Oscillator-to-Oscillator Codes Do Not Have a Threshold

This course explores the concept that oscillator-to-oscillator codes do not have a threshold property, unlike qubit error-correcting codes. The course delves into the encoding of logical bosonic modes into physical modes using Gaussian and auxiliary one-mode Gottesman-Kitaev-Preskill states. It discusses the inability of oscillator-to-oscillator codes, combined with maximum likelihood error decoding, to convert physical displacement noise below a certain threshold to logical noise. The teaching method involves theoretical analysis and mathematical proofs. This course is intended for individuals interested in quantum information, quantum physics, and error-correcting codes.