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

The controllable quantum harmonic oscillator can be used for continuous variable (CV) encoding of quantum information processing and quantum simulation of bosonic systems. In the CV encoding implemented with local phonons of trapped ions, the entanglement can be generated by the phonon hopping. 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 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 shorter than the laser-based method. This short duration of the phase shift gate facilitates the suppression of the gate error. The present method can be applied to the simulation of bosonic systems as well as to the control of entanglement among phonons.