Towards Efficiently Solving Quantum Traveling Salesman Problem

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.