Implementation of Grover’s quantum search algorithm with error mitigation at IBM Q computers

We have constructed the quantum circuits for implementation of the N=4 qubits Grover algorithm at IBM Q quantum computers. The circuit efficiency was achieved by explicit use of the qubits topology, specific for the used machines. For comparison, we implemented the same approach for the 2 and 3 Grover’s algorithms. While the classical simulation led to a high probability of finding the searched object, the running at the IBM Q quantum machine resulted to the search probability below the recognition. This was a consequence of the decoherence errors, which has grown with the number of the circuit elements. We have experimented with zero-noise extrapolation method as well as error correction codes to mitigate and correct the errors of the circuit, leading to improvements in the implemented search.