An on-demand beam splitter for trapped-ion quantum computers

When the distance between ions are far enough so that the coupling strength between individual ion's motion is much smaller than the energy of the ion's secular motion, the local mode picture becomes relevant. The local mode of ions has been applied to bosonic quantum error correction codes and quantum simulation of bosonic systems. However, control of entanglement among local modes remains difficult because entaglement among resonant local modes is governed by the Coulomb interaction, which is not switchable.

We propose a method of a beam splitter for trapped-ion quantum computers and analog quantum simulator, where the secular frequency of each mode is dynamically controllable. The neighboring modes are far detuned except when the beam splitter needs to be applied to them. The analytical formula of the proposed method is derived using the Lewis-Riesenfeld invariant theory and its validity is numerically confirmed by simulating the SWAP gate between two Gottesman-Kitaev-Preskill states.