Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1508.02264 · Physical Review A

Generation of cluster states in optomechanical quantum systems

Oussama Houhou, H. Aissaoui, Alessandro Ferraro

Published Dec 28, 2015• 49 citations
arXivHTMLPDF

Abstract

We consider an optomechanical quantum system composed of a single cavity mode interacting with $N$ mechanical resonators. We propose a scheme for generating continuous-variable graph states of arbitrary size and shape, including the so-called cluster states for universal quantum computation. The main feature of this scheme is that, differently from previous approaches, the graph states are hosted in the mechanical degrees of freedom rather than in the radiative ones. Specifically, via a $2N$-tone drive, we engineer a linear Hamiltonian which is instrumental to dissipatively drive the system to the desired target state. The robustness of this scheme is assessed against finite interaction times and mechanical noise, confirming it as a valuable approach towards quantum state engineering for continuous-variable computation in a solid-state platform.

DOI
10.1103/physreva.92.063843

Related papers

Multimode Gaussian steady-state engineering in optomechanical systems with a squeezed reservoir

Nahid Yazdi, Stefano Zippilli, David Vitali

We investigate a theoretical protocol for the dissipative stabilization of mechanical quantum states in a multimode optomechanical system composed of multiple optical and mechanical modes. The scheme employs a single squeezed reservoir that drives one of the optical modes, while the remaining optical modes mediate an effective phonon-phonon interaction Hamiltonian. The interplay between these coherent interactions and the dissipation provided by the squeezed bath enables the steady-state preparation of targeted quantum states of the mechanical modes. In the absence of significant uncontrolled noise sources, the resulting dynamics closely approximate the model introduced in [Zippilli , ]. We analyze the performance of this protocol in generating mechanical cluster states defined on rectangular graphs.

arXiv:2509.16371•Physical Review A•May 4, 2026•0 citations

Pulsed generation of continuous-variable cluster states in a phononic quantum network

Anuvetha Govindarajan, Mitch Mazzei, Hailin Wang +1 more

Cluster states are multipartite entangled states that are maximally connected and resilient to decoherence, making them valuable resources for quantum information processing. Continuous-variable (CV) cluster states have been extensively investigated for such applications. Here we present a pulsed protocol for generating 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 generated cluster states through the average nullifier of the CV modes. Our numerical results show that high-quality CV cluster states can be generated with moderate squeezing parameters, whereas strong squeezing and the resulting large phonon occupations can degrade the cluster states in the presence of finite dissipation. We further show that, under moderate squeezing and dissipation, the average nullifier can decrease with increasing system size $N$, demonstrating the scalability of the proposed scheme. As a direct application, we demonstrate that distant mechanical modes can be entangled through local measurements.

arXiv:2509.12529•Physical Review A•Jul 7, 2026•0 citations

Ultracompact generation of continuous-variable cluster states

Nicolas C. Menicucci, Steven T. Flammia, Hussain Zaidi +1 more

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.

arXiv:quant-ph/0703096•Physical Review A•Jul 12, 2007•105 citations

Generation of stable Gaussian cluster states in optomechanical systems with multifrequency drives

Nahid Yazdi, Stefano Zippilli, David Vitali

Abstract We show how to dissipatively stabilize the quantum state of N mechanical resonators in an optomechanical system, where the resonators interact by radiation pressure with N optical modes, which are driven by properly selected multifrequency drives. We analyze the performance of this approach for the stationary preparation of Gaussian cluster states.

arXiv:2309.08686•Quantum Science and Technology•Mar 22, 2024•5 citations

Quantum effects in optomechanical systems

Claudiu Genes, Andrea Mari, David Vitali +1 more

The search for experimental demonstrations of the quantum behavior of macroscopic mechanical resonators is a fastly growing field of investigation and recent results suggest that the generation of quantum states of resonators with a mass at the microgram scale is within reach. In this chapter we give an overview of two important topics within this research field: cooling to the motional ground state, and the generation of entanglement involving mechanical, optical and atomic degrees of freedom. We focus on optomechanical systems where the resonator is coupled to one or more driven cavity modes by the radiation pressure interaction. We show that robust stationary entanglement between the mechanical resonator and the output fields of the cavity can be generated, and that this entanglement can be transferred to atomic ensembles placed within the cavity. These results show that optomechanical devices are interesting candidates for the realization of quantum memories and interfaces for continuous variable quantum communication networks.

arXiv:0901.2726•Jan 19, 2009•6 citations

Quantum computing with continuous-variable clusters

Mile Gu, Christian Weedbrook, Nicolas C. Menicucci +2 more

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.

arXiv:0903.3233•Physical Review A•Jun 17, 2009•354 citations
We consider an optomechanical quantum system composed of a single cavity mode interacting with NNN mechanical resonators. We propose a scheme for generating continuous-variable graph states of arbitrary size and shape, including the so-called cluster states for universal quantum computation. The main feature of this scheme is that, differently from previous approaches, the graph states are hosted in the mechanical degrees of freedom rather than in the radiative ones. Specifically, via a 2N2N2N-tone drive, we engineer a linear Hamiltonian which is instrumental to dissipatively drive the system to the desired target state. The robustness of this scheme is assessed against finite interaction times and mechanical noise, confirming it as a valuable approach towards quantum state engineering for continuous-variable computation in a solid-state platform.
We investigate a theoretical protocol for the dissipative stabilization of mechanical quantum states in a multimode optomechanical system composed of multiple optical and mechanical modes. The scheme employs a single squeezed reservoir that drives one of the optical modes, while the remaining optical modes mediate an effective phonon-phonon interaction Hamiltonian. The interplay between these coherent interactions and the dissipation provided by the squeezed bath enables the steady-state preparation of targeted quantum states of the mechanical modes. In the absence of significant uncontrolled noise sources, the resulting dynamics closely approximate the model introduced in [Zippilli , ]. We analyze the performance of this protocol in generating mechanical cluster states defined on rectangular graphs.
Cluster states are multipartite entangled states that are maximally connected and resilient to decoherence, making them valuable resources for quantum information processing. Continuous-variable (CV) cluster states have been extensively investigated for such applications. Here we present a pulsed protocol for generating 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 generated cluster states through the average nullifier of the CV modes. Our numerical results show that high-quality CV cluster states can be generated with moderate squeezing parameters, whereas strong squeezing and the resulting large phonon occupations can degrade the cluster states in the presence of finite dissipation. We further show that, under moderate squeezing and dissipation, the average nullifier can decrease with increasing system size NNN, demonstrating the scalability of the proposed scheme. As a direct application, we demonstrate that distant mechanical modes can be entangled through local measurements.
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.
The search for experimental demonstrations of the quantum behavior of macroscopic mechanical resonators is a fastly growing field of investigation and recent results suggest that the generation of quantum states of resonators with a mass at the microgram scale is within reach. In this chapter we give an overview of two important topics within this research field: cooling to the motional ground state, and the generation of entanglement involving mechanical, optical and atomic degrees of freedom. We focus on optomechanical systems where the resonator is coupled to one or more driven cavity modes by the radiation pressure interaction. We show that robust stationary entanglement between the mechanical resonator and the output fields of the cavity can be generated, and that this entanglement can be transferred to atomic ensembles placed within the cavity. These results show that optomechanical devices are interesting candidates for the realization of quantum memories and interfaces for continuous variable quantum communication networks.
Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.