Implementation of Grover's search algorithm using entangled `clock state' qubits*

We experimentally demonstrate Grover's search algorithm over a space of N=4 elements with n=2 trapped $^{111}$Cd$^{+ }$ion qubits. One of the four states is marked, and with a single query it is recovered on average with a 60{\%} probability. This exceeds the performance of any possible classical search, which can only succeed with 50{\%} probability following a single query. The algorithm consists of two Molmer-Sorensen entangling gates paired with several single-qubit rotations and near-perfect qubit measurements. The Molmer-Sorensen gate has the unique advantage that it can entangle magnetic field insensitive `clock-state' qubits and hence can be relatively insensitive to an important source of noise in trapped ion quantum gates.