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Showing posts with label number. Show all posts
Showing posts with label number. Show all posts

Thursday, September 20, 2012

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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The above story is reprinted from materials provided by University of California - Santa Barbara.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

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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Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.


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Monday, June 11, 2012

'Sounds of silence' proving a hit: World's fastest random number generator

ScienceDaily (Apr. 13, 2012) — Researchers at The Australian National University have developed the fastest random number generator in the world by listening to the 'sounds of silence'.

The researchers -- Professor Ping Koy Lam, Dr Thomas Symul and Dr Syed Assad from the ANU ARC Centre of Excellence for Quantum Computation and Communication Technology -- have tuned their very sensitive light detectors to listen to vacuum -- a region of space that is empty.

Professor Lam said vacuum was once thought to be completely empty, dark, and silent until the discovery of the modern quantum theory. Since then scientists have discovered that vacuum is an extent of space that has virtual sub-atomic particles spontaneously appearing and disappearing.

It is the presence of these virtual particles that give rise to random noise. This 'vacuum noise' is omnipresent and may affect and ultimately pose a limit to the performances of fibre optic communication, radio broadcasts and computer operation.

"While it has always been thought to be an annoyance that engineers and scientists would like to circumvent, we instead exploited this vacuum noise and used it to generate random numbers," Professor Lam said.

"Random number generation has many uses in information technology. Global climate prediction, air traffic control, electronic gaming, encryption, and various types of computer modelling all rely on the availability of unbiased, truly random numbers.

"To date, most random number generators are based on computer algorithms. Although computer generated random numbers can be useful, knowing the input conditions to the algorithm will lead to predictable and reproducible output, thus making the numbers not truly random. To overcome this issue, random number generators relying on inherently random physical processes, such as radioactive decay and chaotic behaviour in circuits, have been developed."

Dr Thomas Symul added: "Vacuum noise is one of the ultimate sources of randomness because it is intrinsically broadband and its unpredictability is guaranteed by quantum theory. Because of this, we are able to generate billions of random numbers every second."

Dr Syed Assad said the team has linked their table-top laser experiment directly to the internet. "We can easily push this technology even faster but currently we have already reached the capacity of our Internet connection," he said.

The random number generator is online and can be accessed from anywhere, anytime around the world at http://photonics.anu.edu.au/qoptics/Research/qrng.php Moreover, anyone who downloaded live random numbers from the ANU website will get a fresh and unique sequence of numbers that is different from all other users.

In collaboration with QuintessenceLabs, an Australian quantum technology company, the ANU team is now looking into commercialising this device. The team hopes to have this technology miniaturised down to the size of a thumb drive.

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The above story is reprinted from materials provided by The Australian National University.

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