An upper bound on quantum fault tolerant thresholds

In this paper we calculate upper bounds on fault tolerance, without restrictions on the overhead involved. Optimally adaptive recovery operators are used, and the Shannon entropy is used to estimate the thresholds. By allowing for unrealistically high levels of overhead, we find a quantum fault tolerant threshold of 6.88% for the depolarizing noise used by Knill, which compares well to "above 3%" evidenced by Knill. We conjecture that the optimal threshold is 6.90%, based upon the hashing rate. We also perform threshold calculations for types of noise other than that discussed by Knill.