Robust engineering of universal Gaussian cluster states in harmonic lattices with a single-site squeezed reservoir

We first show that any Gaussian cluster state of N bosonic modes can be generated by a multi-mode squeezing transformation. and provide the explicit recipe. We then use this result to show that a large class of pure entangled CV Gaussian states, including 2D-cluster states, can be robustly generated as unique steady state of a dissipative dynamics employing minimal resources. In fact, this is achievable using only a single-site squeezed driving and passive bilinear interactions. We provide the explicit protocol which corresponds to the engineering of a suitable excitation number conserving Hamiltonian.This fact can be used for the implementation of universal continuous variable measurement-based-quantum computation on various platforms.

[1] S. Zippilli, and D. Vitali
"Any Gaussian cluster state can be generated by a multi-mode squeezing transformation“; arXiv:2007.12772
[2] S. Zippili, and D. Vitali
"Dissipative engineering of Gaussian entangled states in harmonic lattices with a single-site squeezed reservoir"
arXiv:2008.02539