  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.
