Quantum Logic Between Distant Trapped Ions

Trapped atomic ions have proven to be one of the most promising candidates for the realization of quantum computation due to their long trapping times, excellent coherence properties, and exquisite control of the internal atomic states. Integrating ions (quantum memory) with photons (distance link) offers a unique path to large-scale quantum computation and long-distance quantum communication. In this article, we present a detailed review of the experimental implementation of a heralded photon-mediated quantum gate between remote ions, and the employment of this gate to perform a teleportation protocol between two ions separated by a distance of about one meter.

[1]  B. Blinov,et al.  Trapped ion imaging with a high numerical aperture spherical mirror , 2009, 0901.4742.

[2]  David J. Wineland,et al.  Minimization of ion micromotion in a Paul trap , 1998 .

[3]  A. Zeilinger,et al.  Experimental one-way quantum computing , 2005, Nature.

[4]  G. Milburn,et al.  Linear optical quantum computing with photonic qubits , 2005, quant-ph/0512071.

[5]  L-M Duan,et al.  Efficient quantum computation with probabilistic quantum gates. , 2005, Physical review letters.

[6]  J. Britton,et al.  Sympathetic cooling of 9 Be + and 24 Mg + for quantum logic , 2003 .

[7]  U. Peschel,et al.  A new 4π geometry optimized for focusing on an atom with a dipole-like radiation pattern , 2007 .

[8]  Shih,et al.  Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by type-II parametric down-conversion. , 1993, Physical review letters.

[9]  R. March.  Quadrupole ion trap mass spectrometry: theory, simulation, recent developments and applications , 1998 .

[10]  R. Blatt,et al.  Towards fault-tolerant quantum computing with trapped ions , 2008, 0803.2798.

[11]  L-M Duan,et al.  Scalable generation of graph-state entanglement through realistic linear optics. , 2006, Physical review letters.

[12]  M. A. Rowe,et al.  Heating of trapped ions from the quantum ground state , 2000 .

[13]  C. Monroe,et al.  Architecture for a large-scale ion-trap quantum computer , 2002, Nature.

[14]  É. Biémont,et al.  Lifetime calculations in Yb II , 1998 .

[15]  D. Matsukevich,et al.  Quantum State Transfer Between Matter and Light , 1999, Science.

[16]  A. Braun,et al.  Electrodynamically trapped Yb + ions for quantum information processing , 2006 .

[17]  J. Laurat,et al.  Conditional control of the quantum states of remote atomic memories for quantum networking , 2006 .

[18]  Christoph Becher,et al.  A single-photon source based on a single Ca+ ion , 2004 .

[19]  O. Gühne,et al.  03 21 7 2 3 M ar 2 00 6 Scalable multi-particle entanglement of trapped ions , 2006 .

[20]  H. Dehmelt,et al.  Radiofrequency Spectroscopy of Stored Ions I: Storage , 1968 .

[21]  T. Ralph,et al.  Quantum process tomography of a controlled-NOT gate. , 2004, Physical review letters.

[22]  M. G. Boshier,et al.  Destabilization of dark states and optical spectroscopy in Zeeman-degenerate atomic systems , 2002 .

[23]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[24]  N. Lutkenhaus,et al.  Experimental procedures for entanglement verification , 2007 .

[25]  Blatt,et al.  Population trapping in excited Yb ions. , 1989, Physical review letters.

[26]  C. Monroe,et al.  Scaling and suppression of anomalous heating in ion traps. , 2006, Physical review letters.

[27]  J. Cirac,et al.  Creation of entangled states of distant atoms by interference , 1998, quant-ph/9810013.

[28]  Benjamin G. Norton,et al.  Scalable, efficient ion-photon coupling with phase fresnel lenses for large-scale quantum computing , 2008, Quantum Inf. Comput..

[29]  H. J. Kimble,et al.  The quantum internet , 2008, Nature.

[30]  T. Wilk,et al.  Single-Atom Single-Photon Quantum Interface , 2007, Science.

[31]  Patrick M. Fitzpatrick.  Advanced Calculus: A Course in Mathematical Analysis , 1995 .

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

[33]  S. Olmschenk,et al.  Quantum Teleportation Between Distant Matter Qubits , 2009, Science.

[34]  Isaac L. Chuang,et al.  Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations , 1999, Nature.

[35]  T. Wilk,et al.  Time-resolved two-photon quantum interference , 2003, quant-ph/0308024.

[36]  J J García-Ripoll,et al.  Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing. , 2003, Physical review letters.

[37]  H. Weinfurter,et al.  Free-Space distribution of entanglement and single photons over 144 km , 2006, quant-ph/0607182.

[38]  Geoffrey P. Barwood,et al.  Investigation of the s-2(1/2)-d-2(5/2) clock transition in a single ytterbium ion , 1997 .

[39]  Klein,et al.  Laser cooling of trapped ytterbium ions using a four-level optical-excitation scheme. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[40]  Quantum interference of electromagnetic fields from remote quantum memories. , 2006, Physical review letters.

[41]  Blatt,et al.  Trapped ions in the strong-excitation regime: Ion interferometry and nonclassical states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[42]  King,et al.  Demonstration of a fundamental quantum logic gate. , 1995, Physical review letters.

[43]  Michel Devoret,et al.  Superconducting quantum bits , 2005 .

[44]  Jacob F. Sherson,et al.  Quantum teleportation between light and matter , 2006, Nature.

[45]  Christopher Monroe,et al.  Robust probabilistic quantum information processing with atoms, photons, and atomic ensembles , 2008 .

[46]  J M Amini,et al.  High-fidelity transport of trapped-ion qubits through an X-junction trap array. , 2009, Physical review letters.

[47]  D. Stick,et al.  Planar ion trap geometry for microfabrication , 2004 .

[48]  D. Matsukevich,et al.  Bell inequality violation with two remote atomic qubits. , 2008, Physical review letters.

[49]  P. Maunz,et al.  Ultrafast Coherent Coupling of Atomic Hyperfine and Photon Frequency Qubits , 2006 .

[50]  Gerd Leuchs,et al.  Stylus ion trap for enhanced access and sensing , 2009 .

[51]  R. Feynman.  Simulating physics with computers , 1999 .

[52]  Atomic qubit manipulations with an electro-optic modulator. , 2003, Optics letters.

[53]  D. Leibfried,et al.  Ion traps with enhanced optical and physical access , 2008, 0810.2647.

[54]  Andrew G. White,et al.  Measurement of qubits , 2001, quant-ph/0103121.

[55]  T. Schaetz,et al.  Simulating a quantum magnet with trapped ions , 2008 .

[56]  A. Drezet.  Comment on 'Single-particle entanglement' , 2006 .

[57]  S. J. van Enk,et al.  Single-particle entanglement , 2005 .

[58]  B. Blinov,et al.  Barium ions for quantum computation , 2009, 0905.2701.

[59]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[60]  D Hayes,et al.  Heralded quantum gate between remote quantum memories. , 2009, Physical review letters.

[61]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[62]  L. Maleki,et al.  Lifetime Measurements of the 4f(sup 14)5d Metastable States in Single Ytterbium Ions , 2000 .

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

[64]  D. Matsukevich,et al.  Entanglement of single-atom quantum bits at a distance , 2007, Nature.

[65]  C. Monroe,et al.  Ultrafast coherent excitation of a trapped ion qubit for fast gates and photon frequency qubits. , 2006, Physical review letters.

[66]  N. Lutkenhaus,et al.  Bell measurements for teleportation , 1998, quant-ph/9809063.

[67]  Jian-Wei Pan,et al.  Experimental entanglement of six photons in graph states , 2006, quant-ph/0609130.

[68]  Geoffrey P. Barwood,et al.  Observation of the 2 S 1/2 - 2 F 7/2 electric octupole transition in a single 171 Yb + ion , 2000 .

[69]  R. B. Blakestad,et al.  Microfabricated surface-electrode ion trap for scalable quantum information processing. , 2006, Physical review letters.

[70]  M. Horodecki,et al.  General teleportation channel, singlet fraction and quasi-distillation , 1998, quant-ph/9807091.

[71]  Shih,et al.  New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion. , 1988, Physical review letters.

[72]  Jian-Wei Pan,et al.  Experimental demonstration of a BDCZ quantum repeater node , 2008, Nature.

[73]  N. Mclachlan.  Theory and Application of Mathieu Functions , 1965 .

[74]  Paul G. Kwiat,et al.  Photonic State Tomography , 2005 .

[75]  W. Paul.  Electromagnetic traps for charged and neutral particles , 1990 .

[76]  S. Olmschenk,et al.  Manipulation and detection of a trapped Yb+ hyperfine qubit , 2007, 0708.0657.

[77]  S. Kleineidam,et al.  Some Observations on Higher‐order Non‐linear Resonances in a Paul Trap , 1996 .

[78]  Jian-Wei Pan,et al.  Memory-built-in quantum teleportation with photonic and atomic qubits , 2007, 0705.1256.

[79]  F. L. Walls,et al.  Radiation-Pressure Cooling of Bound Resonant Absorbers , 1978 .

[80]  C. F. Roos,et al.  Quantum teleportation with atoms: quantum process tomography , 2007, 0704.2027.

[81]  C. Monroe,et al.  Experimental Issues in Coherent Quantum-State Manipulation of Trapped Atomic Ions , 1997, Journal of research of the National Institute of Standards and Technology.

[82]  David J. Wineland,et al.  Sympathetic cooling of 9Be+ and 24Mg+ for quantum logic , 2003 .

[83]  Kuhn,et al.  Vacuum-stimulated raman scattering based on adiabatic passage in a high-finesse optical cavity , 2000, Physical review letters.

[84]  F. Schmidt-Kaler,et al.  Deterministic quantum teleportation with atoms , 2004, Nature.

[85]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[86]  Lu-Ming Duan,et al.  Scalable trapped ion quantum computation with a probabilistic ion-photon mapping , 2004, Quantum Inf. Comput..

[87]  Peter Maunz,et al.  Quantum networking with photons and trapped atoms (Invited) , 2007 .

[88]  C. Monroe,et al.  Observation of entanglement between a single trapped atom and a single photon , 2004, Nature.

[89]  H. Walther,et al.  A calcium ion in a cavity as a controlled single-photon source , 2004 .

[90]  I. Bloch.  Quantum coherence and entanglement with ultracold atoms in optical lattices , 2008, Nature.

[91]  E. Knill,et al.  Deterministic quantum teleportation of atomic qubits , 2004, Nature.

[92]  P. Maunz,et al.  Probabilistic quantum gates between remote atoms through interference of optical frequency qubits , 2006, quant-ph/0603285.

[93]  S. Olmschenk,et al.  Ion trap in a semiconductor chip , 2006 .

[94]  M. Ali Can,et al.  Single-particle entanglement , 2004 .

[95]  E. H. Pinnington,et al.  Beam-laser lifetime measurements for four resonance levels of Yb II , 1993 .

[96]  J Laurat,et al.  Direct measurement of decoherence for entanglement between a photon and stored atomic excitation. , 2006, Physical review letters.

[97]  T. Monz,et al.  Raman spectroscopy of a single ion coupled to a high-finesse cavity , 2008, 0810.2792.

[98]  K. Toyoda,et al.  Experimental study of the coherence of a terahertz-separated metastable-state qubit in C 40 a + , 2009 .

[99]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[100]  Kimble,et al.  Unconditional quantum teleportation , 1998, Science.

[101]  C. Tamm,et al.  Collisional Population Trapping and Optical Deexcitation of Ytterbium Ions in a Radiofrequency Trap , 1992 .

[102]  H. Weinfurter,et al.  Observation of entanglement of a single photon with a trapped atom. , 2006, Physical review letters.

[103]  L. Deslauriers,et al.  T-junction ion trap array for two-dimensional ion shuttling, storage, and manipulation , 2005, quant-ph/0508097.

[104]  C. Schuck,et al.  Entanglement of distant atoms by projective measurement: the role of detection efficiency , 2008, 0806.1052.

[105]  R. Blatt,et al.  Entangled states of trapped atomic ions , 2008, Nature.

[106]  H. Weinfurter,et al.  Experimental quantum teleportation , 1997, Nature.

[107]  W. C. Martin,et al.  Handbook of Basic Atomic Spectroscopic Data , 2005 .

[108]  David Leibrandt,et al.  Suppression of heating rates in cryogenic surface-electrode ion traps. , 2007, Physical review letters.

[109]  J. Cirac,et al.  Long-distance quantum communication with atomic ensembles and linear optics , 2001, Nature.

[110]  C. F. Roos,et al.  Experimental quantum-information processing withC43a+ions , 2008, 0804.1261.

[111]  Christian Kurtsiefer,et al.  Experimental study of anomalous heating and trap instabilities in a microscopic 137 Ba ion trap , 2002 .

[112]  M. Sellars,et al.  Accurate measurement of the 12.6 GHz "clock" transition in trapped (171)Yb(+) ions. , 1997, IEEE transactions on ultrasonics, ferroelectrics, and frequency control.

[113]  J. P. Home,et al.  Deterministic entanglement and tomography of ion-spin qubits , 2006 .

[114]  H. Weinfurter,et al.  Entanglement-based quantum communication over 144km , 2007 .

[115]  Michael Pepper,et al.  Electrically Driven Single-Photon Source , 2001, Science.

[116]  A. D. Boozer,et al.  Deterministic Generation of Single Photons from One Atom Trapped in a Cavity , 2004, Science.

[117]  Mann,et al.  Measurement of the Bell operator and quantum teleportation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[118]  P.T.H. Fisk,et al.  Accurate measurement of the 12.6 GHz "clock" transition in trapped /sup 171/Yb/sup +/ ions , 1997, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[119]  Wolfgang Dür,et al.  Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication , 1998 .

[120]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[121]  R. Blatt,et al.  Single-ion two-photon source. , 2007, Physical review letters.

[122]  Jörg Schmiedmayer,et al.  Demonstration of a stable atom-photon entanglement source for quantum repeaters. , 2007, Physical review letters.

[123]  N Ashby,et al.  Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance. , 2007, Physical review letters.

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

[125]  M. Hohenstatt,et al.  "Optical-sideband Cooling of Visible Atom Cloud Confined in Parabolic Well" , 1978 .

[126]  I. Chuang,et al.  Quantum Teleportation is a Universal Computational Primitive , 1999, quant-ph/9908010.

[127]  F. Schmidt-Kaler,et al.  Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap , 2007, 0712.3249.

[128]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[129]  L-M Duan.  Scaling ion trap quantum computation through fast quantum gates. , 2004, Physical review letters.

[130]  C. Monroe,et al.  Quantum interference of photon pairs from two remote trapped atomic ions , 2006, quant-ph/0608047.

[131]  D. Wineland,et al.  Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks; Metrology at the 17th Decimal Place , 2008, Science.

[132]  C. Simon,et al.  Quantum Repeaters based on Single Trapped Ions , 2009, 0902.3127.

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