The Optical Frequency Comb as a One-Way Quantum Computer

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 up-front 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 Phys. Rev. Lett. 101, 130501 (2008).Comment: 20 pages, 8 figures. v2 corrects minor error in published versio

One-Way Quantum Computing in the Optical Frequency Comb

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 radically new approach: 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.Comment: v2: changed author order; 4 pages, 3 figures; supplemental movie available at http://faculty.virginia.edu/quantum/torus.mo

Entangling the optical frequency comb: simultaneous generation of multiple 2x2 and 2x3 continuous-variable cluster states in a single optical parametric oscillator

We report on our research effort to generate large-scale multipartite optical-mode entanglement using as few physical resources as possible. We have previously shown that cluster- and GHZ-type N-partite continuous-variable entanglement can be obtained in an optical resonator that contains a suitably designed second-order nonlinear optical medium, pumped by at most O(N^2) fields. In this paper, we show that the frequency comb of such a resonator can be entangled into an arbitrary number of independent 2x2 and 2x3 continuous-variable cluster states by a single optical parametric oscillator pumped by just a few optical modes.Comment: Third version has corrected eqs. (10-14) and revised notation "Q" in lieu of "X" for amplitude quadrature operato

Ultracompact Generation of Continuous-Variable Cluster States

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 multi-frequency 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.Comment: 4 pages, 1 figure; v2 improved discussion of the implications of our result; added discussion of finite squeezing effect

Graphical calculus for Gaussian pure states

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semi-local Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term "CV graph state" currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the "closest" CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this new graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.Comment: (v3) shortened title, very minor corrections (v2) minor corrections, reference added, new figures for CZ gate and beamsplitter graph rules; (v1) 25 pages, 11 figures (made with TikZ

Playing the quantum harp: Multipartite squeezing and entanglement of harmonic oscillators

The frequency comb of an optical resonator is a naturally large set of exquisitely well defined quantum systems, such as in the broadband mode-locked lasers which have redefined time/frequency metrology and ultraprecise measurements in recent years. High coherence can therefore be expected in the quantum version of the frequency comb, in which nonlinear interactions couple different cavity modes, as can be modeled by different forms of graph states. We show that is possible to thereby generate states of interest to quantum metrology and computing, such as multipartite entangled cluster and Greenberger-Horne-Zeilinger states

The Highly Miniaturised Radiation Monitor

We present the design and preliminary calibration results of a novel highly miniaturised particle radiation monitor (HMRM) for spacecraft use. The HMRM device comprises a telescopic configuration of active pixel sensors enclosed in a titanium shield, with an estimated total mass of 52 g and volume of 15 cm$^3$. The monitor is intended to provide real-time dosimetry and identification of energetic charged particles in fluxes of up to 10$^8$ cm$^{-2}$ s$^{-1}$ (omnidirectional). Achieving this capability with such a small instrument could open new prospects for radiation detection in space.Comment: 17 pages, 15 figure

Quantum coherent control of highly multipartite continuous-variable entangled states by tailoring parametric interactions

The generation of continuous-variable multipartite entangled states is important for several protocols of quantum information processing and communication, such as one-way quantum computation or controlled dense coding. In this article we theoretically show that multimode optical parametric oscillators can produce a great variety of such states by an appropriate control of the parametric interaction, what we accomplish by tailoring either the spatio-temporal shape of the pump, or the geometry of the nonlinear medium. Specific examples involving currently available optical parametric oscillators are given, hence showing that our ideas are within reach of present technology.Comment: 14 pages, 5 figure

Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators

The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology