  We investigate the performance of Grover's quantum search algorithm on a
register which is subject to loss of the particles that carry the qubit
information. Under the assumption that the basic steps of the algorithm are
applied correctly on the correspondingly shrinking register, we show that the
algorithm converges to mixed states with 50% overlap with the target state in
the bit positions still present. As an alternative to error correction, we
present a procedure that combines the outcome of different trials of the
algorithm to determine the solution to the full search problem. The procedure
may be relevant for experiments where the algorithm is adapted as the loss of
particles is registered, and for experiments with Rydberg blockade interactions
among neutral atoms, where monitoring of the atom losses is not even necessary.
