BQP is the set of problems solvable in polynomial time for a given error tolerance, and it is suspected to be larger than P (and BPP, which is probably equal to P). However, inability for the gates to act perfectly, etc would require error-checking overhead. What is the overhead cost in the algorithm? In particular, does either the time or the number of q-bits overhead grow more than polynomially in the problem size (if it did then BQP would be altered)?
The threshold theorem says that if the error rate is below the threshold, a quantum algorithm with T locations (breadth times depth) can be made fault-tolerant with a blow-up (in both number of qubits and circuit size) by a factor which is a polynomial in the log of T. This is not enough to change BQP.