Experimental Realization of Bruschweiler's exponentially fast search algorithm in a 3-qubit homo-nuclear system

Searching marked items from an unsorted database is a very important problem and has many practical applications. In a classical computer, this is done by exhaustive search and requires O(N) steps. In a quantum computer, Grover's quantum search algorithm achieves quadratic speedup over classical algorithms. The Bruschweiler algorithm combines the ideas of DNA computing with that of quantum computing. It achieves an exponential speedup. In this paper, we report the experimental realization of the algorithm in a 3 qubit NMR ensemble system. The pulse sequences are given for the algorithms. In particular, we have modified the measurement part of Bruschweiler's original paper. Instead of measuring quantitatively the spin projection of the aucilla bit, we measure the shape of the aucilla bit. By just looking at the downwardness or upwardness of the corresponding peaks in the aucilla bit spectrum, we can read out the bit value of the marked state. The geometric nature of this read-out makes the algorithm robust against errors