Manipulating Spin Lattice Geometries in Trapped Ion Systems by Shelving

We propose a method for engineering diverse spin lattice geometries in one- and two-dimensional trapped ion systems by shelving selected ions into metastable states outside the qubit space. This shelving technique excludes specific ions from participating in effective spin-spin interactions, enabling precise and efficient control over the remaining ions in the system. We discuss an experiment to demonstrate the modified spin-spin interactions during shelving while ensuring that the residual coupling between shelved ions and the computational ions is negligible. We also characterize sources of error, such as repumping rates out of the shelved states. This approach provides a promising platform for investigating quantum many-body phenomena, including geometric frustration and quantum spin liquids, as well as potential applications in quantum error correction, that are inaccessible to conventional trapped-ion geometries.