Cancellation of phonon hopping in trapped ions by modulation of the trap potential

The local modes of trapped ions can be used to construct an analog quantum simulator and a digital quantum computer. However, the control of the phonon hopping remains difficult because it proceeds among all the local modes through the Coulomb coupling. We propose a method to cancel the phonon hopping among a given set of local modes by applying a sequence of phase shift gates implemented through the modulation of the trap potential. We analyze the error scaling in the algorithm to treat three or more modes and show that the error can be suppressed by repeating the pulse sequence. The duration of the phase shift gate in the present method can be as short as a few microseconds, which is an order of magnitude faster than the laser-based method. This short duration of the phase shift gate facilitates the suppression of the gate error. We finally show how the present method can be applied to the implementation of the beam splitter. The present method can also be applied to the simulation of bosonic systems as well as to the continuous variable encoding of quantum computing using trapped ions.