecular and quantum computing, a third approach, biological computing, relies on living mechanism to perform logic operations.
Bioengineers have long understood how to manipulate genes to function as switches that activate other genes. Now they’re using the technique to build rudimentary computer “clocks” and logic gates inside bacteria such as E. coli. Other researchers use genes to prod microorganisms into states that represent information. A team headed by Thomas Knight at the MIT Artificial Intelligence Laboratory genetically manipulates luciferase, an enzyme in luminescent creatures such as fireflies, to generate light that serves as a medium of cell-to-cell communication.
One of biological computing’s biggest challenges is calculating with elements that are flawed, unreliable and decentralized. To that end, Knight’s amorphous computing group studies ways to encourage bacteria to organize themselves into parallel-processing computers. “I don’t think of it as likely to be the path to making conventional computers,” Knight says. “It will be the way in which we build the molecular-scale computers.”
Molecular computers face similar reliability challenges. At HP, researchers used fault-tolerant algorithms to construct a silicon-based computer called Teramac that worked despite having 220,000 defects. Kuekes, Teramac’s project manager, says the company is now exploring ways to translate what they’ve learned to molecular computing.
Farther out on the biological curve is DNA computing, which attempts to exploit the way DNA strands recognize each other and combine into structures that could perform large, compute-intensive calculations in parallel.
Few in the biological community expect biocomputers to replace the general-purpose silicon computer. They hope instead to manufacture molecular computers cheaply and efficiently with organisms that can orient themselves into logic circuits or transform vats of chemicals to manufacture other chemicals.
Still more exciting possibilities come from the potential of special-purpose biological computers to interact with other biological systems. Miniature computers could be injected into living tissue to reprogram cancer-causing genes, for example, or administer insulin shots.
For now, all these applications loom distant on the horizon. But researchers agree that silicon’s days are numbered, and that radical new approaches will be needed to keep computers zooming through the 21st century.


Quantum computers offer the promise of processing information much more efficiently than classical computers. But before quantum computers can be built, scientists must confront several challenges, one of which is quantum computers' vulnerability to their surroundings. Interaction with outside forces would immediately damage a quantum computer's information; this problem is known as "decoherence."
One method to coherently process quantum information involves cavity quantum electrodynamics (QED). In this method, scientists use a small cavity to achieve coherent dynamics between an atom and a photon by manipulating an atom's radiation properties with mirrors. Scientists from the California Institute of Technology are among the leaders in cavity QED, and have recently reported an important advance to enable a coherent distribution of quantum information across a network.
In their paper published in Physical Review Letters, physicist David Boozer and his colleagues have demonstrated the reversible state transfer of a coherent light pulse to and from the internal state of an atom trapped in an optical cavity. This observation is the first verification of atomic physicist Ignacio Cirac's proposal for the reversible mapping of quantum states between light and matter using cavity QED to provide strong coupling for the atom-photon interaction.
“The most significant result of this work is the demonstration of reversibility (i.e., coherence) for the light emission and absorption processes,” Boozer told PhysOrg.com. “The fact that this process is coherent means that it preserves superpositions of quantum states, hence it is a way of mapping quantum information between an atom and light.”
In quantum networks, qubits (the information states for quantum computers) can be represented by either atoms or photons. Atoms, which have long coherence times, serve as "stationary" qubits, or nodes of a network, where they are stored and locally manipulated. Photons, on the other hand, serve as "flying" qubits, or quantum channels that connect nodes over long distances. While many single-photon sources have been demonstrated in the past decade, none have been experimentally shown to be reversible until now.
“In principle, in a quantum computer there are several logic gates, each of which performs an elementary quantum operation on one or two stationary qubits,” Boozer explained. “The gates are connected together in a network, so that the output of one gate can be transported as a flying qubit to the input of the next gate. Hence, one needs a way to turn stationary qubits into flying qubits and vice-versa, which is what our recent work has demonstrated.”
In the Caltech scientists' experiment, a cesium atom is localized within the cavity by a far off-resonant optical trap, where it repeatedly undergoes a series of light absorption and reemission cycles, lasting a total of 360 ms. During each such cycle, the cavity is first illuminated by an incident pulse of coherent light. Whenever the atom-cavity system absorbs this pulse, the quantum state of the light is written onto the internal state of the atom.
After a delay of about 300 ns, the atomic state gets mapped back onto an emitted pulse of light, which is allowed to interfere with the source of the original coherent pulse. Observing the resulting interference fringe demonstrates the reversibility of the overall absorption-reemission process.
“Our optical cavity has a very small mode volume (the cavity length is only 42 microns), which ensures that the coherent interaction between the atom and light field occurs on a much faster time scale than the decoherence caused by atomic spontaneous emission or cavity leakage,” Boozer explained. “Thus the atom and cavity field can exchange quantum information coherently many times before an incoherent process occurs. This regime is known as strong-coupling in cavity QED.”
The scientists explain that the efficiency of the light-to-atom transfer is limited in this scenario by factors such as passive mirror losses, equal transmission coefficients of the cavity mirrors, and the coupling of the atom to both polarization modes of the cavity.
With the ability to reversibly transfer a qubit's state from "flying" to "stationary" and back again, the scientists have taken a step toward coherently transferring quantum information across a network, without disruption with the outside world. Still, Boozer and his colleagues look forward to future improvements.
“In the present work, the qubit is encoded in the photon-number states of light and in the hyperfine levels of the atom,” he said. “A more robust scheme which we may pursue in the future would be to instead use the polarization degree of freedom of the light, and the magnetic sublevels of the atom. Another future goal will be to increase the efficiency of the state transfer process, for instance by using cavity mirrors with unequal transmissivities and/or even higher reflectivities.”
Citation: Boozer, A. D., Boca, A., Miller, R., Northup, T. E., and Kimble, H. J. "Reversible State Transfer between Light and a Single Trapped Atom." Physical Review Letters 98, 193601 (2007).
Copyright 2007 PhysOrg.com.
All rights reserved. This material may not be published, broadcast, rewritten or redistributed in whole or part without the express written permission of PhysOrg.com.
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Quantum mechanics isn’t what it used to be. Several decades ago it was all about how, at the very small scales of atoms, energy comes in chunks or “quanta”: not continuous, like water, but discrete, like money. Even light is grainy, divided up into little packets of energy called photons.
But never mind all that. Today, quantum physicists aren’t really talking about quanta, they’re talking about information. They suspect that at its root quantum mechanics is a theory about what can and can’t be known about the world. The famous uncertainty principle, and the idea that quantum objects might be either here or there, are examples of that idea.
It’s not all theory, though. The new view offers potential applications in the form of so-called quantum information technology: ways of storing, transmitting and manipulating information that work using quantum rules rather than the “classical” rules of our everyday world. The most celebrated manifestation of this technology is the quantum computer, which could exploit quantum principles to achieve far greater power than the devices on which I’m writing and you are reading.
Although it’s clear to those in the field how quantum computers should work, no one knows how to make one. Scientists have made “toy” quantum computers with just a handful of bits (compared to the billions in your smart phone), and some companies are even starting to offer primitive versions for sale – to the scepticism of some experts. But despite tantalising reports of incremental breakthroughs over the past few years, there’s still no prospect that you’ll have a useful quantum laptop in the coming future.
However, scientists in Germany have just reported what could be a significant step forward. They say that the ideal material for a quantum computer could be diamond.
Don’t despair – that doesn’t mean they will cost the earth. The very thin films of diamond needed for such devices don’t have to be mined; they can be made artificially from carbon-rich gases such as methane. It’s not exactly cheap, but neither are the methods needed to make semiconductor films for a host of existing electronic devices.
Both conventional and quantum computers work by encoding and manipulating information in binary form; as “bits”, represented as zeroes and ones. Florian Dolde at the University of Stuttgart and his colleagues think the ideal elements that will store this information on a quantum computer are individual nitrogen atoms implanted into a diamond film. Nitrogen atoms have one more electron than the carbon atoms in diamond, and this spare electron can exist in two different quantum states thanks to a property called spin. Rather like the poles of a magnet (which are used to store information in magnetic disks and tapes), an electron spin can be considered to point either “up” or “down”.
That much has been known for some time, and others have experimented with nitrogen-doped diamond for quantum computing. The advance made by Dolde and colleagues is to show how they can place these spins in nitrogen electrons without having to cool the diamond to very low temperatures.
In a spin
The reason quantum computers could be so powerful is that a collection of bits could exist in many more different states than the same number of “classical” bits. That’s because quantum particles can exist in two or more different states at the same time – in a so-called superposition of states. So each quantum bit (qubit) can be not just a 1 or a 0 but mixtures of both. As a result, a group of qubits could perform many different calculations at once, rather than having to do them sequentially like an ordinary computer.
To enable that, it’s generally thought that the qubits have to be entangled. This means that the quantum state of one of them depends on the states of the others – even though these states aren’t actually assigned until they are measured. In other words, if you entangle a pair of spins that have opposite orientations, and measure one of them as being “up”, the other instantly becomes “down”, no matter how far away it is. Some early quantum theorists, including Einstein, thought this would be impossible, but this entanglement is now a well-established fact.
But here’s the rub: like most quantum properties, entanglement seems to be very delicate. Amid all the jostling of other atoms, a pair of entangled particles can lose their special connection so that their states become independent of each other. Sustaining entanglement has tended to mean cooling the particles down close to absolute zero to remove that jostling. But a quantum computer that needs to be so cold won’t ever find much of a market.
Dolde and colleagues have shown, however, that two nitrogen atoms trapped in diamond tens of nanometres apart can be kept entangled at room temperature for more than a millisecond (thousandth of a second), which could be long enough to perform quantum calculations. They used microwave photons to nudge the atoms into an entangled state, by firing a beam of nitrogen ions (charged atoms) at a diamond film though a mask with holes about 20 nanometres apart.
The case for nitrogen-doped diamond quantum computers is boosted further by a paper from Martin Plenio of the University of Ulm in Germany and his co-workers, who have shown that in theory – no more than that yet – such a system could be used as a “quantum simulator”: a kind of quantum computer that can calculate how other quantum systems will behave. The mathematics needed to predict quantum behaviour is complicated, and ordinary computers struggle to accommodate it. But a quantum simulator, working by quantum rules, already has the “quantum-ness” built in to its components, and so can carry out such calculations much more easily. Diamond, of all things, could take the hardness out of the problem.