Motional state engineering for continuous-variable quantum computation

Abstract

The standard approach to quantum computation uses qubits, which are well-described as a two-level system. An alternative approach to quantum computation is continuous-variable quantum computation (CVQC), which uses physical observables, such as the strength of an electromagnetic field or the position of a particle in space, whose numerical values belong to continuous intervals. Trapped ions are well-developed for quantum computation, and they possess both qubit and continuous degrees of freedom that can be precisely controlled, making them a good candidate for a realization of CVQC. Although there exist software frameworks capable of simulating CVQC experiments, these frameworks do not incorporate realistic noise sources and cannot be tailored to a specific trapped-ion setup. In this work, we develop a computational framework for simulating CVQC operations using trapped ions in a realistic system with realistic noise sources. We do so first with ideal Hamiltonians and then with Hamiltonians generated directly from the electric potential and fields that can be applied to the trapped ion in a representative Paul trap. This allows for the direct simulation of a squeezing operation that can be implemented through application of voltages in trapped-ion experiments. These methods can be applied to other CVQC operations in order to allow for their direct simulation as well. We package these tools into a usable application with which we can load information about an experimental configuration and then use this simulation procedure to design and test experiments in CVQC achievable with an ion-trap setup, thus facilitating the experimental design process and eventually allowing for prediction of system behavior and comparison with experimental results.