Prospect of using Grover's search in the noisy-intermediate-scale
  quantum-computer era
In order to understand the bounds of utilization of the Grover's search
algorithm for the large unstructured data in presence of the quantum computer
noise, we undertake a series of simulations by inflicting various types of
noise, modelled by the IBM QISKit. We apply three forms of Grover's algorithms:
(1) the standard one, with 4-10 qubits, (2) recently published modified
Grover's algorithm, set to reduce the circuit depth, and (3) the algorithms in
(1) and (2) with multi-control Toffoli's modified by addition of an ancilla
qubit. Based on these simulations, we find the upper bound of noise for these
cases, establish its dependence on the quantum depth of the circuit and provide
comparison among them. By extrapolation of the fitted thresholds, we predict
what would be the typical gate error bounds when apply the Grover's algorithms
for the search of a data in a data set as large as thirty two thousands.
Yulun Wang Predrag S. Krstic