# Theory of measurement-based quantum computing

This naturally leads to unitary circuit models, which are models of computation in which unitary operators are expressed as a product of "elementary" unitary transformations.

However, unitary transformations can also be effected as a composition of operations which are not all unitary themselves: the one-way measurement model is one such model of quantum computation.

In this thesis, we examine the relationship between representations of unitary operators and decompositions of those operators in the one-way measurement model.

In particular, we consider different circumstances under which a procedure in the one-way measurement model can be described as simulating a unitary circuit, by considering the combinatorial structures which are common to unitary circuits and two simple constructions of one-way based procedures.

These structures lead to a characterization of the one-way measurement patterns which arise from these constructions, which can then be related to efficiently testable properties of graphs.

We also consider how these characterizations provide automatic techniques for obtaining complete measurement-based decompositions, from unitary transformations which are specified by operator expressions bearing a formal resemblance to path integrals.

These techniques are presented as a possible means to devise new algorithms in the one-way measurement model, independently of algorithms in the unitary circuit model.

Advisor:

School:University of Waterloo

School Location:Canada - Ontario

Source Type:Master's Thesis

Keywords:quantum computing one way measurement model stabilizer formalism postselection combinatorics and optimization

ISBN:

Date of Publication:01/01/2008