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arXiv:2408.06317 · Science Advances

Generation of reconfigurable hypercubic graph states in one to four dimensions in a simple optical system

Zhifan Zhou, Luı́s E. E. de Araujo, M. T. DiMario, Jing Su, Meng-Chang Wu, Brian E. Anderson, Jie Zhao, K. M. Jones, Paul D. Lett

Published Apr 24, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1126/sciadv.aea8426

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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.
Error correction in measurement-based quantum computing schemes will require the construction of cluster states in at least 3 dimensions. Here, we generate 1-, 2-, 3-, and 4-dimensional optical frequency-mode cluster states 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, 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 the scaling of optical cluster states to multiple dimensions without increasing loss.
An optical frequency comb comprises a cluster of equally spaced, phase-locked spectral lines. Replacing these classical components with correlated quantum light gives rise to cluster quantum frequency combs, providing abundant quantum resources for measurement-based quantum computation, and multi-user quantum networks. We propose and generate cluster quantum microcombs within an on-chip optical microresonator driven by multi-frequency lasers. Through resonantly enhanced four-wave mixing processes, continuous-variable cluster states with 60 qumodes are deterministically created. The graph structures can be programmed into one- and two-dimensional lattices by adjusting the configurations of the pump lines, which are confirmed inseparable based on the measured covariance matrices. Our work demonstrates the largest-scale cluster states with unprecedented raw squeezing levels from a photonic chip, offering a compact and scalable platform for computational and communicational tasks with quantum advantages.
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We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs, which can be engineered into a single optical parametric oscillator (OPO). The desired CV cluster state is produced directly from a joint squeezing operation on the vacuum, using a multifrequency pump beam. This method has potential for ultracompact experimental implementation. As an illustration, we detail an experimental proposal for creating a four-mode square CV cluster state with a single OPO.
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