Measurement-free Quantum Error Correction for Gaussian Noise using Gottesman-Kitaev-Preskill States

Gaussian noise is common in bosonic systems; however, No-Go theorems state that we require non-Gaussian resources such as Gottesman-Kitaev-Preskill (GKP) States to correct Gaussian noise. Here, we bypass the No-Go results by using the phase conjugation to reduce dependence on non-Gaussian states. In particular, we propose a measurement-free bosonic quantum error correction (QEC) scheme and a measurement-free bosonic quantum error distillation (QED) scheme to reduce the number of required GKP states and the required squeezing ability. Furthermore, we can arbitrarily suppress the quadrature noise variance if the squeezing ability is strong. In addition, we show a trade-off between finite squeezing ability and finite number of required GKP states. Thus, we can resource-efficiently correct Gaussian Noise if the squeezing ability is sufficiently large.