Science Current Events | Science News | Brightsurf.com
 
Email a Friend Send to a friend
Printer Friendly Print Dream of quantum computing closer to reality as mathematicians chase key breakthrough

Dream of quantum computing closer to reality as mathematicians chase key breakthrough

December 22, 2008

The ability to exploit the extraordinary properties of quantum mechanics in novel applications, such as a new generation of super-fast computers, has come closer following recent progress with some of the remaining underlying mathematical problems. In particular, the operator theory used to describe interactions between particles at atomic scales or smaller where quantum mechanical properties are significant needs to be enhanced to deal with systems where digital information is processed or transmitted. In essence, the theory involves mathematical analysis based on Hilbert Spaces, which are extensions of the conventional three dimensional Euclidean geometry to cope with additional dimensions, as are required to describe quantum systems.

These challenges in mathematical analysis and prospects for imminent progress were discussed at a recent conference on operator theory and analysis organised by the European Science Foundation (ESF) in collaboration with the European Mathematical Society and the Mathematical Research and Conference Center in Bedlewo, Poland. The conference brought together some of the world's leading mathematical physicists and quantum mechanics specialists to tackle the key fields relating to spectral theory, according to the conference's co-chair Pavel Kurasov from the Lund Institute of Technology in Sweden. Among the participants were Uzy Smilansky, one of the leading authorities on quantum chaos, from the Weizmann Institute of Technology in Israel, and Vladimir Peller, specialist in pure mathematical analysis at Michigan State University in the US.




As Kurasov pointed out, a big challenge lies in extending current operator theory to describe and analyse quantum transport in wires, as will be needed for a new generation of quantum computers. Such computers will allow some calculations to be executed much more quickly in parallel by exploiting quantum coherence, whereby a processing element can represent digital bits in multiple states at once. There is also the prospect of exploiting another quantum mechanical property, quantum entanglement, for quantum cryptography where encryption key information can be transmitted with the ability to detect any attempt at tampering or eavesdropping, facilitating totally secure communication. In fact quantum cryptography has already been demonstrated over real telecommunications links and will be one of the first commercial applications based exclusively on quantum mechanics.

The operator theory required for quantum information processing and transmission is already well developed for what are known as self-adjoint operators, which are used to describe the different quantum states of an ideal system, but cannot be used for systems like a communications network where dissipation occurs. "So far only self-adjoint models have been considered, but in order to describe systems with dissipation even non-self-adjoint operators should be used," said Kurasov. The aim set out at the ESF conference was to extend the theory to non self-adjoint operators, which can be used to analyse real systems. "These operators may be used to describe quantum transport in wires and waveguides and therefore will be used in design of the new generation of computers," said Kurasov."Physicists are doing experiments with such structures, but the theory is not developed yet. An important question here is fitting of the parameters so that models will describe effects that may be observed in experiments." This question was discussed during inspiring lecture by Boris Pavlov from Auckland University, New Zealand - world leading specialist in mathematical analysis who became interested in physical applications.

Intriguingly Kurasov hinted that a breakthrough was likely before the next ESF conference on the subject in two years time, on the problem of reconstructing the so called quantum graphs used to represent states and interactions of quantum systems from actual observations. This will play a vital role in constructing the intermediate components of a quantum computer needed to monitor its own state and provide output.

Kurasov noted that this ESF conference was one in a series on the operator analysis field organized every second year, with proceedings published regularly in a book series Operator Theory: Advances and Applications.

European Science Foundation



Related Quantum Mechanics Current Events and Quantum Mechanics News Articles Quantum Mechanics Current Events and Quantum Mechanics News RSS Quantum Mechanics Current Events and Quantum Mechanics News RSS
NIST demonstrates 'universal' programmable quantum processor
Physicists at the National Institute of Standards and Technology (NIST) have demonstrated the first "universal" programmable quantum information processor able to run any program allowed by quantum mechanics-the rules governing the submicroscopic world-using two quantum bits (qubits) of information.

First Bose-Einstein condensation of strontium
In an international first, scientists from the Institute of Quantum Optics and Quantum Information (IQOQI) produced a Bose-Einstein condensate of the alkaline-earth element strontium, thus narrowly winning an international competition between many first-rate scientific groups

Quantum gas microscope offers glimpse of quirky ultracold atoms
Physicists at Harvard University have created a quantum gas microscope that can be used to observe single atoms at temperatures so low the particles follow the rules of quantum mechanics, behaving in bizarre ways.

Quantum computer chips now 1 step closer to reality
In the quest for smaller, faster computer chips, researchers are increasingly turning to quantum mechanics -- the exotic physics of the small. The problem: the manufacturing techniques required to make quantum devices have been equally exotic. That is, until now.

Field experiment on a robust hierarchical metropolitan quantum cryptography network
Key Laboratory of Quantum Information (CAS), University of Science and Technology of China has recently demonstrated a metropolitan Quantum Cryptography Network (QCN) for Government Administration in Wuhu, China. Because of its scientific significance and social impact, the project is reported in Volume 54, Issue 17 (September, 2009) of the Chinese Science Bulletin authored by Fang-xing Xu et al.

UA scientists discover quantum fingerprints of chaos
Chaotic behavior is the rule, not the exception, in the world we experience through our senses, the world governed by the laws of classical physics.

Building a better qubit
Exploiting quantum mechanics for transmitting information is a tantalizing possibility because it promises secure, high speed communications.

Physicists at UC Santa Barbara make discovery in quantum mechanics
Physicists at UC Santa Barbara have made an important advance in quantum mechanics using a superconducting electrical circuit. The finding is reported in this week's issue of the journal Nature.

A tiny, tunable well of light, and a string theorist's toolbox
Photonics, the science of using photons to carry information, promises to continue improving a wide variety of technologies, from computing to high-speed communication.

Atoms don't dance the 'bose nova'
Hanns-Christoph Naegerl's research group has investigated how ultracold quantum gases behave in lower spatial dimensions. They successfully realized an exotic state, where, due to the laws of quantum mechanics, atoms align along a one-dimensional structure.
More Quantum Mechanics Current Events and Quantum Mechanics News Articles
The Quantum World: Quantum Physics for Everyone

The Quantum World: Quantum Physics for Everyone
by Kenneth W. Ford (Author), Diane Goldstein (Contributor)

As Kenneth W. Ford shows us in The Quantum World, the laws governing the very small and the very swift defy common sense and stretch our minds to the limit. Drawing on a deep familiarity with the discoveries of the twentieth century, Ford gives an appealing account of quantum physics that will help the serious reader make sense of a science that, for all its successes, remains mysterious. In order to make the book even more suitable for classroom use, the author, assisted by Diane Goldstein, has included a new section of Quantum Questions at the back of the book. A separate answer manual to these 300+ questions is available; visit The Quantum World website for ordering information.

There is also a cloth edition of this book, which does not include the "Quantum Questions"...

Introduction to Quantum Mechanics (2nd Edition)

Introduction to Quantum Mechanics (2nd Edition)
by David J. Griffiths (Author)

This book first teaches learners how to do quantum mechanics, and then provides them with a more insightful discussion of what it means. Fundamental principles are covered, quantum theory presented, and special techniques developed for attacking realistic problems. The book's two-part coverage organizes topics under basic theory, and assembles an arsenal of approximation schemes with illustrative applications.

Principles of Quantum Mechanics

Principles of Quantum Mechanics
by R. Shankar (Author)

'An excellent text....The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succint manner.'--American Scientist, from a review of the First Edition The author introduces major additions and updates key presentations in the long-awaited new edition of this classic text. New features of the Second Edition include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications.

Quantum Physics: A Beginner's Guide

Quantum Physics: A Beginner's Guide
by Alastair I. M. Rae (Author)

As Alastair Rae points out in his introduction, “quantum physics is not rocket science”. It may have gained a reputation as the theory that no one really understands, but its practical applications are all around us in everyday life. If it were not for quantum physics, computers would not function, metals would not conduct electricity, and the power stations that heat our homes would not produce energy. Assuming no prior scientific or mathematical knowledge, this clear and concise introduction provides a step-by-step guide to quantum theory, right from the very basic principles to the most cutting-edge developments, such as super-fast computers and unbreakable codes, which could soon become reality. Finally, Rae turns to the philosophical questions posed by quantum physics and asks:...

Quantum Mechanics (2 vol. set)

Quantum Mechanics (2 vol. set)
by Claude Cohen-Tannoudji (Author), Bernard Diu (Author), Frank Laloe (Author)

This didactically unrivalled textbook and timeless reference by Nobel Prize Laureate Claude Cohen-Tannoudji separates essential underlying principles of quantum mechanics from specific applications and practical examples and deals with each of them in a different section. Chapters emphasize principles; complementary sections supply applications. The book provides a qualitative introduction to quantum mechanical ideas; a systematic, complete and elaborate presentation of all the mathematical tools and postulates needed, including a discussion of their physical content and applications.
The book is recommended on a regular basis by lecturers of undergraduate courses.

Quantum Mechanics for Scientists and Engineers (Classroom Resource Materials)

Quantum Mechanics for Scientists and Engineers (Classroom Resource Materials)
by David A. B. Miller (Author)

If you need a book that relates the core principles of quantum mechanics to modern applications in engineering, physics, and nanotechnology, this is it. Students will appreciate the book's applied emphasis, which illustrates theoretical concepts with examples of nanostructured materials, optics, and semiconductor devices. The many worked examples and more than 160 homework problems help students to problem solve and to practice applications of theory. Without assuming a prior knowledge of high-level physics or classical mechanics, the text introduces Schrodinger's equation, operators, and approximation methods. Systems, including the hydrogen atom and crystalline materials, are analyzed in detail. More advanced subjects, such as density matrices, quantum optics, and quantum information,...

Quantum Mechanics (2 Volumes in 1)

Quantum Mechanics (2 Volumes in 1)
by Albert Messiah (Author)

Simple enough for students yet sufficiently comprehensive to serve as a reference for working physicists, this classic text is celebrated for its clarity and coherence of presentation as well as the author’s fluid and literate style. Subjects include a detailed treatment of formalism and its interpretation, an analysis of simple systems, symmetries and invariance, methods of approximation, and a review of the elements of relativistic quantum mechanics. "Strongly recommended"—American Journal of Physics.


Quantum Mechanics Demystified

Quantum Mechanics Demystified
by David McMahon (Author)

Fun format makes this complex subject easy to grasp solutions to typical problems that are explained in full detail. It is perfect for self-study or class supplement. It is great for quick review or help prepare for the Physics qualifying exam. Learn quantum mechanics at warp speed! Now anyone can master the basics of quantum mechanics - without formal training, unlimited time, or a genius IQ. In "Quantum Mechanics Demystified", physicist (and student-savvy author) David McMahon provides an effective and illuminating way to learn the essentials of quantum mechanics.With "Quantum Mechanics Demystified", you master the subject one step at a time - at your own speed. This unique self-teaching guide is filled with solved examples throughout, and offers problems to try at the end of each...

Schaum's Outline of Quantum Mechanics (Schaum's)

Schaum's Outline of Quantum Mechanics (Schaum's)
by Eliahu Zaarur (Author), Phinik Reuven (Author)

This powerful study guide makes sometimes-daunting material accessible. More than 240 problems solved step-by-step help students gain a firm grasp of proper methods and a solid foundation for further study. All the essentials of this basic course are covered clearly and concisely, cutting study time and making important points memorable. The next-best thing to a private tutor, this study guide helps boost grades and proves ideal for professionals, too, who wish to study solo to master this discipline.

Modern Quantum Mechanics (Revised Edition)

Modern Quantum Mechanics (Revised Edition)
by J. J. Sakurai (Author)

Revised edition includes discussions of fundamental topics and newer developments such as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell's inequality. DLC: Quantum theory.

© 2009 BrightSurf.com