Continuous Variable Quantum Computing with Trapped Ions*

The standard approach to quantum computation uses qubits, which are well-described as a two-level system. An alternative approach is continuous-variable quantum computation (CVQC), which uses observables with a continuum of values such as the position and momentum of a particle. In this work, we use the motional modes of trapped ions as our continuous variable. CVQC has been explored in other physical platforms, such as superconducting qubits and photonic systems, but there remain open questions about the feasibility and implementation for trapped ions. We report progress simulating the motional coherence of CVQC operations implemented with electric fields. Further, we explore using composite sideband laser pulses, which provide a Jaynes-Cummings-like interaction, to read out information stored in the ion's bosonic modes. We present a computational framework for simulating CVQC operations in a realistic trapped-ion system with realistic noise sources, as well as preliminary experimental results implementing these operations on $^{88}Sr^+$ ions.