Generation of reconfigurable hypercubic graph states in one to four 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 three dimensions. Here, we generate one-, two-, three-, and four-dimensional optical frequency-mode graph states, which would become cluster states at higher squeezing levels than obtained here, by sending broadband two-mode vacuum-squeezed light through an electro-optical modulator (EOM) driven with multiple frequencies. We create the squeezed light using four-wave mixing in Rb atomic vapor and mix the sideband frequencies (qumodes) using an EOM, 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.