Experimental realization of an order-finding algorithm with an NMR quantum computer

Abstract

This paper reports the experimental implementation of a quantum algorithm for finding the order of permutation; its structure is the same as for Shor's factoring algorithm and it scales exponentially faster than any classical algorithm and it scales exponentially faster than any classical algorithm for the problem. The realization of this algorithm was made possible by the synthesis of an unusual molecule with five pairwise coupled, easily addressable 19F spins, and by the introduction of two new techniques: an efficient and effective temporal labeling scheme for initial state preparation, and a method for precise simultaneous rotations of multiple spins at nearby frequencies.