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Randomized and Approximate Computation

Objective

We aim to pursue studies in the areas of randomised, approximate, and quantum computation. Our investigations will cover novel and enhanced methods for the design and analysis of efficient randomised and quantum algorithms for problems of measurement and communication theory, which are totally intractable by existing methods.
We aim to pursue studies in the areas of randomised, approximate, and quantum computation. Our investigations will cover novel and enhanced methods for the design and analysis of efficient randomised and quantum algorithms for problems of measurement and communication theory, which are totally intractable by existing methods.

OBJECTIVES
1. To examine the foundations of randomised, approximate and quantum computation.
2. To obtain new improved methods for the design and analysis of efficient randomised and quantum algorithms for problems particularly in the areas of optimisation, measurement and communications.
3. To understand what are the basic characteristics of a problem, which make it impossible to even obtain good approximate answers.

DESCRIPTION OF WORK
We intend to carry out the following programme:
1. To study at the fundamental level the power of randomised versus quantum computation; particularly with reference to approximate computation. A major focus of our work will be the Hidden Subgroup problem, which seems to be a key separator between random/quantum computation. The other main problem will be to relate the quantum class BQP with the classical (Turing) hierarchy.
2. To obtain improved faster or better approximation algorithms for key benchwork problems of optimisation and measurement. Members of the Bonn and Paris groups have already developed fast (polynomial time) good approximation schemes for a range of problems, which have certain "nice features". It is hoped to extend these ideas to other technical problems, which do not have these properties.
3. To apply the techniques developed to a selection of practical problems in biological science and communications. In order to achieve this we hope to combine the expertise developed in constructing and analysing protocols by the Edinburgh and Bonn groups with the practical know-how developed in Oxford and Lund to obtain practical algorithms, which are based on theory rather than the existing ad hoc methods.

Funding Scheme

THN - Thematic network contracts

Coordinator

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
University Offices, Wellington Square
OX1 2JD Oxford
United Kingdom

Participants (6)

LUNDS UNIVERSITET
Sweden
Address
Paradisgatan 5C
221 00 Lund
RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAET BONN
Germany
Address
Regina-pacis-weg 3
53113 Bonn
THE UNIVERSITY OF EDINBURGH
United Kingdom
Address
Old College, South Bridge
EH8 9YL Edinburgh
THE WEIZMANN INSTITUTE OF SCIENCE
Israel
Address
Herzel Street 2
76100 Rehovot
UNIVERSITE DE PARIS XI PARIS-SUD
France
Address
15, Rue Georges Clemenceau
91405 Orsay Cedex
UNIVERSITY OF LEEDS
United Kingdom
Address
Woodhouse Lane
LS2 9JT Leeds