Quantum accuracy threshold for distance-5 codes

A quantum computer can only solve classically intractable problems like factoring large integers if it can perform quantum computations scalably. The minimum accuracy required among the components of a quantum computer to perform scalable computation is called the quantum accuracy threshold, epsilon 0. We explore the accuracy threshold for Calderbank-Shor-Steane codes of distance 5. Our accuracy thresholds are based on the threshold theorem proven by Aliferis et al. [3]. Their threshold theorem is applicable to concatenated codes and can be used to derive a rigorous lower bound on the threshold. In this thesis we consider degenerate codes with parameters [[17,1,5]] and [[19,1,5]], and a non-degenerate [[21,1,5]] code. For each code we design a set of logical operations sufficient to perform universal computation. We estimate the thresholds using simulation tools for an independent stochastic error model. Our simulations incorporate randomized sampling techniques to estimate the number of ways our largest logical operation can fail. A lower bound of epsilon0 ≥ 3.624 x 10-5 is derived for the [[17,1,5]] code