Programmable quantum simulations on a trapped-ions quantum computer with a global drive

Abstract:

NISQ devices, employed for quantum simulation tasks, are inherently error-prone. To overcome this challenge, it becomes imperative to employ methods capable of entangling multiple qubit pairs simultaneously in a single, programmable step. This approach facilitates the execution of simulations using shallow circuits, thereby minimizing error propagation. In this work, we focus on the simulation of Ising and XY models with a transverse field on a small-scale trapped ions quantum computer. Our approach centers on an entanglement scheme executed by a homogeneous global laser drive, which implements non-trivial qubit couplings by engineering the drive spectrum and utilizing all the motional modes of the ion-crystal. This method makes it possible to simulate systems with a wide range of geometries that are unconstrained by the physical one-dimensionality of the ion-crystal, such as nearest neighbor coupling with periodic or antiperiodic boundary conditions. Specifically, we simulate a 4-spin Ising quantum ring characterized by nearest-neighbor interactions and antiperiodic boundary conditions. We observe the dynamics under this Hamiltonian, as well as with the addition of a transverse field. We benchmark the simulation steps and are able to verify a high-quality of realization of the simulation by using our entanglement scheme.