Engineering Spin-Motion Interactions in Trapped Ions for Quantum Simulation and Computation

Abstract

Trapped ions are perhaps the most mature platform in both quantum computing and quantum simulation. The interaction between the qubit states and the motion of an ion lies at the heart of this platform. In most contexts, this interaction is generated using the gradient of traveling waves that drive either quadrupole or Raman transitions. Until recently, this was used solely for the purpose of entangling two spins together. Holding information in the motional states was avoided because of incoherent interactions with the environment that rendered these states too noisy. As engineering of ion traps has progressed through the years, these trapping potentials and motional modes have become significantly more stable, opening the door to use these modes for more than just spin-spin entanglement. Of particular interest is the notion of using them in analog and hybrid simulations to model spin-boson interactions. In this thesis, we discuss the implementation and progress of a trapped ion quantum computer in a cryogenic setup that is capable of controlling up to 32 ions in parallel. We also discuss a novel technique for using the spin-motion interactions to generate a Hamiltonian of interest in quantum chemistry. In that same work, we extend a known protocol to measure the information held in the motional states of an ion to two modes, allowing us to reconstruct the ions wavefunction. We also demonstrate a novel technique for generating spin-motion entanglement via the gradient of a laser using higher-order Hermite-Gaussian optical modes. We use these modes to drive a Raman transition that couples to the motion without parasitic carrier coupling and with less sensitivity to heating. We describe how spin-spin entangling gates as well as analog and hybrid simulations can be performed using this technique.