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. CVQC has been explored in other physical platforms, such as superconducting and photonic systems, but there remain open questions about the feasibility and implementation for trapped-ions. In this work, we use the motional modes of trapped ions as our continuous variable and develop protocols for a hybrid boson-qubit system by coupling the bosonic mode to the ion’s electronic state. We report progress toward implementing CVQC operations with electric fields and bi-chromatic laser pulses. We explore using bi-chromatic sideband laser pulses, which provide a spin-dependent displacement on the motional modes, to store and manipulate information 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 and preliminary experimental results implementing these operations on ⁸⁸Sr⁺ ions.