Projective squeezing for translation symmetric bosonic codes

Understand

The design of translation symmetric bosonic codes, e.g., Gottesmann-Kitaev-Preskill and squeezed cat codes, is robust against photon loss, but the computation accuracy is limited by the available squeezing level.

• Here, we introduce the \textit{projective squeezing} (PS) method for computing outcomes for a higher squeezing level by revealing that a linear combination of displacement operators with periodic displacement values constitutes the smeared projector onto the better code space; we also show the analytical relationship between the increased squeezing level and the projection probability.
• We introduce concrete implementation methods for PS based on linear-combination-of-unitaries and virtual quantum error detection.
• We also numerically verify our analytical arguments and show that our protocol can mitigate the effect of photon loss.