  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.
