Saving the cat: Approximate quantum error correction using squeezed Schrödinger cat states

A promising road to quantum error correction is that of bosonic codes, whereby a logical quantum bit is robustly encoded in well-chosen states of a quantum harmonic oscillator. Schrödinger cat codes in particular can correct phase-flip errors in the limit of large displacement of the boson field, while they are still vulnerable to bit-flip errors induced by photon loss. Other bosonic codes - such as the four-legged cat code, the binomial code, or the GKP code - have been studied. A bosonic code that can correct both bit-flip and phase-flip errors within an experimentally viable and scalable scheme is still however a challenge. Here we show that adding squeezing as a resource, squeezed-cat states allow a partial correction of the bit-flip error, therefore suppressing the logical error rate, while improving the protection against phase-flip errors. We develop a full parity-check and recovery protocol that is suitable to be implemented on currently available superconducting architectures. With parameters typical of the experimental state-of-the-art, the code can suppress the logical bit-flip error rate by more than one order of magnitude, already with a moderate amount of squeezing.