Reliable Final Computational Results from Faulty Quantum Computation

In this paper we extend both standard fault tolerance theory and Kitaev’s model for quantum computation, combining them so as to yield quantitative results that reveal the interplay between the two. Our analysis establishes a methodology that allows us to quantitatively determine design parameters for a quantum computer, the values of which ensure that an overall computation of interest 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 a specific example of the practical application of our approach, we explicitly calculate the number of levels of error correction concatenation needed to achieve a correct final result for the overall computation with some prescribed success probability. Since our methodology allows one to determine parameters required in order to achieve the correct final result for the overall quantum computation, as opposed to merely ensuring that the desired final quantum state is produced, our method enables the determination of complete quantum computational resource requirements associated to the actual solution of practical problems.