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Abstract: In this paper we extend both standard fault tolerance theory and Kitaev-smodel for quantum computation, combining them so as to yield quantitativeresults that reveal the interplay between the two. Our analysis establishes amethodology that allows us to quantitatively determine design parameters for aquantum computer, the values of which ensure that an overall computation ofinterest yields a correct *final result* with some prescribed probability ofsuccess, as opposed to merely ensuring that the desired *final quantum state*is obtained. As a specific example of the practical application of ourapproach, we explicitly calculate the number of levels of error correctionconcatenation needed to achieve a correct final result for the overallcomputation with some prescribed success probability. Since our methodologyallows one to determine parameters required in order to achieve the correctfinal result for the overall quantum computation, as opposed to merely ensuringthat the desired final quantum state is produced, our method enables thedetermination of complete quantum computational resource requirementsassociated to the actual solution of practical problems.

Autor: Gerald Gilbert, Michael Hamrick, Yaakov S. Weinstein


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