Objective Goals of this project are the construction of new quantum algorithms as well as the investigation of the theoretical realisability of their implementations in devices based on realistic physical structures. The study of microscopic complex regularities of the physical interactions and the symmetries mirroring the system's invariance with respect to specific state space transformations is planned which might lead to outstanding fast algorithms for hard problems in combinatorics. Parallel to this, we intend to provide a compiler capable to perform the transition from an algebraic specified signal transformation to a sequence of elementary quantum gates.Goals of this project are the construction of new quantum algorithms as well as the investigation of the theoretical realisability of their implementations in devices based on realistic physical structures. The study of microscopic complex regularities of the physical interactions and the symmetries mirroring the system's invariance with respect to specific state space transformations is planned which might lead to outstanding fast algorithms for hard problems in combinatorics. Parallel to this, we intend to provide a compiler capable to perform the transition from an algebraic specified signal transformation to a sequence of elementary quantum gates.OBJECTIVESThe key idea of this proposal is to use quantum superposition, entanglement and controlled quantum mechanical evolution to speed up computation with respect to the classical case. It is promising to apply non-abelian Fourier transforms and other unitary signal transforms to graph theoretical and combinatorial problems (such as the evaluation of the permanent of large matrices), which have turned out to be notoriously hard for any classical computer. Since a systematic approach to the study and development of quantum algorithms is lacking we intend to fill in this gap by providing tools for the development of quantum algorithms. These are designed to help engineering quantum state transformations on a very fine grain level enabling the programmer to find efficient factorisations of desired transformations automatically. Attention will be devoted in particular to approaches based on non-abelian harmonic analysis.DESCRIPTION OF WORKA thorough understanding of the principles on which the known quantum algorithms are based on is a precondition for the design of new quantum algorithms. The basic research part of the work will yield a candidate list of combinatorial problems, which can be tackled on a quantum computer. A language to express quantum programs will be written on a high level of abstraction using computer algebra systems. There are options to extend this programming language by assembler-like operations depending on the physical hardware chosen. One of our objectives is to provide a tool to obtain ultra-fast quantum circuits for generalised Fourier transforms and other signal transforms in an automatic fashion.The appearing symmetries are captured by group and representation theoretical methods, which can best be handled by computer algebra systems. It is intended to model operations using algebraic data types representing them as sparse as possible. As for algorithms, attention will be devoted in particular to approaches based on non-abelian harmonic analysis of graph theoretical and combinatorial problems, such as the evaluation of the permanent of large matrices. Graphs with regular auto morphism groups appear naturally in meso- and carbon physics as symmetry groups of the systems. Therefore also crystallographic groups and their spectral properties will be analysed by the developed means. Fields of science natural sciencescomputer and information sciencessoftwareagricultural sciencesagriculture, forestry, and fisheriesagriculturegrains and oilseedsnatural sciencesmathematicspure mathematicsalgebraengineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringcomputer hardwarequantum computersnatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Programme(s) FP5-IST - Programme for research, technological development and demonstration on a "User-friendly information society, 1998-2002" Topic(s) 1.1.2.-6.2.1 - FET P1: Quantum information processing and communications Call for proposal Data not available Funding Scheme CSC - Cost-sharing contracts Coordinator UNIVERSITAET KARLSRUHE (TH) EU contribution No data Address KAISERSTRASSE 12 76131 KARLSRUHE Germany See on map Total cost No data Participants (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all FONDAZIONE ISTITUTO PER L'INTERSCAMBIO SCIENTIFICO Italy EU contribution No data Address VIALE SETTIMIO SEVERO 65 10133 TORINO See on map Total cost No data
