To perform useful quantum computations, one needs access to quantum systems which can be manipulated efficiently, while being robust against external noise. One approach in this direction is to encode the quantum information into a continuous variable quantum system, such as an optical field. A particularly promising continuous variable encoding scheme is the Gottesman-Kitaev-Preskill (GKP) encoding, which has seen a tremendous amount of interest in recent years. In addition to being robust against physically relevant noise sources, most of the operations required to perform quantum computations can be efficiently implemented with simple components. However, one class of operations, known as non-Clifford operations which is critical to performing useful quantum computations, is less trivial to implement. In this work, we analyze the only two known ways of performing non-Clifford operations with the GKP encoding. We show that one of these approaches fails when considering physically realizable systems. This leaves the other approach, known as magic state teleportation, as the only viable method to perform non-Clifford operations. Our work thus points towards a clear direction for how to operate GKP qubits, focusing the efforts of future research.
The work was carried out in collaboration with associate professor Nicolas Menicucci from RMIT University, Australia. The work is available at: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.032409