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Optica Quantum

Continuous-variables cluster states in photonic time-crystals

Mordechai Segev, Mark D. Lyubarov, Ohad Segal, Michael Birk, Alexey A. Gorlach, Liat Nemirovsky Levy, Yonatan Plotnik

Published Jun 26, 2025• 5 citations
Publisher

Abstract

Photonic quantum computing has been rapidly advancing over the past decade, with measurement-based approaches emerging as particularly promising. A crucial requirement for these approaches is the generation of large-scale cluster states. In this work, we present a method to create cluster states using Photonic Time Crystals (PTCs)—dielectric materials with their refractive index rapidly modulated in time. PTCs effectively function as a set of optical parametric oscillators and beam-splitters, producing simultaneous two-mode squeezing for many pairs of photonic modes with opposite wavevectors. We utilize this capability to propose a method for generating two-dimensional cluster states, offering important advantages over existing protocols.

DOI
10.1364/opticaq.558274

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Photonic quantum computing has been rapidly advancing over the past decade, with measurement-based approaches emerging as particularly promising. A crucial requirement for these approaches is the generation of large-scale cluster states. In this work, we present a method to create cluster states using Photonic Time Crystals (PTCs)—dielectric materials with their refractive index rapidly modulated in time. PTCs effectively function as a set of optical parametric oscillators and beam-splitters, producing simultaneous two-mode squeezing for many pairs of photonic modes with opposite wavevectors. We utilize this capability to propose a method for generating two-dimensional cluster states, offering important advantages over existing protocols.
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.
Entanglement is the key resource for measurement-based quantum computing. It is stored in quantum states known as cluster states, which are prepared offline and enable quantum computing by means of purely local measurements. Universal quantum computing requires cluster states that are both large and possess (at least) a two-dimensional topology. Continuous-variable cluster states-based on bosonic modes rather than qubits-have previously been generated on a scale exceeding one million modes, but only in one dimension. Here, we report generation of a large-scale two-dimensional continuous-variable cluster state. Its structure consists of a 5- by 1240-site square lattice that was tailored to our highly scalable time-multiplexed experimental platform. It is compatible with Bosonic error-correcting codes that, with higher squeezing, enable fault-tolerant quantum computation.
Enabling large-scale and high-speed quantum computation is a key to practical quantum computation. Continuous-variable approach in optical systems offer advantages in scalability and speed by leveraging their temporal degree of freedom and inherent large carrier frequency. In this paper, we investigate the generation and manipulation of quantum entanglement through a time-domain multiplexing approach. By employing time-domain multiplexing, we generate a two-dimensional cluster state—a universal resource for large-scale quantum computation—and perform quantum operations in the time domain with cluster state. Additionally, our ongoing research focuses on the generation and measurement of broadband optical quantum entanglement through an optical parametric oscillator, which holds potential as a foundation for high-speed quantum computing surpassing limitations of existing systems. By further engineering the quantum entanglement, we have also theoretically formulated a practical teleportation-based architectures for quantum computation in time domain. These advancements form the groundwork for the development of practical optical quantum computation.
Quantum optical cluster states have been increasingly explored in the light of their importance for measurement-based quantum computing. Here we set forth a method for generating quantum controlled cluster states: pumping an optical parametric oscillator with spatially structured light. We show that state-of-the-art techniques for producing clusters in the spectral and temporal domains are improved by a structured light pump, which manipulates the spatial mode couplings in the parametric interaction. We illustrate the method considering a second-order pump structure and show that a simple mode rotation yields different cluster states, including but not limited to the two-dimensional square and hexagonal lattices. We also introduce a novel technique for generating nonuniform cluster states and propose a simple setup for its implementation.