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arXiv:0811.2799 · Journal of Physics B Atomic Molecular and Optical Physics

The optical frequency comb as a one-way quantum computer

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

Published May 15, 2009• 64 citations
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Abstract

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).

DOI
10.1088/0953-4075/42/11/114009

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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.
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.
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.
The quantum optical frequency comb (QOFC) of a single optical parametric oscillator (OPO) is a scalable platform for quantum information as a generator of large size cluster states. We show that the phase modulation of the QOFCs emitted by an OPO is a powerful graph engineering technique that can increase the topological dimension of the generated cluster state, from zero (independent EPR pairs) to one (linear cluster state), and from one to two (square-lattice cluster state), thereby allowing the creation and tailoring of universal quantum computing resources. This concept is highly compatible with integrated photonics.
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.
We propose and fully analyze the simplest technique to date (to our knowledge) for generating light-based universal quantum computing resources, namely, 2D, 3D, and n -hypercubic cluster states in general. The technique uses two standard optical components: first, a single optical parametric oscillator pumped below threshold by a monochromatic field, which generates Einstein–Podolsky–Rosen entangled states, a.k.a. two-mode squeezed states, over the quantum optical frequency comb; second, phase modulation at frequencies that are multiples of the comb spacing (via RF or optical means). The compactness of this technique paves the way to implementing quantum computing on chip using quantum nanophotonics.