Comment on 'Grover Search with Pairs of Trapped Ions'

In this brief comment on `Grover search with pairs of trapped Ions' [Phys. Rev. A 63, 052308, (2001)], we show that Grover's algorithm may be performed exactly using the gate set given provided that small changes are made to the gate sequence. An analytic expression for the probability of success of Grover's algorithm for any unitary operator, U, instead of Hadamard is presented.