  We describe an implementation of Grover's fixed-point quantum search
algorithm on a nuclear magnetic resonance (NMR) quantum computer, searching for
either one or two matching items in an unsorted database of four items. In this
new algorithm the target state (an equally weighted superposition of the
matching states) is a fixed point of the recursive search operator, and so the
algorithm always moves towards the desired state. The effects of systematic
errors in the implementation are briefly explored.
