Measurement-based quantum computation with cluster states

In this thesis we describe the one-way quantum computer (QCc), a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multi-particle state, the cluster state. We prove universality of the QCc, describe the underlying computational model and demonstrate that the QCc can be operated fault-tolerantly. In Chapter 2 we show that the QCc can be regarded as a simulator of quantum logic networks. In this way, we give the universality proof and establish the link to the network model, the common model of quantum computation. We also indicate that the description of the QCc as a network simulator is not adequate in every respect. In Chapter 3 we derive the computational model underlying the one-way quantum computer, which is very different from the quantum logic network model. The QCc has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of QCc-quantum algorithms. Further, all information that is processed with the QCc are the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The QCc is nevertheless quantum mechanical as it uses a highly entangled cluster state as the central physical resource. In Chapter 4 we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the QCc. Further, we outline the concept of checksums in the context of the QCc which may become an element in future practicable and adequate methods for fault-tolerant QCc-computation.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Ludwig-Maximilians-Universität

Year

2003

Author dc:creator

• Raussendorf, Robert

Repository record source_url

https://edoc.ub.uni-muenchen.de/1367/

OAI identifier oai:identifier

oai:edoc.ub.uni-muenchen.de:1367