Quantum Information Processing with Spin and Motional States of Trapped Ions

Trapped atomic ions are one of the leading candidates for scalable quantum computation and simulation. As the system scales up, both high-performance hardware and robust quantum control are essential for building a reliable large-scale quantum computer: high-performance hardware suppresses the external noise level and robust quantum control guarantees high-fidelity quantum gates under external noise. Moreover, for analog simulations and computations, using bosonic states for quantum information processing can be beneficial but characterizing complex bosonic states is challenging. In this thesis we report our progress on both hardware and software control of trapped ion systems. We design and construct a compact cryogenic trapped-ion platform that is easy to integrate and manufacture, and characterize the system behavior which shows several advantages over conventional trapped-ion systems in UHV chambers. We develop a robust modulated two-qubit gate scheme using pulse design to improve the robustness of two-qubit gates to mode frequency drift and verify its robustness on the compact cryogenic platform. We also report our work on characterizing complex motional states in a long ion chain by using Jaynes-Cummings-type interactions between bosonic states and two-level systems. We measured the Fock state population of various complex motional states and the density matrix of a motional Bell state. These works offer us new insights into building a high-performance, large-scale quantum computing platform as well as characterizing complex quantum states.