MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES
Abstract
In this thesis, we describe the one-way quantum computer 
, a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the 
, describe the underlying computational model and demonstrate that the 
can be operated fault-tolerantly.
In Sec. 2, we show that the 
can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the 
as a network simulator is not adequate in every respect.
In Sec. 3, we derive the computational model underlying the 
, which is very different from the quantum logic network model. The 
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 
quantum algorithms. Further, all information that is processed with the 
is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The 
is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource.
In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the 
. Further, we outline the concept of checksums in the context of the 
, which may become an element in future practical and adequate methods for fault-tolerant 
computation.
Dissertation for a Ph.D.
