  We investigate the problem of quantum searching on a noisy quantum computer.
Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve
the task for various different noise strengths, which are possibly unknown
beforehand. We prove lower bounds on the runtime of such algorithms and thereby
find that the quadratic speedup is necessarily lost (in our noise models).
However, for low but constant noise levels the algorithms we provide (based on
Grover's algorithm) still outperform the best noiseless classical search
algorithm.
