## The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. | |

Dissertation for the degree of Doctor of Science in Technology to be
presented with due permission of the Department of Engineering Physics
and Mathematics for public examination and debate in Auditorium F1
at Helsinki University of Technology (Espoo, Finland)
on the 26^{th} of November, 2004, at 12 noon.

Overview in PDF format (ISBN 951-38-6421-9) [828 KB]

VTT Publications 552, ISSN 1455-0849

Dissertation is also available in print (ISBN 951-38-6420-0)

Copyright © 2004 VTT Technical Research Centre of Finland

VTT Publications 552, ISSN 1235-0621

VTT-PUBS-552

TKK-DISS-1919

Ever since Peter Shor's ground-breaking discovery in 1994 of an algorithm capable of factoring large integers on a quantum-mechanical computer exponentially faster than using any known classical method, research on quantum computing has boomed. Quantum information – a unique mixture of computer science, physics and mathematics – has developed into a new branch of information theory. On the experimental side, physicists from many different disciplines including atomic, solid-state and low-temperature physics, as well as optics, are striving today towards a practical quantum computer. All the candidate quantum bit (qubit) technologies have one thing in common: They rely on the controlled time-evolution of a closed quantum system, a seemingly paradoxical task.

In this Thesis the temporal control of quantum systems is studied. The topics included can be divided into two according to the type of temporal evolution; geometrical or dynamical. Geometrical realization-independent methods for quantum computing are studied first. Then the study is extended into dynamical quantum computing and the so-called Josephson charge-qubit register is considered as a test bench. Finally, a spin-off application of the geometrical evolution of a Josephson junction system is studied, i.e. Cooper pair pumping. A novel Cooper pair pump, the Cooper pair "sluice", is introduced.

The work on quantum computing reported in this Thesis is theoretical while the Cooper pair "sluice" is studied both theoretically and experimentally. Numerical simulations, both sequential and parallel, are used extensively throughout the Thesis. The experiments were carried out under cryogenic mK conditions and the sample fabrication was done using e-beam nanolithography.

Because the execution time of a quantum algorithm is always limited by the inevitable process of decoherence, it is important to utilize any measure available for accelerating quantum computations. It is found that practical quantum algorithms could greatly benefit from classical computer-aided optimization. Moreover, it is found that even a modest demonstrator of a full quantum algorithm using Josephson charge qubits is just barely realizable within present-day coherence times. However, the experimental part of this Thesis shows clear evidence of the functioning of the "sluice". While the worldwide effort of improving the coherence properties of qubits is underway, the "sluice" could well find practical use, e.g., in metrology in the foreseeable future.

This thesis consists of an overview and of the following 7 publications:

- A. O. Niskanen, M. Nakahara, and M. M. Salomaa, Realization of arbitrary gates in holonomic quantum computation, Physical Review A 67, 012319 (2003). © 2003 American Physical Society. By permission.
- A. O. Niskanen, M. Nakahara, and M. M. Salomaa, Optimal holonomic quantum gates, Quantum Information and Computation 2, 560-577 (2002). © 2002 Rinton Press. By permission.
- A. O. Niskanen, J. J. Vartiainen, and M. M. Salomaa, Optimal multiqubit operations for Josephson charge qubits, Physical Review Letters 90, 197901 (2003). © 2003 American Physical Society. By permission.
- J. J. Vartiainen, A. O. Niskanen, M. Nakahara, and M. M. Salomaa, Acceleration of quantum algorithms using three-qubit gates, International Journal of Quantum Information 2, 1-10 (2004). © 2004 World Scientific Publishing Company. By permission.
- J. J. Vartiainen, A. O. Niskanen, M. Nakahara, and M. M. Salomaa, Implementing Shor's algorithm on Josephson charge qubits, Physical Review A 70, 012319 (2004). © 2004 American Physical Society. By permission.
- A. O. Niskanen, J. P. Pekola, and H. Seppä, Fast and accurate single-island charge pump: Implementation of a Cooper pair pump, Physical Review Letters 91, 177003 (2003). © 2003 American Physical Society. By permission.
- A. O. Niskanen, J. M. Kivioja, H. Seppä, and J. P. Pekola, Evidence of Cooper pair pumping with combined flux and voltage control, submitted, 4 pages (2004); cond-mat/0410758. © 2004 by authors.

**Keywords:**
quantum systems, quantum mechanics, quantum computing, quantum algorithms,
Cooper pair pumping

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© 2004 Helsinki University of Technology

Last update 2011-05-26