Washington, December 23 : Super-fast computers based on quantum mechanics may have come closer to reality, with mathematicians chasing some of the major mathematical problems.

A discussion on this was held at a conference on the operator theory-which is 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-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 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 the conference, which brought together some of the world''s leading mathematical physicists and quantum mechanics specialists to tackle the key fields relating to spectral theory.

The conference''s co-chair Pavel Kurasov, from the Lund Institute of Technology in Sweden, pointed out that a big challenge lied in extending current operator theory to describe and analyse quantum transport in wires, as will be needed for a new generation of quantum computers.

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 main objective set out at the ESF conference was to extend the theory to non self-adjoint operators, which could 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. 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," said Kurasov.

Kurasov said that a breakthrough was expected 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.

According to Kurasov, this will be crucial to constructing the intermediate components of a quantum computer needed to monitor its own state and provide output. (ANI)