Projective squeezing for translation symmetric bosonic codes

TL;DR

This paper introduces projective squeezing, a method to enhance the performance of translation symmetric bosonic codes by effectively increasing squeezing levels, thereby improving error correction against photon loss.

Contribution

It proposes the novel projective squeezing technique, linking higher squeezing levels to improved code space projection, with practical implementation strategies and numerical validation.

Findings

Analytical relationship between squeezing level and projection probability

Method to mitigate photon loss effects in bosonic codes

Implementation strategies for projective squeezing

Abstract

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.