22.12.2008

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.

The ESF conference Operator Theory, Analysis and Mathematical Physics was held at the Mathematical Research and Conference Center, Bedlewo in Poland in June 2008

Thomas Lau | alfa

Further information:

http://www.esf.org

Fraunhofer FIT joins Facebook's Telecom Infra Project

25.10.2016 | Fraunhofer-Institut für Angewandte Informationstechnik FIT

Stanford researchers create new special-purpose computer that may someday save us billions

21.10.2016 | Stanford University

Ultrafast lasers have introduced new possibilities in engraving ultrafine structures, and scientists are now also investigating how to use them to etch microstructures into thin glass. There are possible applications in analytics (lab on a chip) and especially in electronics and the consumer sector, where great interest has been shown.

This new method was born of a surprising phenomenon: irradiating glass in a particular way with an ultrafast laser has the effect of making the glass up to a...

Terahertz excitation of selected crystal vibrations leads to an effective magnetic field that drives coherent spin motion

Controlling functional properties by light is one of the grand goals in modern condensed matter physics and materials science. A new study now demonstrates how...

Researchers from the Institute for Quantum Computing (IQC) at the University of Waterloo led the development of a new extensible wiring technique capable of controlling superconducting quantum bits, representing a significant step towards to the realization of a scalable quantum computer.

"The quantum socket is a wiring method that uses three-dimensional wires based on spring-loaded pins to address individual qubits," said Jeremy Béjanin, a PhD...

In a paper in Scientific Reports, a research team at Worcester Polytechnic Institute describes a novel light-activated phenomenon that could become the basis for applications as diverse as microscopic robotic grippers and more efficient solar cells.

A research team at Worcester Polytechnic Institute (WPI) has developed a revolutionary, light-activated semiconductor nanocomposite material that can be used...

By forcefully embedding two silicon atoms in a diamond matrix, Sandia researchers have demonstrated for the first time on a single chip all the components needed to create a quantum bridge to link quantum computers together.

"People have already built small quantum computers," says Sandia researcher Ryan Camacho. "Maybe the first useful one won't be a single giant quantum computer...

Anzeige

Anzeige

Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

Agricultural Trade Developments and Potentials in Central Asia and the South Caucasus

14.10.2016 | Event News

World Health Summit – Day Three: A Call to Action

12.10.2016 | Event News

Latest News

Ice shelf vibrations cause unusual waves in Antarctic atmosphere

25.10.2016 | Earth Sciences

Fluorescent holography: Upending the world of biological imaging

25.10.2016 | Power and Electrical Engineering

Etching Microstructures with Lasers

25.10.2016 | Process Engineering

VideoLinks

NASA | A Year in the Life of Earth's CO2

NASA Computer Model Provides a New Portrait of Carbon Dioxide

Black Holes Come to the Big Screen

The new movie "Interstellar" explores a longstanding fascination, but UA astrophysicists are using cutting-edge technology to go one better.

NASA's Swift Mission Observes Mega Flares from a Mini Star

NASA's Swift satellite detected the strongest, hottest, and longest-lasting sequence of stellar flares ever seen from a nearby red dwarf star.

NASA | Global Hawks Soar into Storms

NASA's airborne Hurricane and Severe Storm Sentinel or HS3 mission, will revisit the Atlantic Ocean for the third year in a row.

Baffin Island - Disappearing ice caps

Giff Miller, geologist and paleoclima-tologist, is walking the margins of melting glaciers on Baffin Island, Nunavut, Canada.

The Infrasound Network and how it works

The CTBTO uses infrasound stations to monitor the Earth mainly for atmospheric explosions.

B2B-VideoLinks

Drying and curing of paints on glass and ceramics

Bright and brilliant paints on glass and ceramics require safe solutions for drying and curing.

JULABO World of Temperature

Explore the World of Temperature with JULABO - Superior Temperature Technology for a Better Life.

Acoustic Wave Separation: How It Works

In this animated video, see how Acoustic Wave Separation technology works in full detail.

Infrared Heat for printed electronics

Drying and sintering of printed electronics by specialty light sources from Heraeus

All about Data Logger, how to use

Wolfgang Rudolph explains: all information worth knowing about the data logger and the practical test by means of a drone