Generation of reconfigurable hypercubic graph states in 1-4 dimensions in a simple optical system

Entangled graph states can be used for quantum sensing and computing
applications. In some measurement-based quantum computing schemes, error
correction will require the construction of cluster states in at least 3
dimensions. Here, we generate 1-, 2-, 3-, and 4-dimensional optical
frequency-mode graph states, which become cluster states at sufficiently
high squeezing levels, by sending broadband 2-mode vacuum-squeezed light
through an electro-optical modulator (EOM) driven with multiple
frequencies. We create the squeezed light using 4-wave mixing in Rb atomic
vapor and mix the sideband frequencies (qumodes) using an EOM, as proposed
by Zhu et al. [Optica 8, 281 (2021)], producing a pattern of entanglement
correlations that constitute continuous-variable graph states containing
up to several hundred qumodes. We verify the entanglement structure by
using homodyne measurements to construct the covariance matrices and
evaluate the nullifiers. This technique enables scaling of optical cluster
states to multiple dimensions without increasing loss.