  Motivated by the result that an `approximate' evaluation of the Jones
polynomial of a braid at a $5^{th}$ root of unity can be used to simulate the
quantum part of any algorithm in the quantum complexity class BQP, and results
relating BQP to the counting class GapP, we introduce a form of additive
approximation which can be used to simulate a function in BQP. We show that all
functions in the classes #P and GapP have such an approximation scheme under
certain natural normalisations. However we are unable to determine whether the
particular functions we are motivated by, such as the above evaluation of the
Jones polynomial, can be approximated in this way. We close with some open
problems motivated by this work.
