DS-2004-01:
Röhrig, Hein Philipp
(2004)
*Quantum Query Complexity and Distributed Computing.*
Doctoral thesis, University of Amsterdam.

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## Abstract

Quantum Query Complexity and Distributed Computing

Hein Roehrig

In complexity theory, the strengths and limitations of computers are

investigated on abstract models of computation. The choice of these models is

governed by three considerations: (1) how close is the model to existing

computers or computers that could be built in principle? (2) how well does it

lend itself to proving interesting properties of computers? (3) how elegant is

the model mathematically?

Quantum computation appeals to all three criteria. In functional analysis,

quantum mechanics has a beautiful mathematical underpinning, which benefits

quantum computing through new applications of linear algebra and matrix

analysis. Nowadays it is a widely-held belief that the physical theory of

quantum mechanics describes reality accurately at very small scales of length,

time, and energy. Where classical probabilistic Turing machines may be seen as

capturing the power of computers operating according to finite- precision

classical physics, the computational model of quantum circuits aims at modeling

what realistic computers in a quantum mechanical world can do. Query

complexity, a variant of time complexity, has a close analogue for quantum

computers; as in the classical case, our current mathematical tools are more

amenable to this restricted complexity measure than to general time complexity.

Sometimes, the implications of quantum query complexity shed new light even on

classical complexity theory.

This thesis investigates the properties and applications of quantum query

complexity and the related quantum communication complexity. It suggests new

cryptographic protocols and new experiments for probing the predictions of

quantum mechanics. Quantum states are very sensitive; this thesis examines ways

to deal with imperfections and errors in a number of different situations.

Item Type: | Thesis (Doctoral) |
---|---|

Report Nr: | DS-2004-01 |

Series Name: | ILLC Dissertation (DS) Series |

Year: | 2004 |

Subjects: | Computation |

Depositing User: | Dr Marco Vervoort |

Date Deposited: | 14 Jun 2022 15:16 |

Last Modified: | 14 Jun 2022 15:16 |

URI: | https://eprints.illc.uva.nl/id/eprint/2040 |

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