Pulsed Generation of Continuous-Variable Cluster States in a Phononic Quantum Network

Cluster states are multipartite entangled states that are maximally connected and resilient to decoherence, making them valuable resources for quantum information processing. Here we will present our recent work on generating continuous-variable (CV) cluster states in a phononic quantum network composed of phonon waveguides, mechanical resonators, and optical cavities. A key feature of this architecture is its modular design, where pairs of mechanical modes serve as building blocks with only local, tunable interactions between mechanical and cavity modes. We characterize the resulting cluster states by evaluating the adjacency matrix and the nullifiers of the CV modes, and we analyze the impact of mechanical and cavity losses on their robustness. In addition, we demonstrate that distant mechanical modes can be entangled through local quadrature measurements on the cluster states.