End-to-end fault tolerance

In this review we survey both standard fault tolerance theory and Kitaev’s model for quantum computation, and demonstrate how they can be combined to yield quantitative results that reveal the interplay between the two. This analysis establishes a methodology allowing one to quantitatively determine design parameters for quantum computers, the values of which ensure that an overall computation yields a correct final result with some prescribed probability of success, as opposed to merely ensuring that the desired final quantum state is obtained. As an example, we explicitly calculate the number of levels of error correction concatenation needed to achieve a correct final result with some prescribed success probability. This methodology allows one to determine parameters required in order to achieve the correct final result for the quantum computation, as opposed to merely ensuring that the desired final quantum state is produced.