### Efficient unstructured search implementation on current ion-trap quantum processors

#### Vladyslav Hlembotskyi, Rafał Burczyński, Witold Jarnicki, Adam Szady, Jan Tułowiecki

So far, only the results on 3 qubit spaces (both on superconducting and ion-trap realisations of
quantum processors) have beaten the classical unstructured search in the expected number of oracle
calls using optimal protocols in both settings. We present experimental results on running unstructured
search in spaces defined by 4, 5 and 6 qubits on ion-trapped quantum processor. Our best circuits
obtained respectively 66\%, 26\% and 6\% average probability of measuring the marked element. In the
case of 4 and 5 qubit spaces we obtained fewer expected number of oracle calls required to find a
marked element than any classical approach. Viability of the theoretical result by Grover at these
qubit counts is, to authors' knowledge demonstrated experimentally for the first time. Also at 6
qubits, a circuit using a single oracle call returned a measured probability of success exceeding any
possible classical approach. These results were achieved using a variety of unstructured search
algorithms in conjunction with recent developments in reducing the number of entangling gates. The
latter are currently considered to be a dominating source of errors in quantum computations. Some of
these improvements have been made possible by using mid-circuit measurements. To our knowledge the
latter feature is currently available only on the H0 quantum processor we run on.

Publication can be found
here