  We present a framework for efficiently solving Approximate Traveling Salesman
Problem (Approximate TSP) for Quantum Computing Models. Existing
representations of TSP introduce extra states which do not correspond to any
permutation. We present an efficient and intuitive encoding for TSP in quantum
computing paradigm. Using this representation and assuming a Gaussian
distribution on tour-lengths, we give an algorithm to solve Approximate TSP
(Euclidean) within BQP resource bounds. Generalizing this strategy for any
distribution, we present an oracle based Quantum Algorithm to solve Approximate
TSP. We present a realization of the oracle in the quantum counterpart of PP.
