Performance of Uncoded Implementation of Grover's Algorithm on Today's Quantum Processors

This work tests the performance of Grover's search circuits on some IBM superconducting quantum devices in case of the size of search space $N=2^4$ and $N=2^5$. Ideally, we expect to get an outcome probability distribution that is clearly peaked at the goal (marked) state. However, the quantum circuit executed on real devices is vulnerable to noise which leads to fluctuations in the results. The contributions of the paper are therefore the following: a) it presents two new Grover's search circuits for $N=16$ which were not yet reported in the state of the art; b) it shows performance difference between simulation results and results obtained on real devices; c) it shows the need of adding error-correction on the circuit for $N\ge 2^5$.