Tartaglia-Pascal triangle and quantum mechanics

The paper I wrote with Alfonso Farina and Matteo Sedehi about the link between the Tartaglia-Pascal triangle and quantum mechanics is now online (see here). This paper contains as a statement my theorem that provides a connection between the square root of a Wiener process and the Schrödinger equation that arose a lot of interest and much criticisms by some mathematicians (see here). So, it is worthwhile to tell how all this come about.

On fall 2011, Alfonso Farina called me as he had an open problem after he and his colleagues got published a paper on Signal, Image and Video Processing, a journal from Springer, where it was shown how the Tartaglia-Pascal triangle is deeply connected with diffusion and the Fourier equation. The connection comes out from the binomial coefficients, the elements of the Tartaglia-Pascal triangle, that in some limit give a Gaussian and this Gaussian, in the continuum, is the solution of the Fourier equation of heat diffusion. This entails a deep connection with stochastic processes. Stochastic processes, for most people working in the area of radar and sensors, are essential to understand how these device measure through filtering theory. But, in the historic perspective Farina & al. put their paper, they were not able to get a proper connection for the Schrödinger equation, notwithstanding they recognized there is a deep formal analogy with the Fourier equation. This was the open question: How to connect Tartaglia-Pascal triangle and Schrödinger equation?

People working in quantum physics are aware of the difficulties researchers have met to link stochastic processes a la Wiener and quantum mechanics. Indeed, skepticism is the main feeling of all of us about this matter. So, the question Alfonso put forward to me was not that easy. But Alfonso & al. paper contains also a possible answer: Just start from discrete and then go back to continuum. So, the analog of the heat equation is the Schrödinger equation for a free particle and its kernel and, indeed, the evolution of a Gaussian wave-packet can be managed on the discrete and gives back the binomial coefficient. What you get in this way are the square root of binomial coefficients. So, the link with the Tartaglia-Pascal triangle is rather subtle in quantum mechanics and enters through a square root, reminiscent of the Dirac’s work and his greatest achievement, Dirac equation. This answered Alfonso’s question and in a way that was somewhat unexpected.

Then, I thought that this connection could be deeper than what we had found. I tried to modify Ito calculus to consider fractional powers of a Wiener process. I posted my paper on arxiv and performed both experimental and numerical computations. All this confirms my theorem that the square root of a Wiener process has as a diffusion equation the Schrödinger equation. You can easily take the square root of a natural noise (I did it) or compute this on your preferred math software. It is just interesting that mathematicians never decided to cope with this and still claim that all this evidence does not exist, basing their claims on a theory that can be easily amended.

We have just thrown a seed in the earth. This is our main work. And we feel sure that very good fruits will come out. Thank you very much Alfonso and Matteo!

Farina, A., Frasca, M., & Sedehi, M. (2013). Solving Schrödinger equation via Tartaglia/Pascal triangle: a possible link between stochastic processing and quantum mechanics Signal, Image and Video Processing DOI: 10.1007/s11760-013-0473-y

Marco Frasca (2012). Quantum mechanics is the square root of a stochastic process arXiv arXiv: 1201.5091v2

Farina, A., Giompapa, S., Graziano, A., Liburdi, A., Ravanelli, M., & Zirilli, F. (2011). Tartaglia-Pascal’s triangle: a historical perspective with applications Signal, Image and Video Processing, 7 (1), 173-188 DOI: 10.1007/s11760-011-0228-6

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Let’s Explore Quantum Computing

A quantum computer would be able to store more bits of information in its memory than there are particles in the universe. Image Credit: Alengo/iStockPhoto

It’s fairly easy to surmise how quantum computing will evolve in the future if/when it becomes a reality. Devices that are currently based around a system of electronic circuits would eventually die off. Quantum devices would ultimately become the new standard in computing. While Peter Shor’s research showed how quantum algorithms would speed up advanced calculations, they never really demonstrated why people would want to do this.

Today we have plenty of areas where quantum computing would certainly shine. Speed usually isn’t important when it comes to data storage and retrieval systems. Entertainment devices, however, are getting increasingly complex. This shouldn’t be taken as a suggestion that quantum computing would only be useful for a new generation of video game consoles, however.

Society would eventually start to merge all forms of media into one. Whether this would be the trigger to bring on the singularity is hard to say, but it’s easy to imagine that it would certainly usher in a very different form of art. Like the interactive media movement, quantum art would fundamentally change the way that people interact with the world.

Storage systems could still see a boost from the field of quantum computing as well. Electronic quantum holography also looks pretty promising. Holograms loaded with data could be projected onto a small mass. A piece of software could then reconstruct information from these holograms in the same way that software currently reconstructs data from magnetic or electrical impulses.

Some amount of energy would need to be expended to ensure that the holograms remain in a viable state. This shouldn’t be too much of a problem. Battery backup memory has worked that way for years. Even flash memory has to maintain a small amount of voltage to ensure that it works as desired. Electronic quantum holography could be viewed as the natural extension of these already proven examples of information technology.

Interestingly enough, no one has really been able to demonstrate the reason that quantum circuits would be superior to their regular electronic contemporaries. Most of what researchers believe is based wholly on assumptions/theory. While some people feel that quantum devices will never really replace microprocessors, it’s easy to imagine the microchip going the way of the vacuum tube. While transistors have almost completely replaced electronic valves, there remains few niche industries that continue to use them today.

On the totally other side of the spectrum, some people feel that quantum computers will someday be able to violate the basic theories of cognitive science. The idea of a self-aware machine has been bandied about for quite some time. When talking about the possibilities, it’s important to remember a few things. What currently defines a computer is at least in part based on the old Church-Turing thesis.

When this is violated, the whole idea of computational notions cease to be individual, autonomous units. Since quantum computers could solve equations that modern computers have found impossible, they force researchers to redefine the abstracts of efficient algorithms.

Superposition principles tell us that the bit is the smallest unit a machine can handle. A regular bit can only exhibit the features of one of two states. This is where the basic rules of binary math come from. Any single bit can be classified as 1 or 0. However, quantum computing defies these rules. By definition, a quantum computer is one that can handle bits assigned a third state. This state is somewhere between the two. Currently, computers can only tell if a circuit is switched on or not. A quantum computer would probably sense different voltages to ascribe values to some fraction of power. Some researchers use creative names like qubits to describe the components of quantum logic gates.

Quantum logic doesn’t even need to rely on electronics, however. Unconventional designs will probably evolve in the near future. Chemical computer systems, which are sometimes derisively referred to as gooware, would assign values to different chemical reactions. While it might seem weird to leave a tub of chemicals on a desk, practical designs might be closer to a dry cell battery. They could be quite small and portable.

Other logic systems have been proposed as well. Logic gates built around photons would allow nonlinear calculations. Photonic controlled gates would allow quantum computers to be built around electromagnetic models. Even with these types of advances however, future consumers would probably be more apt to buy something close to what they already know – at least in the early years of quantum computing. That makes photonic logic a good option for companies who want to pursue something they could actually market early on.

Reference:

Benningshof OW, Mohebbi HR, Taminiau IA, Miao GX, & Cory DG (2013). Superconducting microstrip resonator for pulsed ESR of thin films. Journal of magnetic resonance (San Diego, Calif. : 1997), 230C, 84-87 PMID: 23454577

Petersson KD, McFaul LW, Schroer MD, Jung M, Taylor JM, Houck AA, & Petta JR (2012). Circuit quantum electrodynamics with a spin qubit. Nature, 490 (7420), 380-3 PMID: 23075988

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Quantum computing with recycled particles

Oct. 23, 2012 — A research team from the University of Bristol's Centre for Quantum Photonics (CQP) have brought the reality of a quantum computer one step closer by experimentally demonstrating a technique for significantly reducing the physical resources required for quantum factoring.

The team have shown how it is possible to recycle the particles inside a quantum computer, so that quantum factoring can be achieved with only one third of the particles originally required. The research is published in the latest issue of Nature Photonics.

Using photons as the particles, the Bristol team constructed a quantum optical circuit that recycled one of the photons to set a new record for factoring 21 with a quantum algorithm -- all previous demonstrations have factored 15.

Dr Anthony Laing, who led the project, said: "Quantum computers promise to harness the counterintuitive laws of quantum mechanics to perform calculations that are forever out of reach of conventional classical computers. Realising such a device is one of the great technological challenges of the century."

While scientists and mathematicians are still trying to understand the full range of capabilities of quantum computers, the current driving application is the hard problem of factoring large numbers. The best classical computers can run for the lifetime of the universe, searching for the factors of a large number, yet still be unsuccessful.

In fact, Internet cryptographic protocols are based on this exponential overhead in computational time: if a third party wants to spy on your emails, they will need to solve a hard factoring problem first. A quantum computer, on the other hand, is capable of efficiently factoring large numbers, but the physical resources required mean that constructing such a device is highly challenging.

CQP PhD student Enrique Martín-López, who performed the experiment, said: "While it will clearly be some time before emails can be hacked with a quantum computer, this proof of principle experiment paves the way for larger implementations of quantum algorithms by using particle recycling."

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Journal Reference:

Enrique Martín-López, Anthony Laing, Thomas Lawson, Roberto Alvarez, Xiao-Qi Zhou, Jeremy L. O'Brien. Experimental realization of Shor's quantum factoring algorithm using qubit recycling. Nature Photonics, 2012; DOI: 10.1038/nphoton.2012.259

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Simulating reality: Less memory required on quantum computer than on classical computer, study shows

ScienceDaily (May 3, 2012) — Simulations of reality would require less memory on a quantum computer than on a classical computer, new research from scientists at the University of Bristol, published in Nature Communications, has shown.

The study by Dr Karoline Wiesner from the School of Mathematics and Centre for Complexity Sciences, together with researchers from the Centre for Quantum Technologies in Singapore, demonstrates a new way in which computers based on quantum physics could beat the performance of classical computers.

When confronted with a complicated system, scientists typically strive to identify underlying simplicity which is then articulated as natural laws and fundamental principles. However, complex systems often seem immune to this approach, making it difficult to extract underlying principles.

Researchers have discovered that complex systems can be less complex than originally thought if they allow quantum physics to help: quantum models of complex systems are simpler and predict their behaviour more efficiently than classical models.

A good measure of the complexity of a particular system or process is how predictable it is. For example, the outcome of a fair coin toss is inherently unpredictable and any resources (beyond a random guess) spent on predicting it would be wasted. Therefore, the complexity of such a process is zero.

Other systems are quite different, for example neural spike sequences (which indicate how sensory and other information is represented in the brain) or protein conformational dynamics (how proteins -- the molecules that facilitate biological functions -- undergo structural rearrangement). These systems have memory and are predictable to some extent; they are more complex than a coin toss.

The operation of such complex systems in many organisms is based on a simulation of reality. This simulation allows the organism to predict and thus react to the environment around it. However, if quantum dynamics can be exploited to make identical predictions with less memory, then such systems need not be as complex as originally thought.

Dr Wiesner added: "On a more fundamental level, we found that the efficiency of prediction still does not reach the lower bound given by the principles of thermodynamics -- there is room for improvement. This might hint at a source of temporal asymmetry within the framework of quantum mechanics; that it is fundamentally impossible to simulate certain observable statistics reversibly and hence with perfect efficiency."

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Journal Reference:

Mile Gu, Karoline Wiesner, Elisabeth Rieper, Vlatko Vedral. Quantum mechanics can reduce the complexity of classical models. Nature Communications, 2012; 3: 762 DOI: 10.1038/ncomms1761

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Researchers make quantum processor capable of factoring a composite number into prime factors

ScienceDaily (Aug. 19, 2012) — Computing prime factors may sound like an elementary math problem, but try it with a large number, say one that contains more than 600 digits, and the task becomes enormously challenging and impossibly time-consuming. Now, a group of researchers at UC Santa Barbara has designed and fabricated a quantum processor capable of factoring a composite number -- in this case the number 15 -- into its constituent prime factors, 3 and 5.

Although modest compared to a 600-digit number, the achievement represents a milestone on the road map to building a quantum computer capable of factoring much larger numbers, with significant implications for cryptography and cybersecurity. The results are published in the advance online issue of the journal Nature Physics.

"Fifteen is a small number, but what's important is we've shown that we can run a version of Peter Shor's prime factoring algorithm on a solid state quantum processor. This is really exciting and has never been done before," said Erik Lucero, the paper's lead author. Now a postdoctoral researcher in experimental quantum computing at IBM, Lucero was a doctoral student in physics at UCSB when the research was conducted and the paper was written.

"What is important is that the concepts used in factoring this small number remain the same when factoring much larger numbers," said Andrew Cleland, a professor of physics at UCSB and a collaborator on the experiment. "We just need to scale up the size of this processor to something much larger. This won't be easy, but the path forward is clear."

Practical applications motivated the research, according to Lucero, who explained that factoring very large numbers is at the heart of cybersecurity protocols, such as the most common form of encoding, known as RSA encryption. "Anytime you send a secure transmission -- like your credit card information -- you are relying on security that is based on the fact that it's really hard to find the prime factors of large numbers," he said. Using a classical computer and the best-known classical algorithm, factoring something like RSA Laboratory's largest published number -- which contains over 600 decimal digits -- would take longer than the age of the universe, he continued.

A quantum computer could reduce this wait time to a few tens of minutes. "A quantum computer can solve this problem faster than a classical computer by about 15 orders of magnitude," said Lucero. "This has widespread effect. A quantum computer will be a game changer in a lot of ways, and certainly with respect to computer security."

So, if quantum computing makes RSA encryption no longer secure, what will replace it? The answer, Lucero said, is quantum cryptography. "It's not only harder to break, but it allows you to know if someone has been eavesdropping, or listening in on your transmission. Imagine someone wiretapping your phone, but now, every time that person tries to listen in on your conversation, the audio gets jumbled. With quantum cryptography, if someone tries to extract information, it changes the system, and both the transmitter and the receiver are aware of it."

To conduct the research, Lucero and his colleagues designed and fabricated a quantum processor to map the problem of factoring the number 15 onto a purpose-built superconducting quantum circuit. "We chose the number 15 because it is the smallest composite number that satisfies the conditions appropriate to test Shor's algorithm -- it is a product of two prime numbers, and it's not even," he explained.

The quantum processor was implemented using a quantum circuit composed of four superconducting phase qubits -- the quantum equivalents of transistors -- and five microwave resonators. The complexity of operating these nine quantum elements required building a control system that allows for precise operation and a significant degree of automation -- a prototype that will facilitate scaling up to larger and more complex circuits. The research represents a significant step toward a scalable quantum architecture while meeting a benchmark for quantum computation, as well as having historical relevance for quantum information and cryptography.

"After repeating the experiment 150,000 times, we showed that our quantum processor got the right answer just under half the time" Lucero said. "The best we can expect from Shor's algorithm is to get the right answer exactly 50 percent of the time, so our results were essentially what we'd expect theoretically."

The next step, according to Lucero, is to increase the quantum coherence times and go from nine quantum elements to hundreds, then thousands, and on to millions. "Now that we know 15=3x5, we can start thinking about how to factor larger -- dare I say -- more practical numbers," he said.

Other UCSB researchers participating in the study include John Martinis, professor of physics; Rami Barends, Yu Chen, Matteo Mariantoni, and Y. Yin, postdoctoral fellows in physics; and physics graduate students Julian Kelly, Anthony Megrant, Peter O'Malley, Daniel Sank, Amit Vainsencher, Jim Wenner, and Ted White.

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Journal Reference:

Erik Lucero, R. Barends, Y. Chen, J. Kelly, M. Mariantoni, A. Megrant, P. O’Malley, D. Sank, A. Vainsencher, J. Wenner, T. White, Y. Yin, A. N. Cleland & John M. Martinis. Computing prime factors with a Josephson phase qubit quantum processor. Nature Physics, 19 August 2012 DOI: 10.1038/nphys2385

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Paving the way to a scalable device for quantum information processing

ScienceDaily (July 24, 2012) — Researchers at NPL have demonstrated for the first time a monolithic 3D ion microtrap array which could be scaled up to handle several tens of ion-based quantum bits (qubits). The research, published in Nature Nanotechnology, shows how it is possible to realise this device embedded in a semiconductor chip, and demonstrates the device's ability to confine individual ions at the nanoscale.

As the UK's National Measurement Institute, NPL is interested in how exotic quantum states of matter can be used to make high precision measurements, of for example, time and frequency, ever more accurate. This research, however, has implications wider than measurement. The device could be used in quantum computation, where entangled qubits are used to execute powerful quantum algorithms. As an example, factorisation of large numbers by a quantum algorithm is dramatically faster than with a classical algorithm.

Scalable ion traps consisting of a 2D array of electrodes have been developed, however 3D trap geometries can provide a superior potential for confining the ions. Creating a successful scalable 3D ion trapping device is based on maintaining two qualities -- the ability to scale the device to accommodate increasing numbers of atomic particles, whilst preserving the trapping potential which enables precise control of ions at the atomic level. Previous research resulted in compromising at least one of these factors, largely due to limitations in the manufacturing processes.

The team at NPL has now produced the first monolithic ion microtrap array which uniquely combines a near ideal 3D geometry with a scalable fabrication process -- a breakthrough in this field. In terms of elementary operating characteristics, the microtrap chip outperforms all other scalable devices for ions.

Using a novel process based on conventional semiconductor fabrication technology, scientists developed the microtrap device from a silica-on-silicon wafer. The team were able to confine individual and strings of up to 14 ions in a single segment of the array. The fabrication process should enable device scaling to handle greatly increased numbers of ions, whilst retaining the ability to individually control each of them.

Due to the enormous progress in nanotechnology, the power of classical processor chips has been scaled up according to Moore's Law. Quantum processors are in their infancy, and the NPL device is a promising approach for advancing the scale of such chips for ion-based qubits.

Alastair Sinclair, Principal Scientist, NPL said: "We managed to produce an essential device or tool, which is critical for state of the art research and development in quantum technologies. This could be the basis of a future atomic clock device, with relevance for location, timing, navigation services or even the basis of a future quantum processor chip based on trapped ions, leading to a quantum computer and a quantum information network."

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Journal Reference:

Guido Wilpers, Patrick See, Patrick Gill, Alastair G. Sinclair. A monolithic array of three-dimensional ion traps fabricated with conventional semiconductor technology. Nature Nanotechnology, 2012; DOI: 10.1038/nnano.2012.126

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Quantum computers will be able to simulate particle collisions

ScienceDaily (June 1, 2012) — Quantum computers are still years away, but a trio of theorists has already figured out at least one talent they may have. According to the theorists, including one from the National Institute of Standards and Technology (NIST), physicists might one day use quantum computers to study the inner workings of the universe in ways that are far beyond the reach of even the most powerful conventional supercomputers.

Quantum computers require technology that may not be perfected for decades, but they hold great promise for solving complex problems. The switches in their processors will take advantage of quantum mechanics -- the laws that govern the interaction of subatomic particles. These laws allow quantum switches to exist in both on and off states simultaneously, so they will be able to consider all possible solutions to a problem at once.

This unique talent, far beyond the capability of today's computers, could enable quantum computers to solve some currently difficult problems quickly, such as breaking complex codes. But they could look at more challenging problems as well.

"We have this theoretical model of the quantum computer, and one of the big questions is, what physical processes that occur in nature can that model represent efficiently?" said Stephen Jordan, a theorist in NIST's Applied and Computational Mathematics Division. "Maybe particle collisions, maybe the early universe after the Big Bang? Can we use a quantum computer to simulate them and tell us what to expect?"

Questions like these involve tracking the interaction of many different elements, a situation that rapidly becomes too complicated for today's most powerful computers.

The team developed an algorithm -- a series of instructions that can be run repeatedly -- that could run on any functioning quantum computer, regardless of the specific technology that will eventually be used to build it. The algorithm would simulate all the possible interactions between two elementary particles colliding with each other, something that currently requires years of effort and a large accelerator to study.

Simulating these collisions is a very hard problem for today's digital computers because the quantum state of the colliding particles is very complex and, therefore, difficult to represent accurately with a feasible number of bits. The team's algorithm, however, encodes the information that describes this quantum state far more efficiently using an array of quantum switches, making the computation far more reasonable.

A substantial amount of the work on the algorithm was done at the California Institute of Technology, while Jordan was a postdoctoral fellow. His coauthors are fellow postdoc Keith S.M. Lee (now a postdoc at the University of Pittsburgh) and Caltech's John Preskill, the Richard P. Feynman Professor of Theoretical Physics.

The team used the principles of quantum mechanics to prove their algorithm can sum up the effects of the interactions between colliding particles well enough to generate the sort of data that an accelerator would provide.

"What's nice about the simulation is that you can raise the complexity of the problem by increasing the energy of the particles and collisions, but the difficulty of solving the problem does not increase so fast that it becomes unmanageable," Preskill says. "It means a quantum computer could handle it feasibly."

Though their algorithm only addresses one specific type of collision, the team speculates that their work could be used to explore the entire theoretical foundation on which fundamental physics rests.

"We believe this work could apply to the entire standard model of physics," Jordan says. "It could allow quantum computers to serve as a sort of wind tunnel for testing ideas that often require accelerators today."

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Journal Reference:

S. P. Jordan, K. S. M. Lee, J. Preskill. Quantum Algorithms for Quantum Field Theories. Science, 2012; 336 (6085): 1130 DOI: 10.1126/science.1217069

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Quantum computers move closer to reality, thanks to highly enriched and highly purified silicon

ScienceDaily (June 7, 2012) — The quantum computer is a futuristic machine that could operate at speeds even more mind-boggling than the world's fastest super-computers.

Research involving physicist Mike Thewalt of Simon Fraser University offers a new step towards making quantum computing a reality, through the unique properties of highly enriched and highly purified silicon.

Quantum computers right now exist pretty much in physicists' concepts, and theoretical research. There are some basic quantum computers in existence, but nobody yet can build a truly practical one -- or really knows how.

Such computers will harness the powers of atoms and sub-atomic particles (ions, photons, electrons) to perform memory and processing tasks, thanks to strange sub-atomic properties.

What Thewalt and colleagues at Oxford University and in Germany have found is that their special silicon allows processes to take place and be observed in a solid state that scientists used to think required a near-perfect vacuum.

And, using this 28Si they have extended to three minutes -- from a matter of seconds -- the time in which scientists can manipulate, observe and measure the processes.

"It's by far a record in solid-state systems," Thewalt says. "If you'd asked people a few years ago if this was possible, they'd have said no. It opens new ways of using solid-state semi-conductors such as silicon as a base for quantum computing.

"You can start to do things that people thought you could only do in a vacuum. What we have found, and what wasn't anticipated, are the sharp spectral lines (optical qualities) in the 28Silicon we have been testing. It's so pure, and so perfect. There's no other material like it."

But the world is still a long way from practical quantum computers, he notes.

Quantum computing is a concept that challenges everything we know or understand about today's computers.

Your desktop or laptop computer processes "bits" of information. The bit is a fundamental unit of information, seen by your computer has having a value of either "1" or "0."

That last paragraph, when written in Word, contains 181 characters including spaces. In your home computer, that simple paragraph is processed as a string of some 1,448 "1"s and "0"s.

But in the quantum computer, the "quantum bit" (also known as a "qubit") can be both a "1" and a "0" -- and all values between 0 and 1 -- at the same time.

Says Thewalt: "A classical 1/0 bit can be thought of as a person being either at the North or South Pole, whereas a qubit can be anywhere on the surface of the globe -- its actual state is described by two parameters similar to latitude and longitude."

Make a practical quantum computer with enough qubits available and it could complete in minutes calculations that would take today's super-computers years, and your laptop perhaps millions of years.

The work by Thewalt and his fellow researchers opens up yet another avenue of research and application that may, in time, lead to practical breakthroughs in quantum computing.

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Journal Reference:

M. Steger, K. Saeedi, M. L. W. Thewalt, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H.- J. Pohl. Quantum Information Storage for over 180 s Using Donor Spins in a 28Si 'Semiconductor Vacuum'. Science, 2012; 336 (6086): 1280 DOI: 10.1126/science.1217635

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Quantum computers could help search engines keep up with the Internet's growth

ScienceDaily (June 12, 2012) — Most people don't think twice about how Internet search engines work. You type in a word or phrase, hit enter, and poof -- a list of web pages pops up, organized by relevance.

Behind the scenes, a lot of math goes into figuring out exactly what qualifies as most relevant web page for your search. Google, for example, uses a page ranking algorithm that is rumored to be the largest numerical calculation carried out anywhere in the world. With the web constantly expanding, researchers at USC have proposed -- and demonstrated the feasibility -- of using quantum computers to speed up that process.

"This work is about trying to speed up the way we search on the web," said Daniel Lidar, corresponding author of a paper on the research that appeared in the journal Physical Review Letters on June 4.

As the Internet continues to grow, the time and resources needed to run the calculation -- which is done daily -- grow with it, Lidar said.

Lidar, who holds appointments at the USC Viterbi School of Engineering and the USC Dornsife College of Letters, Arts and Sciences, worked with colleagues Paolo Zanardi of USC Dornsife and first author Silvano Garnerone, formerly a postdoctoral researcher at USC and now of the University of Waterloo, to see whether quantum computing could be used to run the Google algorithm faster.

As opposed to traditional computer bits, which can encode distinctly either a one or a zero, quantum computers use quantum bits or "qubits," which can encode a one and a zero at the same time. This property, called superposition, some day will allow quantum computers to perform certain calculations much faster than traditional computers.

Currently, there isn't a quantum computer in the world anywhere near large enough to run Google's page ranking algorithm for the entire web. To simulate how a quantum computer might perform, the researchers generated models of the web that simulated a few thousand web pages.

The simulation showed that a quantum computer could, in principle, return the ranking of the most important pages in the web faster than traditional computers, and that this quantum speedup would improve the more pages needed to be ranked. Further, the researchers showed that to simply determine whether the web's page rankings should be updated, a quantum computer would be able to spit out a yes-or-no answer exponentially faster than a traditional computer.

This research was funded by number of sources, including the National Science Foundation, the NASA Ames Research Center, the Lockheed Martin Corporation University Research Initiative program, and a Google faculty research award to Lidar.

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Journal Reference:

Silvano Garnerone, Paolo Zanardi, Daniel Lidar. Adiabatic Quantum Algorithm for Search Engine Ranking. Physical Review Letters, 2012; 108 (23) DOI: 10.1103/PhysRevLett.108.230506

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Quantum computers will be able to simulate particle collisions

ScienceDaily (June 1, 2012) — Quantum computers are still years away, but a trio of theorists has already figured out at least one talent they may have. According to the theorists, including one from the National Institute of Standards and Technology (NIST), physicists might one day use quantum computers to study the inner workings of the universe in ways that are far beyond the reach of even the most powerful conventional supercomputers.

Quantum computers require technology that may not be perfected for decades, but they hold great promise for solving complex problems. The switches in their processors will take advantage of quantum mechanics -- the laws that govern the interaction of subatomic particles. These laws allow quantum switches to exist in both on and off states simultaneously, so they will be able to consider all possible solutions to a problem at once.

This unique talent, far beyond the capability of today's computers, could enable quantum computers to solve some currently difficult problems quickly, such as breaking complex codes. But they could look at more challenging problems as well.

"We have this theoretical model of the quantum computer, and one of the big questions is, what physical processes that occur in nature can that model represent efficiently?" said Stephen Jordan, a theorist in NIST's Applied and Computational Mathematics Division. "Maybe particle collisions, maybe the early universe after the Big Bang? Can we use a quantum computer to simulate them and tell us what to expect?"

Questions like these involve tracking the interaction of many different elements, a situation that rapidly becomes too complicated for today's most powerful computers.

The team developed an algorithm -- a series of instructions that can be run repeatedly -- that could run on any functioning quantum computer, regardless of the specific technology that will eventually be used to build it. The algorithm would simulate all the possible interactions between two elementary particles colliding with each other, something that currently requires years of effort and a large accelerator to study.

Simulating these collisions is a very hard problem for today's digital computers because the quantum state of the colliding particles is very complex and, therefore, difficult to represent accurately with a feasible number of bits. The team's algorithm, however, encodes the information that describes this quantum state far more efficiently using an array of quantum switches, making the computation far more reasonable.

A substantial amount of the work on the algorithm was done at the California Institute of Technology, while Jordan was a postdoctoral fellow. His coauthors are fellow postdoc Keith S.M. Lee (now a postdoc at the University of Pittsburgh) and Caltech's John Preskill, the Richard P. Feynman Professor of Theoretical Physics.

The team used the principles of quantum mechanics to prove their algorithm can sum up the effects of the interactions between colliding particles well enough to generate the sort of data that an accelerator would provide.

"What's nice about the simulation is that you can raise the complexity of the problem by increasing the energy of the particles and collisions, but the difficulty of solving the problem does not increase so fast that it becomes unmanageable," Preskill says. "It means a quantum computer could handle it feasibly."

Though their algorithm only addresses one specific type of collision, the team speculates that their work could be used to explore the entire theoretical foundation on which fundamental physics rests.

"We believe this work could apply to the entire standard model of physics," Jordan says. "It could allow quantum computers to serve as a sort of wind tunnel for testing ideas that often require accelerators today."

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The above story is reprinted from materials provided by National Institute of Standards and Technology (NIST).

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Journal Reference:

S. P. Jordan, K. S. M. Lee, J. Preskill. Quantum Algorithms for Quantum Field Theories. Science, 2012; 336 (6085): 1130 DOI: 10.1126/science.1217069

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Quantum computers move closer to reality, thanks to highly enriched and highly purified silicon

ScienceDaily (June 7, 2012) — The quantum computer is a futuristic machine that could operate at speeds even more mind-boggling than the world's fastest super-computers.

Research involving physicist Mike Thewalt of Simon Fraser University offers a new step towards making quantum computing a reality, through the unique properties of highly enriched and highly purified silicon.

Quantum computers right now exist pretty much in physicists' concepts, and theoretical research. There are some basic quantum computers in existence, but nobody yet can build a truly practical one -- or really knows how.

Such computers will harness the powers of atoms and sub-atomic particles (ions, photons, electrons) to perform memory and processing tasks, thanks to strange sub-atomic properties.

What Thewalt and colleagues at Oxford University and in Germany have found is that their special silicon allows processes to take place and be observed in a solid state that scientists used to think required a near-perfect vacuum.

And, using this 28Si they have extended to three minutes -- from a matter of seconds -- the time in which scientists can manipulate, observe and measure the processes.

"It's by far a record in solid-state systems," Thewalt says. "If you'd asked people a few years ago if this was possible, they'd have said no. It opens new ways of using solid-state semi-conductors such as silicon as a base for quantum computing.

"You can start to do things that people thought you could only do in a vacuum. What we have found, and what wasn't anticipated, are the sharp spectral lines (optical qualities) in the 28Silicon we have been testing. It's so pure, and so perfect. There's no other material like it."

But the world is still a long way from practical quantum computers, he notes.

Quantum computing is a concept that challenges everything we know or understand about today's computers.

Your desktop or laptop computer processes "bits" of information. The bit is a fundamental unit of information, seen by your computer has having a value of either "1" or "0."

That last paragraph, when written in Word, contains 181 characters including spaces. In your home computer, that simple paragraph is processed as a string of some 1,448 "1"s and "0"s.

But in the quantum computer, the "quantum bit" (also known as a "qubit") can be both a "1" and a "0" -- and all values between 0 and 1 -- at the same time.

Says Thewalt: "A classical 1/0 bit can be thought of as a person being either at the North or South Pole, whereas a qubit can be anywhere on the surface of the globe -- its actual state is described by two parameters similar to latitude and longitude."

Make a practical quantum computer with enough qubits available and it could complete in minutes calculations that would take today's super-computers years, and your laptop perhaps millions of years.

The work by Thewalt and his fellow researchers opens up yet another avenue of research and application that may, in time, lead to practical breakthroughs in quantum computing.

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The above story is reprinted from materials provided by Simon Fraser University.

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Journal Reference:

M. Steger, K. Saeedi, M. L. W. Thewalt, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H.- J. Pohl. Quantum Information Storage for over 180 s Using Donor Spins in a 28Si 'Semiconductor Vacuum'. Science, 2012; 336 (6086): 1280 DOI: 10.1126/science.1217635

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Quantum computers could help search engines keep up with the Internet's growth

ScienceDaily (June 12, 2012) — Most people don't think twice about how Internet search engines work. You type in a word or phrase, hit enter, and poof -- a list of web pages pops up, organized by relevance.

Behind the scenes, a lot of math goes into figuring out exactly what qualifies as most relevant web page for your search. Google, for example, uses a page ranking algorithm that is rumored to be the largest numerical calculation carried out anywhere in the world. With the web constantly expanding, researchers at USC have proposed -- and demonstrated the feasibility -- of using quantum computers to speed up that process.

"This work is about trying to speed up the way we search on the web," said Daniel Lidar, corresponding author of a paper on the research that appeared in the journal Physical Review Letters on June 4.

As the Internet continues to grow, the time and resources needed to run the calculation -- which is done daily -- grow with it, Lidar said.

Lidar, who holds appointments at the USC Viterbi School of Engineering and the USC Dornsife College of Letters, Arts and Sciences, worked with colleagues Paolo Zanardi of USC Dornsife and first author Silvano Garnerone, formerly a postdoctoral researcher at USC and now of the University of Waterloo, to see whether quantum computing could be used to run the Google algorithm faster.

As opposed to traditional computer bits, which can encode distinctly either a one or a zero, quantum computers use quantum bits or "qubits," which can encode a one and a zero at the same time. This property, called superposition, some day will allow quantum computers to perform certain calculations much faster than traditional computers.

Currently, there isn't a quantum computer in the world anywhere near large enough to run Google's page ranking algorithm for the entire web. To simulate how a quantum computer might perform, the researchers generated models of the web that simulated a few thousand web pages.

The simulation showed that a quantum computer could, in principle, return the ranking of the most important pages in the web faster than traditional computers, and that this quantum speedup would improve the more pages needed to be ranked. Further, the researchers showed that to simply determine whether the web's page rankings should be updated, a quantum computer would be able to spit out a yes-or-no answer exponentially faster than a traditional computer.

This research was funded by number of sources, including the National Science Foundation, the NASA Ames Research Center, the Lockheed Martin Corporation University Research Initiative program, and a Google faculty research award to Lidar.

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Journal Reference:

Silvano Garnerone, Paolo Zanardi, Daniel Lidar. Adiabatic Quantum Algorithm for Search Engine Ranking. Physical Review Letters, 2012; 108 (23) DOI: 10.1103/PhysRevLett.108.230506

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Simulating reality: Less memory required on quantum computer than on classical computer, study shows

ScienceDaily (May 3, 2012) — Simulations of reality would require less memory on a quantum computer than on a classical computer, new research from scientists at the University of Bristol, published in Nature Communications, has shown.

The study by Dr Karoline Wiesner from the School of Mathematics and Centre for Complexity Sciences, together with researchers from the Centre for Quantum Technologies in Singapore, demonstrates a new way in which computers based on quantum physics could beat the performance of classical computers.

When confronted with a complicated system, scientists typically strive to identify underlying simplicity which is then articulated as natural laws and fundamental principles. However, complex systems often seem immune to this approach, making it difficult to extract underlying principles.

Researchers have discovered that complex systems can be less complex than originally thought if they allow quantum physics to help: quantum models of complex systems are simpler and predict their behaviour more efficiently than classical models.

A good measure of the complexity of a particular system or process is how predictable it is. For example, the outcome of a fair coin toss is inherently unpredictable and any resources (beyond a random guess) spent on predicting it would be wasted. Therefore, the complexity of such a process is zero.

Other systems are quite different, for example neural spike sequences (which indicate how sensory and other information is represented in the brain) or protein conformational dynamics (how proteins -- the molecules that facilitate biological functions -- undergo structural rearrangement). These systems have memory and are predictable to some extent; they are more complex than a coin toss.

The operation of such complex systems in many organisms is based on a simulation of reality. This simulation allows the organism to predict and thus react to the environment around it. However, if quantum dynamics can be exploited to make identical predictions with less memory, then such systems need not be as complex as originally thought.

Dr Wiesner added: "On a more fundamental level, we found that the efficiency of prediction still does not reach the lower bound given by the principles of thermodynamics -- there is room for improvement. This might hint at a source of temporal asymmetry within the framework of quantum mechanics; that it is fundamentally impossible to simulate certain observable statistics reversibly and hence with perfect efficiency."

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Journal Reference:

Mile Gu, Karoline Wiesner, Elisabeth Rieper, Vlatko Vedral. Quantum mechanics can reduce the complexity of classical models. Nature Communications, 2012; 3: 762 DOI: 10.1038/ncomms1761

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