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arXiv:1309.4105 · Physical Review A

Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states

Pei Wang, Moran Chen, Nicolas C. Menicucci, Olivier Pfister

Published Sep 24, 2014• 46 citations
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Abstract

Cluster states with higher-dimensional lattices that cannot be physically embedded in three-dimensional space have important theoretical interest in quantum computation and quantum simulation of topologically ordered condensed-matter systems. We present a simple, scalable, top-down method of entangling the quantum optical frequency comb into hypercubic-lattice continuous-variable cluster states of a size of about ${10}^{4}$ quantum field modes, using existing technology. A hypercubic lattice of dimension $D$ (linear, square, cubic, hypercubic, etc.) requires but $D$ optical parametric oscillators with bichromatic pumps whose frequency splittings alone determine the lattice dimensionality and the number of copies of the state.

DOI
10.1103/physreva.90.032325

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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.
Quantum computing promises exponential speedup for particular computational tasks, such as integer factoring, which bears importance for encryption technology, and quantum simulation, which holds vast scientific potential. Comparing with the traditional circuit-based quantum computers, one-way quantum computers are experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. In this thesis, I first review the fundamental theory of one-way quantum computing and its experimental implementation using the quantum optical frequency comb. After that, I present two novel schemes for generating ultra-scalable cluster states with rich structures that can be used for universal quantum computing.
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).