In-Situ Rewiring of Two-Dimensional Ion Lattice Interactions Using Metastable State Shelving

When driving quantum dynamics in trapped-ion systems with global entangling beams, the resulting spin–spin interaction graphs are typically governed by the physical ion-crystal geometry. This constraint limits access to interaction graphs with arbitrary connectivity without incurring significant experimental overhead. Here we propose and implement a direct approach to reconfigure the spin-spin interaction geometry. Our method shelves unwanted ions to a long-lived metastable state outside of the qubit subspace, effectively removing them from the quantum dynamics. Using a triangular lattice of three ¹⁷¹Yb⁺ ions interacting under a global Ising-type Hamiltonian, we experimentally demonstrate that shelved qubits in the long-lived ²F_7/2 state no longer participate in the spin evolution. We further characterize the lifetime of shelved state during a quantum simulation, which we find to scale inversely with the square of the applied laser intensity. Our method provides a flexible route to realize a wide range of spin-interaction geometries, enabling studies of diverse many-body phenomena in quantum spin systems with nontrivial geometric dependence.