Grover’s Search with Faults on Some Marked Elements
Dmitry Kravchenko, Nikolajs Nahimovs, Alexander Rivosh · International Journal of Foundations of Computer Science · 2018
Grover’s algorithm is a quantum query algorithm solving the unstructured search problem of size [Formula: see text] using [Formula: see text] queries. It provides a significant speed-up over any classical algorithm [3]. The running time of the algorithm, however, is very sensitive to errors in queries. Multiple authors have analysed the algorithm using different models of query errors and showed the loss of quantum speed-up [2, 6]. We study the behavior of Grover’s algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of marked elements in [Formula: see text] queries. We also analyze the limiting behavior of the algorithm for a large number of steps and show the existence and the structure of a limiting state [Formula: see text].