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Numerical and analytical solutions for problems relevant for quantum computers; Numerische und analytische Loesungen fuer Quanteninformatisch-relevante Probleme

Abstract

Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria  More>>
Authors:
Publication Date:
Jun 05, 2008
Product Type:
Thesis/Dissertation
Report Number:
INIS-DE-0726
Resource Relation:
Other Information: TH: Diss. (Dr.rer.nat.)
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM COMPUTERS; ALGORITHMS; COMPUTERIZED SIMULATION; QUBITS; COMPUTER CODES; ANALYTICAL SOLUTION; DYNAMICS; OPTIMIZATION; NUMERICAL SOLUTION; PARALLEL PROCESSING; COMPUTER CALCULATIONS; QUANTUM MECHANICS; ISING MODEL; RECURSION RELATIONS; LOGIC CIRCUITS; SUPERCONDUCTING DEVICES
OSTI ID:
21209270
Research Organizations:
Technische Univ. Muenchen (Germany). Fakultaet fuer Chemie
Country of Origin:
Germany
Language:
German
Other Identifying Numbers:
TRN: DE09F8840
Availability:
Commercial reproduction prohibited; INIS; OSTI as DE21209270
Submitting Site:
DEN
Size:
235 pages
Announcement Date:
Sep 02, 2009

Citation Formats

Spoerl, Andreas. Numerical and analytical solutions for problems relevant for quantum computers; Numerische und analytische Loesungen fuer Quanteninformatisch-relevante Probleme. Germany: N. p., 2008. Web.
Spoerl, Andreas. Numerical and analytical solutions for problems relevant for quantum computers; Numerische und analytische Loesungen fuer Quanteninformatisch-relevante Probleme. Germany.
Spoerl, Andreas. 2008. "Numerical and analytical solutions for problems relevant for quantum computers; Numerische und analytische Loesungen fuer Quanteninformatisch-relevante Probleme." Germany.
@misc{etde_21209270,
title = {Numerical and analytical solutions for problems relevant for quantum computers; Numerische und analytische Loesungen fuer Quanteninformatisch-relevante Probleme}
author = {Spoerl, Andreas}
abstractNote = {Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)}
place = {Germany}
year = {2008}
month = {Jun}
}