© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1406.6571 · Physical Review A

Continuous-variable cluster-state generation over the optical spatial mode comb

Raphael C. Pooser, Jietai Jing

Published Oct 20, 2014• 43 citations

Abstract

One-way quantum computing uses single-qubit projective measurements performed on a cluster state (a highly entangled state of multiple qubits) in order to enact quantum gates. The model is promising due to its potential scalability; the cluster state may be produced at the beginning of the computation and operated on over time. Continuous variables (CV) offer another potential benefit in the form of deterministic entanglement generation. This determinism can lead to robust cluster states and scalable quantum computation. Recent demonstrations of CV cluster states have made great strides on the path to scalability, utilizing either time or frequency multiplexing in optical parametric oscillators (OPO), both above and below threshold. The techniques relied on a combination of entangling operators and beam-splitter transformations. Here we show that an analogous transformation exists for amplifiers with Gaussian inputs states operating on multiple spatial modes. By judicious selection of local oscillators, the spatial mode distribution is analogous to the optical frequency comb consisting of axial modes in an OPO cavity. We outline an experimental system that generates cluster states across the spatial frequency comb, which can also scale the amount of quantum noise reduction to potentially larger than in other systems.

DOI: 10.1103/physreva.90.043841

Related papers

The optical frequency comb as a one-way quantum computer

Steven T. Flammia, Nicolas C. Menicucci, Olivier Pfister

In the one-way model of quantum computing, quantum algorithms are implemented using only measurements on an entangled initial state. Much of the hard work is done upfront when creating this universal resource, known as a cluster state, on which the measurements are made. Here we detail a new proposal for a scalable method of creating cluster states using only a single multimode optical parametric oscillator (OPO). The method generates a continuous-variable cluster state that is universal for quantum computation and encoded in the quadratures of the optical frequency comb of the OPO. This work expands on the presentation in Menicucci, Flammia and Pfister (2008 Phys. Rev. Lett. 101 , 130501).

arXiv:0811.2799•Journal of Physics B Atomic Molecular and Optical Physics•May 15, 2009•64 citations

One-Way Quantum Computing in the Optical Frequency Comb

Nicolas C. Menicucci, Steven T. Flammia, Olivier Pfister

One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a scalable method that uses a single, multimode optical parametric oscillator (OPO). The method is very efficient and generates a continuous-variable cluster state, universal for quantum computation, with quantum information encoded in the quadratures of the optical frequency comb of the OPO.

arXiv:0804.4468•Physical Review Letters•Sep 22, 2008•313 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 continuous-variable spatial cluster entangled states in optical mode comb

Rongguo Yang, Jingjing Wang, Jing Zhang +2 more

Cluster entangled states are often used as the fundamental resources for one-way quantum computation. In this paper, we put forward a scheme of generating the spatial cluster entangled states of Laguerre–Gaussian modes in a large-Fresnel-number degenerate optical parametric oscillator operating below threshold with type I phase matching, which is pumped by two spatial Laguerre–Gaussian modes with the same frequency. The nonlinear parametric process of each pump mode satisfies momentum, energy, and orbit angular momentum conservation. Eleven-partite spatial cluster entangled states of Laguerre–Gaussian modes can be produced in the optical mode comb under feasible experimental condition, which can be demonstrated by using the entanglement criterion proposed by van Loock and Furusawa.

Journal of the Optical Society of America B•Nov 3, 2016•13 citations

Generation of large-scale continuous-variable cluster states multiplexed both in time and frequency domains

Peilin Du, Yu Wang, Kui Liu +2 more

A large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating a large-scale CV cluster state multiplexed in a time domain is easier to implement and has strong scalability in experiment. Here one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both in time and frequency domains are parallelly generated, which can be further extended to a three-dimensional (3D) CV cluster state by combining two time-delay nondegenerate optical parametric amplification systems with beam-splitters. It is shown that the number of parallel arrays depends on the corresponding frequency comb lines, the partite number of each array can be very large (million), and the scale of the 3D cluster state can be ultra-large. In addition, the concrete quantum computing schemes of applying the generated 1D and 3D cluster states are also demonstrated. Our schemes may pave the way for fault-tolerant and topologically protected MBQC in hybrid domains, by further combining with efficient coding and quantum error correction.

arXiv:2210.10261•Optics Express•Feb 8, 2023•17 citations

One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator

Rafael N. Alexander, Pei Wang, Niranjan Sridhar +3 more

One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but nonuniversal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to ($3\ifmmode\times\else\texttimes\fi{}{10}^{3}$ frequencies) $\ifmmode\times\else\texttimes\fi{}$ (unlimited number of temporal modes) into a computationally universal continuous-variable cluster state. We introduce a generalized measurement protocol to enable improved computational performance on this entanglement resource.

arXiv:1509.00484•Physical Review A•Sep 27, 2016•65 citations

One-way quantum computing uses single-qubit projective measurements performed on a cluster state (a highly entangled state of multiple qubits) in order to enact quantum gates. The model is promising due to its potential scalability; the cluster state may be produced at the beginning of the computation and operated on over time. Continuous variables (CV) offer another potential benefit in the form of deterministic entanglement generation. This determinism can lead to robust cluster states and scalable quantum computation. Recent demonstrations of CV cluster states have made great strides on the path to scalability, utilizing either time or frequency multiplexing in optical parametric oscillators (OPO), both above and below threshold. The techniques relied on a combination of entangling operators and beam-splitter transformations. Here we show that an analogous transformation exists for amplifiers with Gaussian inputs states operating on multiple spatial modes. By judicious selection of local oscillators, the spatial mode distribution is analogous to the optical frequency comb consisting of axial modes in an OPO cavity. We outline an experimental system that generates cluster states across the spatial frequency comb, which can also scale the amount of quantum noise reduction to potentially larger than in other systems.

In the one-way model of quantum computing, quantum algorithms are implemented using only measurements on an entangled initial state. Much of the hard work is done upfront when creating this universal resource, known as a cluster state, on which the measurements are made. Here we detail a new proposal for a scalable method of creating cluster states using only a single multimode optical parametric oscillator (OPO). The method generates a continuous-variable cluster state that is universal for quantum computation and encoded in the quadratures of the optical frequency comb of the OPO. This work expands on the presentation in Menicucci, Flammia and Pfister (2008 Phys. Rev. Lett. 101 , 130501).

One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a scalable method that uses a single, multimode optical parametric oscillator (OPO). The method is very efficient and generates a continuous-variable cluster state, universal for quantum computation, with quantum information encoded in the quadratures of the optical frequency comb of the OPO.

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.

Cluster entangled states are often used as the fundamental resources for one-way quantum computation. In this paper, we put forward a scheme of generating the spatial cluster entangled states of Laguerre–Gaussian modes in a large-Fresnel-number degenerate optical parametric oscillator operating below threshold with type I phase matching, which is pumped by two spatial Laguerre–Gaussian modes with the same frequency. The nonlinear parametric process of each pump mode satisfies momentum, energy, and orbit angular momentum conservation. Eleven-partite spatial cluster entangled states of Laguerre–Gaussian modes can be produced in the optical mode comb under feasible experimental condition, which can be demonstrated by using the entanglement criterion proposed by van Loock and Furusawa.

A large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating a large-scale CV cluster state multiplexed in a time domain is easier to implement and has strong scalability in experiment. Here one-dimensional (1D) large-scale dual-rail CV cluster states multiplexed both in time and frequency domains are parallelly generated, which can be further extended to a three-dimensional (3D) CV cluster state by combining two time-delay nondegenerate optical parametric amplification systems with beam-splitters. It is shown that the number of parallel arrays depends on the corresponding frequency comb lines, the partite number of each array can be very large (million), and the scale of the 3D cluster state can be ultra-large. In addition, the concrete quantum computing schemes of applying the generated 1D and 3D cluster states are also demonstrated. Our schemes may pave the way for fault-tolerant and topologically protected MBQC in hybrid domains, by further combining with efficient coding and quantum error correction.

One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but nonuniversal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to ($3\ifmmode\times\else\texttimes\fi{}{10}^{3}$ frequencies) $\ifmmode\times\else\texttimes\fi{}$ (unlimited number of temporal modes) into a computationally universal continuous-variable cluster state. We introduce a generalized measurement protocol to enable improved computational performance on this entanglement resource.