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 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).

[1]  T. Ralph,et al.  Universal quantum computation with continuous-variable cluster states. , 2006, Physical review letters.

[2]  Pieter Kok,et al.  Efficient high-fidelity quantum computation using matter qubits and linear optics , 2005 .

[3]  M. Fejer,et al.  Quasi-phase-matched second harmonic generation: tuning and tolerances , 1992 .

[4]  T. Hänsch.  Nobel Lecture: Passion for precision* , 2006 .

[5]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[6]  H. Briegel,et al.  Persistent entanglement in arrays of interacting particles. , 2000, Physical review letters.

[7]  Akira Furusawa,et al.  Demonstration of a quantum nondemolition sum gate. , 2008, Physical review letters.

[8]  G. Milburn,et al.  Quantum computation with optical coherent states , 2002, QELS 2002.

[9]  S. Braunstein,et al.  Continuous-variable Gaussian analog of cluster states (5 pages) , 2006 .

[10]  J. Jing,et al.  Experimental continuous-variable entanglement from a phase-difference-locked optical parametric oscillator , 2006, quant-ph/0604134.

[11]  T. Rudolph,et al.  Resource-efficient linear optical quantum computation. , 2004, Physical review letters.

[12]  Olivier Pfister,et al.  Broadband amplitude squeezing in a periodically poled KTiOPO4 waveguide. , 2009, Optics letters.

[13]  B. Yurke.  Optical back-action-evading amplifiers , 1985 .

[14]  M. Olsen,et al.  Bright tripartite entanglement in triply concurrent parametric oscillation , 2005, quant-ph/0505131.

[15]  Steven T. Flammia,et al.  Phase transition of computational power in the resource states for one-way quantum computation , 2007, 0709.1729.

[16]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[17]  N. C. Menicucci,et al.  Ultracompact generation of continuous-variable cluster states , 2007, quant-ph/0703096.

[18]  A. Furusawa,et al.  Experimental generation of four-mode continuous-variable cluster states , 2008, 2008 International Nano-Optoelectronics Workshop.

[19]  P. Loock.  Examples of Gaussian cluster computation , 2006, quant-ph/0606212.

[20]  J Niset,et al.  Experimentally feasible quantum erasure-correcting code for continuous variables. , 2007, Physical review letters.

[21]  Shijun Xiao,et al.  A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory , 2004, IEEE Journal of Quantum Electronics.

[22]  T. Ralph,et al.  Fault-tolerant linear optical quantum computing with small-amplitude coherent States. , 2007, Physical review letters.

[23]  John L. Hall,et al.  Nobel Lecture: Defining and measuring optical frequencies , 2006 .

[24]  M. Nielsen.  Optical quantum computation using cluster States. , 2004, Physical review letters.

[25]  T. Hänsch,et al.  Controlled collisions for multi-particle entanglement of optically trapped atoms , 2003, Nature.

[26]  S. Braunstein.  Squeezing as an irreducible resource , 1999, quant-ph/9904002.

[27]  Hans J. Briegel,et al.  The one-way quantum computer--a non-network model of quantum computation , 2001, quant-ph/0108118.

[28]  Samuel L. Braunstein.  Error Correction for Continuous Quantum Variables , 1998 .

[29]  D. DiVincenzo,et al.  Quantum computation with quantum dots , 1997, cond-mat/9701055.

[30]  H. Yonezawa,et al.  Continuous-variable quantum information processing with squeezed states of light , 2008, 2008 International Nano-Optoelectronics Workshop.

[31]  Richard L. Barnes.  Stabilizer Codes for Continuous-variable Quantum Error Correction , 2004, quant-ph/0405064.

[32]  D. Gross,et al.  Novel schemes for measurement-based quantum computation. , 2006, Physical review letters.

[33]  P. Loock,et al.  Building Gaussian cluster states by linear optics , 2006, quant-ph/0610119.

[34]  S. Braunstein.  Squeezing as an irreducible resource (4 pages) , 2005 .

[35]  Ou,et al.  Realization of the Einstein-Podolsky-Rosen paradox for continuous variables. , 1992, Physical review letters.

[36]  Dutta,et al.  Quantum-noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[37]  Achim Kempf,et al.  Quantum error correction on infinite-dimensional Hilbert spaces , 2008, Journal of Mathematical Physics.

[38]  Wolfgang Dür,et al.  Universal resources for measurement-based quantum computation. , 2006, Physical review letters.

[39]  Franco Nori,et al.  Efficient one-step generation of large cluster states with solid-state circuits , 2007 .

[40]  M. Shirasaki.  Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer. , 1996, Optics letters.

[41]  M. Martinelli,et al.  Generation of bright two-color continuous variable entanglement. , 2005, Physical review letters.

[42]  Timothy C. Ralph,et al.  Quantum information with continuous variables , 2000, Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504).

[43]  Kae Nemoto,et al.  Efficient classical simulation of continuous variable quantum information processes. , 2002, Physical review letters.

[44]  Aaron J. Miller,et al.  Counting near-infrared single-photons with 95% efficiency. , 2008, Optics express.

[45]  N. Bloembergen,et al.  Interactions between light waves in a nonlinear dielectric , 1962 .

[46]  E. Knill,et al.  Error analysis for encoding a qubit in an oscillator (5 pages) , 2005, quant-ph/0510107.

[47]  Carlton M. Caves,et al.  QUANTUM LOGIC GATES IN OPTICAL LATTICES , 1999 .

[48]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[49]  Multipartite continuous-variable entanglement from concurrent nonlinearities , 2004, quant-ph/0404049.

[50]  J. Preskill,et al.  Encoding a qubit in an oscillator , 2000, quant-ph/0008040.

[51]  Observation of triply coincident nonlinearities in periodically poled KTiOPO4. , 2005, Optics letters.

[52]  Xiaolong Su,et al.  Experimental demonstration of quantum entanglement between frequency-nondegenerate optical twin beams. , 2005, Optics letters.

[53]  Akira Furusawa,et al.  Generation of Four‐Mode Continuous‐Variable Cluster States , 2009 .

[54]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[55]  J Eisert,et al.  Percolation, renormalization, and quantum computing with nondeterministic gates. , 2007, Physical review letters.

[56]  Xiaolong Su,et al.  Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables. , 2006, Physical review letters.

[57]  B. E. Kane.  A silicon-based nuclear spin quantum computer , 1998, Nature.

[58]  S. Flammia,et al.  Entangling the optical frequency comb: Simultaneous generation of multiple 2 × 2 and 2 × 3 continuous-variable cluster states in a single optical parametric oscillator , 2007, 0710.4980.

[59]  Simone Severini,et al.  Weighing matrices and optical quantum computing , 2008, 0808.2057.

[60]  S. Braunstein,et al.  Continuous-variable Gaussian analog of cluster states , 2006 .

[61]  N. C. Menicucci,et al.  Quantum Computing with Continuous-Variable Clusters , 2009, 0903.3233.

[62]  S. Braunstein,et al.  Quantum computation over continuous variables , 1998 .

[63]  Reid,et al.  Quantum correlations of phase in nondegenerate parametric oscillation. , 1988, Physical review letters.

[64]  Scott A. Diddams,et al.  Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb , 2007, Nature.

[65]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[66]  Olivier Pfister,et al.  One-way quantum computing in the optical frequency comb. , 2008, Physical review letters.