Quantum computing with trapped ions

Physics Reports

Volumn 469, Issue 4, 2008, Pages 155-203

  Haffner H ^a,b,c,d   Roos, C F ^a,b   Blatt, R ^a,b  

^a ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^b UNIVERSITY OF INNSBRUCK   (Austria)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

Entanglement; Ion traps; Quantum computing and information

Indexed keywords

EID: 56249110212     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2008.09.003     Document Type: Review

References (252)

1. Acton M., Brickman K.-A., Haljan P., Lee P., Deslauriers L., and Monroe C. Near-perfect simultaneous measurement of a qubit register. Quant. Inf. Comp. 6 (2006) 465
2. Aolita L., Kim K., Benhelm J., Roos C.F., and Häffner H. High-fidelity ion-trap quantum computing with hyperfine clock states. Phys. Rev. A 76 4 (2007) 040303
3. Army Research Office (USA), 2005. ARDA quantum computation roadmap. http://qist.lanl.gov/qcomp_map.shtml
4. Barenco A., Bennett C.H., Cleve R., DiVincenzo D.P., Margolus N., Shor P., Sleator T., Smolin J.A., and Weinfurter H. Elementary gates for quantum computation. Phys. Rev. A 52 5 (1995) 3457-3467
5. Barrett M.D., Chiaverini J., Schaetz T., Britton J., Itano W.M., Jost J.D., Knill E., Langer C., Leibfried D., Ozeri R., and Wineland D.J. Deterministic quantum teleportation of atomic qubits. Nature 429 (2004) 737-739
6. + for quantum logic. Phys. Rev. A 68 (2003) 042302
7. +. Phys. Rev. A 62 (2000) 032503
8. Bell J. On the Einstein-Podolsky-Rosen paradox. Physics 1 (1965) 195
9. Bell J. Foundations of Quantum Mechanics (1971), Academic, New York pp. 171-181
10. Benhelm, J., 2008. Precision spectroscopy and quantum information processsing with trapped calcium ions. Ph.D. Thesis, Universität Innsbruck
11. +. Phys. Rev. A 75 (2007) 032506
12. + ions. Phys. Rev. A 77 (2008) 062306
13. Benhelm J., Kirchmair G., Roos C.F., and Blatt R. Towards fault-tolerant quantum computing with trapped ions. Nat. Phys. 4 (2008) 463
14. Bennett C.H., Brassard G., Crépeau C., Jozsa R., Peres A., and Wootters W. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70 (1993) 1895-1899
15. Bennett C.H., Brassard G., Popescu S., Schumacher B., Smolin J., and Wootters W.K. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76 5 (1996) 722-725
16. Bergquist J.C., Hulet R.G., Itano W.M., and Wineland D.J. Observation of quantum jumps in a single atom. Phys. Rev. Lett. 57 14 (1986) 1699-1702
17. Blatt R., and Wineland D. Entangled states of trapped atomic ions. Nature 453 (2008) 1008-1015
18. Blinov B., Deslauriers L., Lee P., Madsen M., Miller R., and Monroe C. Sympathetic cooling of trapped Cd isotopes. Phys. Rev. A 65 (2002) 040304
19. Blinov B.B., Moehring D.L., Duan L.-M., and Monroe C. Observation of entanglement between a single trapped atom and a single photon. Nature 428 6979 (2004) 153-157
20. Blume-Kohout, R., 2006. Optimal, reliable estimation of quantum states. arXiv:quant-ph/0611080
21. + ions. IEEE Trans. Instr. Meas. 40 (1991) 126
22. Brickman, K.-A., 2007. Implementation of grover's quantum search algorithm with two trapped ions. Ph.D. Thesis, University of Michigan
23. Brickman K.-A., Haljan P.C., Lee P.J., Acton M., Deslauriers L., and Monroe C. Implementation of Grover's quantum search algorithm in a scalable system. Phys. Rev. A 72 (2005) 050306-1
24. Britton, J., Leibfried, D., Beall, J., Blakestad, R.B., Bollinger, J.J., Chiaverini, J., Epstein, R.J., Jost, J.D., Kielpinski, D., Langer, C., Ozeri, R., Reichle, R., Seidelin, S., Shiga, N., Wesenberg, J.H., Wineland, D.J., 2006. A microfabricated surface-electrode ion trap in silicon. arXiv:quant-ph/0605170
25. Brossel J., Kastler A., and Winter J. Optical method of creating an inequality of population between Zeeman sub-levels of atomic ground states. J. Phys. Rad. 13 (1952) 668
26. Brune M., Nussenzveig P., Schmidt-Kaler F., Bernardot F., Maali A., Raimond J.M., and Haroche S. From Lamb shift to light shifts: Vacuum and subphoton cavity fields measured by atomic phase sensitive detection. Phys. Rev. Lett. 72 21 (1994) 3339-3342
27. Chiaverini J., Blakestad R.B., Britton J., Jost J.D., Langer C., Leibfried D., Ozeri R., and Wineland D. Surface-electrode architecture for ion-trap quantum information processing. Quant. Inf. Comp. 5 (2005) 419
28. Chiaverini J., Britton J., Leibfried D., Knill E., Barrett M.D., Blakestad R.B., Itano W.M., Jost J.D., Langer C., Ozeri R., Schaetz T., and Wineland D.J. Implementation of the semiclassical quantum Fourier transform in a scalable system. Science 308 (2005) 997-1000
29. Chiaverini J., Leibfried D., Schaetz T., Barrett M.D., Blakestad R.B., Britton J., Itano W.M., Jost J.D., Knill E., Langer C., Ozeri R., and Wineland D.J. Realization of quantum error correction. Nature 432 (2004) 602-605
30. Chiaverini J., W.E., and Lybarger J. Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays. Phys. Rev. A 77 (2008) 022324
31. Childs A.M., and Chuang I.L. Universal quantum computation with two-level trapped ions. Phys. Rev. A 63 (2000) 012306
32. Childs A.M., Chuang I.L., and Leung D.W. Realization of quantum process tomography in NMR. Phys. Rev. A 64 (2001) 012314
33. Chuang I.L., Gershenfeld N., and Kubinec M. Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80 15 (1998) 3408-3411
34. Chuang I.L., and Nielsen M.A. Prescription for experimental determination of the dynamics of a quantum black box. J. Modern Opt. 44 (1997) 2455
35. Chuang I.L., Vandersypen L.M.K., Zhou X., Leung D.W., and Lloyd S. Experimental realization of a quantum algorithm. Nature 393 (1998) 143
36. Cirac I., Zoller P., Kimble J., and Mabuchi H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78 (1997) 3221
37. Cirac J.I., and Zoller P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74 20 (1995) 4091-4094
38. Cirac J.I., and Zoller P. A scalable quantum computer with ions in an array of microtraps. Nature 404 (2000) 579-581
39. Clauser J., and Shimony A. Bell's theorem: Experimental tests and implications. Rep. Progr. Phys. 41 (1978) 1883
40. Clauser J.F., Horne M.A., Shimony A., and Holt R.A. Proposed experiement to test local hidden-variable theories. Phys. Rev. Lett. 23 (1969) 880
41. Coppersmith, D., 1994. An approximate Fourier transform useful in quantum factoring. Tech. Rep. IBM Research Report RC19642
42. Cory D.G., Price M.D., Maas W., Knill E., Laflamme R., Zurek W.H., Havel T.F., and Somaroo S.S. Experimental quantum error correction. Phys. Rev. Lett. 81 (1998) 2152
43. + mono-ion oscillator II (spontaneous quantum jumps). Bull. Am. Phys. Soc. 20 (1975) 60
44. DeMarco B., Ben-Kish A., Leibfried D., Meyer V., Rowe M., Jelenković B.M., Itano W.M., Britton J., Langer C., Rosenband T., and Wineland D.J. Experimental demonstration of a controlled-NOT wave-packet gate. Phys. Rev. Lett. 89 26 (2002) 267901
45. Deslauriers L., Olmschenk S., Stick D., Hensinger W.K., Sterk J., and Monroe C. Scaling and suppression of anomalous heating in ion traps. Phys. Rev. Lett. 97 (2006) 103007
46. Deutsch, D., 1989. Quantum computational networks. In: Proc. R. Soc. London A, 425, p. 73
47. Diedrich F., Bergquist J.C., Itano W.M., and Wineland D.J. Laser cooling to the zero-point energy of motion. Phys. Rev. Lett. 62 (1989) 403-406
48. Diedrich F., Peik E., Chen J.M., Quint W., and Walther H. Observation of a phase transition of stored laser-cooled ions. Phys. Rev. Lett. 59 26 (1987) 2931-2934
49. DiVincenzo D.P. Dogma and heresy in quantum computing. Quant. Inf. Comp. 1 (2001) 1
50. Donley E.A., Heavner T.P., Levi F., Tataw M.O., and Jefferts S.R. Double-pass acousto-optic modulator system. Rev. Sci. Inst. 76 (2005) 063112
51. Drees J., and Paul W. Beschleunigung von Elektronen in einem Plasmabetatron. Z. Phys. 180 (1964) 340
52. Drullinger R., Wineland D., and Bergquist J. High-resolution optical spectra of laser cooled ions. Appl. Phys. 22 (1980) 365
53. Duan L.-M., and Kimble H.J. Scalable photonic quantum computation through cavity-assisted interactions. Phys. Rev. Lett. 92 12 (2004) 127902
54. Dunn T.J., Walmsley I.A., and Mukamel S. Experimental-determination of the quantum-mechanical state of a molecular vibrational-mode using fluorescence tomography. Phys. Rev. Lett. 74 6 (1995) 884-887
55. Dür W., Vidal G., and Cirac J.I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62 (2000) 062314
56. Dyck R.S.V., D.L., Farnham J., Zafonte S.L., and Schwinberg P.B. Ultrastable superconducting magnet system for a Penning trap mass spectrometer. Rev. Sci. Inst. 70 (1999) 1665
57. Ekert A., and Jozsa R. Shor's quantum algorithm for factorising numbers. Rev. Modern Phys. 68 (1996) 733
58. Epstein R.J., Seidelin S., Leibfried D., Wesenberg J.H., Bollinger J.J., Amini J.M., Blakestad R.B., Britton J., Home J.P., Itano W.M., Jost J.D., Knill E., Langer C., Ozeri R., Shiga N., and Wineland D.J. Simplified motional heating rate measurements of trapped ions. Phys. Rev. A 76 (2007) 033411
59. Eschner J., Morigi G., Schmidt-Kaler F., and Blatt R. Laser cooling of trapped ions. J. Opt. Soc. Amer. B 20 (2003) 1003
60. Fano U. Description of states in quantum mechanics by density matrix and operator techniques. Rev. Modern Phys. 29 1 (1957) 74-93
61. Feynman R. Simulating physics with computers. Int. J. Theoret. Phys. 21 (1982) 467
62. Freeman R. Spin Choreography (1997), Spektrum, Oxford
63. Friedenauer H., Schmitz H., Glueckert J., Porras D., and Schaetz T. Simulating a quantum magnet with trapped ions. Nature Physics (2008) Advance Online Publicatio (AOP) on 27 July 2008
64. García-Ripoll J.J., Zoller P., and Cirac J.I. Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing. Phys. Rev. Lett. 91 15 (2003) 157901
65. García-Ripoll J.J., Zoller P., and Cirac J.I. Coherent control of trapped ions using off-resonant lasers. Phys. Rev. A 71 (2005) 062309
66. Garisto R., and Hardy L. Entanglement of projection and a new class of quantum erasers. Phys. Rev. A 60 (1999) 827
67. Gershenfeld N.A., and Chuang I.L. Bulk spin-resonance quantum computation. Science 275 5298 (1997) 350-356
68. Gisin N. Nonlocality criteria for quantum teleportation. Phys. Lett. A 210 (1996) 157
69. Gottesman, D., 1997. Stabilizer codes and quantum error correction. arXiv:quant-ph/9705052v1
70. Gottesman D., and Chuang I.L. Quantum teleportation is a universal computational primitive. Nature 402 (1999) 390
71. Greenberger D.M., Horne M.A., and Zeilinger A. Going beyond Bell's Theorem. Bell's Theorem, Quantum Theory and Conceptions of the Universe (1989), Kluwer Academic, Dordrecht 69-72
72. Griffiths R.B., and Niu C.-S. Semiclassical Fourier transform for quantum computation. Phys. Rev. Lett. 76 17 (1996) 3228-3231
73. +-ions. Ph.D. Thesis, Universität Innsbruck
74. + ions. Proc. R. Soc. Lond. A 361 (2003) 1363-1374
75. Häffner H., Beier T., Djekić S., Hermanspahn N., Kluge H.-J., Quint W., Stahl S., Verdú J., Valenzuela T., and Werth G. Double Penning trap technique for precise g factor determinations in highly charged ions. Eur. Phys. J. D 22 (2003) 163
76. Häffner H., Beier T., Hermanspahn N., Kluge H.J., Quint W., Stahl S., Verdu J., and Werth G. High-accuracy measurement of the magnetic moment anomaly of the electron bound in hydrogenlike carbon. Phys. Rev. Lett. 85 25 (2000) 5308-5311
77. Häffner H., Gulde S., Riebe M., Lancaster G., Becher C., Eschner J., Schmidt-Kaler F., and Blatt R. Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor. Phys. Rev. Lett. 90 (2003) 143602
78. Häffner H., Hänsel W., Roos C.F., Benhelm J., Chek-al-Kar D., Chwalla M., Körber T., Rapol U.D., Riebe M., Schmidt P.O., Becher C., Gühne O., Dür W., and Blatt R. Scalable multiparticle entanglement of trapped ions. Nature 438 7068 (2005) 643-646
79. Häffner H., Schmidt-Kaler F., Hänsel W., Roos C.F., Körber T., Chwalla M., Riebe M., Benhelm J., Rapol U.D., Becher C., and Blatt R. Robust entanglement. Appl. Phys. B 81 (2005) 151
80. Hahn E.L. Spin echoes. Phys. Rev. 80 (1950) 580
81. Haljan P.C., Brickman K.-A., Deslauriers L., Lee P.J., and Monroe C. Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion. Phys. Rev. Lett. 94 15 (2005) 153602
82. Haljan P.C., Lee P.J., Brickman K.-A., Acton M., Deslauriers L., and Monroe C. Entanglement of trapped-ion clock states. Phys. Rev. A 72 (2005) 062316
83. Hall J.L., Notcutt M., and Ye J. Improving laser coherence. In: Hinds E., Ferguson A., and Riis E. (Eds). Proceedings, International Conference on Laser Spectroscopy XVII (2006), World Scientific, Singapore 3
84. Hänsel, W., 2003. Private communication, Innsbruck
85. Happer W. Optical pumping. Rev. Modern Phys. 44 (1972) 169-249
86. Hawkins W.B., and Dicke R.H. The polarization of sodium atoms. Phys. Rev. 91 (1953) 1008
87. Heinzen D., and Wineland D. Quantum-limited cooling and detection of radio-frequency oscillations by laser-cooled ions. Phys. Rev. A 42 (1990) 2977
88. Hensinger W.K., Olmschenk S., Stick D., Hucul D., Yeo M., Acton M., Deslauriers L., and Monroe C. T-junction ion trap array for two-dimensional ion shuttling storage, and manipulation. Appl. Phys. Lett. 88 (2006) 034101
89. Herfurth F., Dilling J., Kellerbauer A., Bollen G., Henry S., Kluge H.-J., Lamour E., Lunney D., Moore R.B., Scheidenberger C., Schwarz S., Sikler G., and Szerypo J. A linear radiofrequency ion trap for accumulation, bunching, and emittance improvement of radioactive ion beams. Nucl. Instrum. Methods Phys. Res., Sect. A 469 (2001) 254-275
90. Home J.P., McDonnell M.J., Lucas D.M., Imreh G., Keitch B.C., Szwer D.J., Thomas N.R., Webster S.C., Stacey D.N., and Steane A.M. Deterministic entanglement and tomography of ion spin qubits. New J. Phys. 8 (2006) 188
91. Home J.P., and Steane A.M. Electrode configurations for fast separation of trapped ions. Quant. Inf. Comp. 6 (2006) 289
92. Hornekaer L., Kjaergaard N., Thommesen A.M., and Drewsen M. Structural properties of two-component Coulomb crystals in linear Paul traps. Phys. Rev. Lett. 86 10 (2001) 1994-1997
93. Hradil Z. Quantum-state estimation. Phys. Rev. A 55 3 (1997) R1561-R1564
94. Huber G., Deuschle T., Schnitzler W., Reichle R., Singer K., and Schmidt-Kaler F. Transport of ions in a segmented linear Paul trap in printed-circuit-board technology. New J. Phys. 10 (2008) 013004
95. Hucul D., Yeo M., Hensinger W., Rabchuk J., Olmschenk S., and Monroe C. On the transport of atomic ions in linear and multidimensional ion trap arrays. Quant. Inf. Comp. 8 (2008) 501-578
96. Hume D.B., Rosenband T., and Wineland D.J. High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements. Phys. Rev. Lett. 99 12 (2007) 120502
97. James D.F.V. Quantum dynamics of cold trapped ions with application to quantum computation. Appl. Phys. B 66 (1998) 181
98. James D.F.V., Kwiat P.G., Munro W.J., and White A.G. Measurement of qubits. Phys. Rev. A 64 5 (2001) 052312
99. Jonathan D., Plenio M.B., and Knight P.L. Fast quantum gates for cold trapped ions. Phys. Rev. A 62 (2000) 042307
100. Jones J., and Mosca M. Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer. J. Chem. Phys. 109 (1998) 1648
101. Jones J.A. NMR quantum computation: A critical evaluation. Fortschr. Phys. 48 (2000) 909
102. Kaplan A., Fredslund Andersen M., and Davidson N. Suppression of inhomogeneous broadening in rf spectroscopy of optically trapped atoms. Phys. Rev. A 66 (2002) 045401
103. Kastler A. Quelques suggestions concernant la production optique et la détection optique d'une inégalité de population des niveaux de quantification spatiale des atomes. J. Phys. Rad. 11 (1950) 255
104. Khaneja N., Reiss T., Kehlet C., Schulte-Herbrüggen T., and Glaser S.J. Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172 (2005) 296
105. Kielpinski, D., 2001. Entanglement and decoherence in a trapped-ion quantum register. Ph.D. Thesis, Department of Physics, University of Colorado, Boulder
106. Kielpinski D., Meyer V., Rowe M.A., Sackett C.A., Itano W.M., Monroe C., and Wineland D.J. A decoherence-free quantum memory using trapped ions. Science 291 5506 (2001) 1013-1015
107. Kielpinski D., Monroe C., and Wineland D.J. Architecture for a large-scale ion-trap quantum computer. Nature 417 6890 (2002) 709-711
108. Kiesel N., Schmid C., Weber U., Ursin R., and Weinfurter H. Linear optics controlled-phase gate made simple. Phys. Rev. Lett. 95 (2005) 210505
109. King, B., 1999. Quantum state engineering and information processing with trapped ions. Ph.D. Thesis, Department of Physics, University of Colorado, Boulder
110. Kjærgaard N., Hornekær L., Thommesen A., Videsen Z., and Drewsen M. Isotope selective loading of an ion trap using resonance-enhanced two-photon ionization. Appl. Phys. B 71 (2000) 207
111. Knill E. Quantum computing with realistically noisy devices. Nature 434 7029 (2005) 39-44
112. Knill E., Laflamme R., Martinez R., and Negrevergne C. Benchmarking quantum computers: The five-qubit error correcting code. Phys. Rev. Lett. 86 25 (2001) 5811-5814
113. Knill E., Laflamme R., and Milburn G.J. A scheme for efficient quantum computation with linear optics. Nature 409 6816 (2001) 46-52
114. Knill E., Leibfried D., Reichle R., Britton J., Blakestad R.B., Jost J.D., Langer C., Ozeri R., Seidelin S., and Wineland D.J. Randomized benchmarking of quantum gates. Phys. Rev. A 77 (2008) 012307
115. + ion in a high finesse cavity. Phys. Rev. Lett. 92 20 (2004) 203002
116. +. Phys. Rev. A 71 3 (2005) 032504
117. Labaziewicz J., Ge Y., Antohi P., Leibrandt D., Brown K., and Chuang I. Suppression of heating rates in cryogenic surface-electrode ion traps. Phys. Rev. Lett. 100 (2008) 013001
118. Labaziewicz, J., Ge, Y., Leibrandt, D., Wang, S.X., Shewmon, R., Chuang, I.L., 2008b. Temperature dependence of electric field noise above gold surfaces. arXiv: 0804.2665v1
119. Langer C., Ozeri R., Jost J.D., Chiaverini J., Demarco B., Ben-Kish A., Blakestad R.B., Britton J., Hume D.B., Itano W.M., Leibfried D., Reichle R., Rosenband T., Schaetz T., Schmidt P.O., and Wineland D.J. Long-lived qubit memory using atomic ions. Phys. Rev. Lett. 95 (2005) 060502
120. Langer, C.E., 2006. High fidelity quantum information processing with trapped ions. Ph.D. Thesis, Department of Physics, University of Colorado, Boulder
121. Lanyon B.P., Weinhold T.J., Langford N.K., O'Brien J.L., Resch K.J., Gilchrist A., and White A.G. Manipulating biphotonic qutrits. Phys. Rev. Lett. 100 6 (2008) 060504
122. Larson D.J., Bergquist J.C., Bollinger J.J., Itano W.M., and Wineland D.J. Sympathetic cooling of trapped ions: A laser-cooled two-species nonneutral ion plasma. Phys. Rev. Lett. 57 1 (1986) 70-73
123. Lee, P.J., 2006. Quantum information processing with two trapped cadmium ions. Ph.D. Thesis, University of Michigan
124. Lee P.J., Brickman K.A., Deslauriers L., Haljan P.C., Duan L., and Monroe C. Phase control of trapped ion quantum gates. J. Opt. B 7 (2005) 371
125. Leibfried D., Barrett M.D., Schaetz T., Britton J., Chiaverini J., Itano W.M., Jost J.D., Langer C., and Wineland D.J. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304 5676 (2004) 1476-1478
126. Leibfried D., Blatt R., Monroe C., and Wineland D. Quantum dynamics of single trapped ions. Rev. Modern Phys. 75 (2003) 281
127. Leibfried D., DeMarco B., Meyer V., Lucas D., Barrett M., Britton J., Itano W.M., Jelenković B., Langer C., Rosenband T., and Wineland D.J. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422 (2003) 412-415
128. Leibfried D., DeMarco B., Meyer V., Rowe M., Ben-Kish A., Britton J., Itano W.M., Jelenković B., Langer C., Rosenband T., and Wineland D.J. Trapped-ion quantum simulator: Experimental application to nonlinear interferometers. Phys. Rev. Lett. 89 24 (2002) 247901
129. Leibfried D., Knill E., Ospelkaus C., and Wineland D.J. Transport quantum logic gates for trapped ions. Phys. Rev. A 76 (2007) 032324
130. Leibfried D., Knill E., Seidelin S., Britton J., Blakestad R.B., Chiaverini J., Hume D.B., Itano W.M., Jost J.D., Langer C., Ozeri R., Reichle R., and Wineland D.J. Creation of a six-atom 'Schrödinger cat' state. Nature 438 (2005) 639-642
131. Leibfried D., Meekhof D.M., King B.E., Monroe C., Itano W.M., and Wineland D.J. Experimental determination of the motional quantum state of a trapped atom. Phys. Rev. Lett. 77 21 (1996) 4281-4285
132. + using a single trapped ion. Phys. Rev. A 72 (2005) 012509
133. Levitt M. Composite pulses. Prog. NMR Spectrosc. 18 (1986) 61
134. Levitt M., and Freeman R. NMR population inversion using a composite pulse. J. Magn. Reson. 33 (1979) 473
135. Linden N., and Popescu S. Good dynamics versus bad kinematics: Is entanglement needed for quantum computation?. Phys. Rev. Lett. 87 (2001) 047901
136. Lloyd S. Universal quantum simulators. Science 273 5278 (1996) 1073-1078
137. Lloyd S., and Braunstein S.L. Quantum computation over continuous variables. Phys. Rev. Lett. 82 (1999) 1784
138. Loss D., and DiVincenzo D.P. Quantum computation with quantum dots. Phys. Rev. A 57 (1998) 120
139. Lucas, D.M., Keitch, B.C., Home, J.P., Imreh, G., McDonnell, M.J., Stacey, D.N., Szwer, D.J., Steane, A.M., 2007. A long-lived memory qubit on a low-decoherence quantum bus. arXiv: 0710.4421v1
140. Majer J., Chow J.M., Gambetta J.M., Koch J., Johnson B.R., Schreier J.A., Frunzio L., Schuster D.I., Houck A.A., Wallraff A., Blais A., Devoret M.H., Girvin S.M., and Schoelkopf R.J. Coupling superconducting qubits via a cavity bus. Nature 449 7161 (2007) 443-447
141. Makhlin Y., Schön G., and Shnirman A. Quantum-state engineering with Josephson-junction devices. Rev. Modern Phys. 73 (2001) 357
142. Marzoli I., Cirac J.I., Blatt R., and Zoller P. Laser cooling of trapped three-level ions: Designing two-level systems for sideband cooling. Phys. Rev. A 49 4 (1994) 2771-2779
143. Massar S., and Popescu S. Optimal extraction of information from finite quantum ensembles. Phys. Rev. Lett. 74 (1995) 1259
144. Matsukevich D., Maunz P., Moehring D.L., Olmschenk S., and Monroe C. Bell inequality violation with two remote atomic qubits. Phys. Rev. Lett. 100 (2008) 150404
145. Maunz P., Moehring D.L., Olmschenk S., Younge K.C., Matsukevich D.N., and Monroe C. Quantum interference of photon pairs from two remote trapped atomic ions. Nature Phys. 3 (2007) 538
146. Meshkov I. Electron cooling-Recent developments and trends. Nucl. Instrum. Methods Phys. Res., Sect. A 391 (1997) 1
147. Milburn G.J., Schneider S., and James D.F. Ion trap quantum computing with warm ions. Fortschr. Phys. 48 (2000) 801
148. Mintert F., and Wunderlich C. Ion-trap quantum logic using long-wavelength radiation. Phys. Rev. Lett. 87 25 (2001) 257904
149. Moehring D.L., Maunz P., Olmschenk S., Younge K.C., Matsukevich D.N., Duan L.-M., and Monroe C. Entanglement of single-atom quantum bits at a distance. Nature 449 7158 (2007) 68-71
150. Mohseni M., and Lidar D.A. Direct characterization of quantum dynamics. Phys. Rev. Lett. 97 17 (2006) 170501
151. Mølmer K., and Sørensen A. Multiparticle entanglement of hot trapped ions. Phys. Rev. Lett. 82 (1999) 1835
152. Monroe, C., Itano, W.M., Kielpinski, D., King, B.E., Leibfried, D., Myatt, C.J., Turchette, Q.A., Wineland, D.J., Wood, C.S., 1999. Quantum logic with a few trapped ions. AIP Conference Proceedings CP457, 378
153. Monroe C., Leibfried D., King B., Meekhof D., Itano W., and Wineland D. Simplified quantum logic with trapped ions. Phys. Rev. A 55 (1997) R2489
154. Monroe C., Meekhof D.M., King B.E., Itano W.M., and Wineland D.J. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75 25 (1995) 4714-4717
155. Monroe C., Meekhof D.M., King B.E., Jefferts S.R., Itano W.M., Wineland D.J., and Gould P.L. Resolved-sideband Raman cooling of a bound atom to the 3D zero-point energy. Phys. Rev. Lett. 75 22 (1995) 4011-4014
156. Morigi G., Eschner J., and Keitel C. Ground state laser cooling using electromagnetically induced transparency. Phys. Rev. Lett. 85 21 (2000) 4458-4461
157. Myerson A.H., Szwer D.J., Webster S.C., Allcock D.T.C., Curtis M.J., Imreh G., Sherman J.A., Stacey D.N., Steane A.M., and Lucas D.M. High-fidelity readout of trapped-ion qubits. Phys. Rev.Lett. 100 (2008) 200502
158. Nagourney W., Sandberg J., and Dehmelt H. Shelved optical electron amplifier: Observation of quantum jumps. Phys. Rev. Lett. 56 26 (1986) 2797-2799
159. Nebendahl, V., Häffner, H., Roos, C.F., 2008. Optimal control of entangling operations for trapped ion quantum computing. arXiv:0809.1414v3 [quant-ph]
160. Neuhauser W., Hohenstatt M., Toschek P., and Dehmelt H. Optical-sideband cooling of visible atom cloud confined in parabolic well. Phys. Rev. Lett. 41 (1978) 233
161. Nielsen M.A., and Chuang I.L. Quantum Computation and Quantum Information (2000), Cambridge Univ. Press, Cambridge
162. Notcutt M., Ma L.-S., Ye J., and Hall J.L. Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity. Opt. Lett. 30 (2005) 1815-1817
163. O'Brien J.L., Pryde G.J., Gilchrist A., James D.F.V., Langford N., Ralph T., and White A.G. Quantum process tomography of a controlled-NOT gate. Phys. Rev. Lett. 93 (2004) 080502
164. Ospelkaus, C., Langer, C.E., Amini, J.M., Brown, K.R., Leibfried, D., Wineland, D.J., 2008. Trapped-ion quantum logic gates based on oscillating magnetic fields. arXiv:0805.2165
165. Ozeri R., Itano W.M., Blakestad R.B., Britton J., Chiaverini J., Jost J.D., Langer C., Leibfried D., Reichle R., Seidelin S., Wesenberg J.H., and Wineland D.J. Errors in trapped-ion quantum gates due to spontaneous photon scattering. Phys. Rev. A 75 (2007) 042329
166. Ozeri R., Langer C., Jost J.D., DeMarco B., Ben-Kish A., Blakestad B.R., Britton J., Chiaverini J., Itano W.M., Hume D.B., Leibfried D., Rosenband T., Schmidt P.O., and Wineland D.J. Hyperfine coherence in the presence of spontaneous photon scattering. Phys. Rev. Lett. 95 3 (2005) 030403
167. In: Paris M., and Rehacek J. (Eds). Quantum State Estimation. Lecture Notes in Physics (2004), Springer
168. Pearson C.E., Leibrandt D.R., Bakr W.S., Mallard W.J., Brown K.R., and Chuang I.L. Experimental investigation of planar ion traps. Phys. Rev. A 73 (2006) 032307
169. Peik E., Abel J., Becker T., von Zanthier J., and Walther H. Sideband cooling of ions in radio-frequency traps. Phys. Rev. A 60 (1999) 439
170. Petta J.R., Johnson A.C., Taylor J.M., Laird E.A., Yacoby A., Lukin M.D., Marcus C.M., Hanson M.P., and Gossard A.C. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309 5744 (2005) 2180-2184
171. Plantenberg J.H., de Groot P.C., Harmans C.J.P.M., and Mooij J.E. Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits. Nature 447 7146 (2007) 836-839
172. Porras D., and Cirac J.I. Bose-Einstein condensation and strong-correlation behavior of phonons in ion traps. Phys. Rev. Lett. 93 (2004) 263602
173. Poyatos J.F., Cirac J.I., and Zoller P. Complete characterization of a quantum process: The two-bit quantum gate. Phys. Rev. Lett. 78 (1997) 390
174. Raimond J.M., Brune M., and Haroche S. Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Modern Phys. 73 (2001) 565
175. Raizen M.C., Bergquist J.C., Gilligan J.M., Itano W.M., and Wineland D.J. Linear trap for high-accuracy spectroscopy of stored ions. J. Modern Opt. 39 (1992) 233
176. Raizen M.G., Gilligan J.M., Bergquist J.C., Itano W.M., and Wineland D.J. Ionic crystals in a linear Paul trap. Phys. Rev. A 45 9 (1992) 6493-6501
177. Rauschenbeutel A., Nogues G., Osnaghi S., Bertet P., Brune M., Raimond J.M., and Haroche S. Step-by-step engineered multiparticle entanglement. Science 288 5473 (2000) 2024-2028
178. Reichle R., Leibfried D., Blakestad R., Britton J., Jost J., Knill E., Langer C., Ozeri R., Seidelin S., and Wineland D. Transport dynamics of single ions in segmented microstructured paul trap arrays. Fortschr. Phys. 54 (2006) 666
179. Reichle R., Leibfried D., Knill E., Britton J., Blakestad R.B., Jost J.D., Langer C., Ozeri R., Seidelin S., and Wineland D.J. Experimental purification of two-atom entanglement. Nature 443 7113 (2006) 838-841
180. Retzker A., Solano E., and Reznik B. Tavis-cummings model and collective multiqubit entanglement in trapped ions. Phys. Rev. A 75 (2007) 022312
181. Riebe M., Chwalla M., Benhelm J., Häffner H., Hänsel W., Roos C.F., and Blatt R. Teleportation with atoms: Quantum process tomography. New J. Phys. 9 (2007) 211
182. Riebe M., Häffner H., Roos C.F., Hänsel W., Benhelm J., Lancaster G.P.T., Körber T.W., Becher C., Schmidt-Kaler F., James D.F.V., and Blatt R. Deterministic quantum teleportation with atoms. Nature 429 6993 (2004) 734-737
183. Riebe M., Kim K., Schindler P., Monz T., Schmidt P.O., Körber T.K., Hänsel W., Häffner H., Roos C.F., and Blatt R. Process tomography of ion trap quantum gates. Phys. Rev. Lett. 97 (2006) 220407
184. Rohde H., Gulde S.T., Roos C.F., Barton P.A., Leibfried D., Eschner J., Schmidt-Kaler F., and Blatt R. Sympathetic ground state cooling and coherent manipulation with two-ion-crystal. J. Opt. B 3 (2001) S34
185. Roos, C., 2000. Controlling the quantum state of trapped ions. Ph.D. Thesis, Universität Innsbruck
186. Roos C., Zeiger T., Rohde H., Nägerl H., Eschner J., Leibfried D., Schmidt-Kaler F., and Blatt R. Quantum state engineering on an optical transition and decoherence in a Paul trap. Phys. Rev. Lett. 83 (1999) 4713
187. Roos C.F. Ion trap quantum gates with amplitude-modulated laser beams. New J. Phys. 10 (2008) 013002
188. Roos C.F., Chwalla M., Kim K., Riebe M., and Blatt R. Designer atoms' for quantum metrology. Nature 443 7109 (2006) 316-319
189. Roos C.F., Lancaster G.P.T., Riebe M., Häffner H., Hänsel W., Gulde S., Becher C., Eschner J., Schmidt-Kaler F., and Blatt R. Bell states of atoms with ultralong lifetimes and their tomographic state analysis. Phys. Rev. Lett. 92 22 (2004) 220402
190. Roos C.F., Leibfried D., Mundt A., Schmidt-Kaler F., Eschner J., and Blatt R. Experimental demonstration of ground state laser cooling with electromagnetically induced transparency. Phys. Rev. Lett. 85 (2000) 5547-5550
191. Roos C.F., Riebe M., Häffner H., Hänsel W., Benhelm J., Lancaster G.P.T., Becher C., Schmidt-Kaler F., and Blatt R. Control and measurement of three-qubit entangled states. Science 304 5676 (2004) 1478-1480
192. + ions in a radio-frequency trap. Phys. Rev. Lett. 94 5 (2005) 053001
193. Rowe M.A., Ben-Kish A., DeMarco B., Leibfried D., Meyer V., Beall J., Britton J., Hughes J., Itano W.M., Jelenković B., Langer C., Rosenband T., and Wineland D.J. Transport of quantum states and separation of ions in a dual RF ion trap. Quant. Inf. Comp. 2 (2002) 257-271
194. Rowe M.A., Kielpinski D., Meyer V., Sackett C.A., Itano W.M., Monroe C., and Wineland D.J. Experimental violation of a Bell's inequality with efficient detection. Nature 409 6822 (2001) 791-794
195. Sackett C.A., Kielpinski D., King B.E., Langer C., Meyer V., Myatt C.J., Rowe M., Turchette Q.A., Itano W.M., Wineland D.J., and Monroe C. Experimental entanglement of four particles. Nature 404 (2000) 256-259
196. Šašura M., and Bužek V. Tutorial review: Cold trapped ions as quantum information processors. J. Modern Opt. 49 (2002) 1593
197. Sauter T., Neuhauser W., Blatt R., and Toschek P.E. Observation of quantum jumps. Phys. Rev. Lett. 57 14 (1986) 1696-1698
198. Schaetz T., Barrett M.D., Leibfried D., Britton J., Chiaverini J., Itano W.M., Jost J.D., Knill E., Langer C., and Wineland D.J. Enhanced quantum state detection efficiency through quantum information processing. Phys. Rev. Lett. 94 1 (2005) 010501
199. Schaetz T., Leibfried D., Chiaverini J., Barrett M., Britton J., DeMarco B., Itano W., Jost J., Langer C., and Wineland D. Towards a scalable quantum computer/simulator based on trapped ions. Appl. Phys. B 79 (2004) 923
200. Schmidt P.O., Rosenband T., Langer C., Itano W.M., Bergquist J.C., and Wineland D.J. Spectroscopy using quantum logic. Science 309 5735 (2005) 749-752
201. + ions. J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 623
202. Schmidt-Kaler F., Häffner H., Gulde S., Riebe M., Lancaster G., Eschner J., Becher C., and Blatt R. Quantized ac-Stark shifts and their use for multiparticle entanglement and quantum gates. Europhys. Lett. 65 (2004) 587
203. Schmidt-Kaler F., Häffner H., Gulde S., Riebe M., Lancaster G.P.T., Deuschle T., Becher C., Hänsel W., Eschner J., Roos C.F., and Blatt R. How to realize a universal quantum gate with trapped ions. Appl. Phys. B 77 (2003) 789
204. Schmidt-Kaler F., Häffner H., Riebe M., Gulde S., Lancaster G.P.T., Deuschle T., Becher C., Roos C.F., Eschner J., and Blatt R. Realization of the Cirac-Zoller controlled-NOT quantum gate. Nature 422 6930 (2003) 408-411
205. Schrader D., Dotsenko I., Khudaverdyan M., Miroshnychenko Y., Rauschenbeutel A., and Meschede D. Neutral atom quantum register. Phys. Rev. Lett. 92 (2004) 150501
206. Schulz S., Poschinger U., Singer K., and Schmidt-Kaler F. Optimization of segmented linear Paul traps and transport of stored particles. Fortschr. Phys. 54 (2006) 648
207. Seidelin S., Chiaverini J., Reichle R., Bollinger J.J., Leibfried D., Britton J., Wesenberg J.H., Blakestad R.B., Epstein R.J., Hume D.B., Itano W.M., Jost J.D., Langer C., Ozeri R., Shiga N., and Wineland D.J. Microfabricated surface-electrode ion trap for scalable quantum information processing. Phys. Rev. Lett. 96 25 (2006) 253003
208. Sengstock K., Sterr U., Rieger V., Bettermann D., Müller J., and Ertmer W. Optical ramsey spectroscopy on laser trapped and thermal Mg-atoms. Appl. Phys. B 59 (1994) 99
209. Shockley W. Currents to conductors induced by a moving point charge. J. Appl. Phys. 9 (1938) 635
210. Shor P.W. Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, Nov. 20-22 (1994), IEEE Computer Society Press 124-134
211. Shor P.W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52 4 (1995) R2493-R2496
212. Smithey D.T., Beck M., Raymer M.G., and Faridani A. Measurement of the Wigner distribution and the density-matrix of a light mode using optical homodyne tomography-Application to squeezed states and the vacuum. Phys. Rev. Lett. 70 9 (1993) 1244-1247
213. Solano, E., 2005. Private communication, Munich
214. Solano E., de Matos Filho R.L., and Zagury N. Deterministic Bell states and measurement of the motional state of two trapped ions. Phys. Rev. A 59 (1999) R2539-R2543
215. Sørensen A., and Mølmer K. Quantum computation with ions in thermal motion. Phys. Rev. Lett. 82 (1999) 1971
216. Sørensen A., and Mølmer K. Entanglement and quantum computation with ions in thermal motion. Phys. Rev. A 62 (2000) 022311
217. Sørensen A.S., van der Wal C.H., Childress L.I., and Lukin M.D. Capacitive coupling of atomic systems to mesoscopic conductors. Phys. Rev. Lett. 92 6 (2004) 063601
218. Staanum P., and Drewsen M. Trapped-ion quantum logic utilizing position-dependent ac-Stark shifts. Phys. Rev. A 66 (2002) 040202
219. Staanum P., Drewsen M., and Mølmer K. Geometric quantum gate for trapped ions based on optical dipole forces induced by gaussian laser beams. Phys. Rev. A 70 (2004) 052327
220. Steane A. The ion trap quantum information processor. Appl. Phys. B 64 (1997) 623
221. Steane A., Roos C.F., Stevens D., Mundt A., Leibfried D., Schmidt-Kaler F., and Blatt R. Speed of ion-trap quantum-information processors. Phys. Rev. A 62 (2000) 042305
222. Steane A.M. Error correcting codes in quantum theory. Phys. Rev. Lett. 77 5 (1996) 793-797
223. Steane, A.M., 2004. How to build a 300 bit, 1 giga-operation quantum computer. arXiv:quant-ph/0412165
224. Steffen M., Ansmann M., Bialczak R.C., Katz N., Lucero E., McDermott R., Neeley M., Weig E.M., Cleland A.N., and Martinis J.M. Measurement of the entanglement of two superconducting qubits via state tomography. Science 313 5792 (2006) 1423-1425
225. Stenholm S. Semiclassical theory of laser cooling. Rev. Modern Phys. 58 (1986) 699
226. Thompson R.C. Precision measurement aspects of ion traps. Meas. Sci. Technol. 1 (1990) 93
227. Tian L., Blatt R., and Zoller P. Scalable ion trap quantum computing without moving ions. Eur. Phys. J. D 32 (2005) 201
228. Tian L., Rabl P., Blatt R., and Zoller P. Interfacing quantum-optical and solid-state qubits. Phys. Rev. Lett. 92 24 (2004) 247902
229. Timoney N., Elman V., Glaser S., Weiss C., Johanning M., Neuhauser W., and Wunderlich C. Error-resistant single-qubit gates with trapped ions. Phys. Rev. A 77 (2008) 052334
230. Tittel W., Brendel J., Zbinden H., and Gisin N. Violation of Bell inequalities by photons more than 10 km apart. Phys. Rev. Lett. 81 17 (1998) 3563-3566
231. Tittel W., and Weihs G. Photonic entanglement for fundamental tests and quantum communication. Quant. Inf. Comp. 1 (2001) 3
232. Turchette Q., Wood C., King B., Myatt C., Leibfried D., Itano W., Monroe C., and Wineland D. Deterministic entanglement of two ions. Phys. Rev. Lett. 81 (1998) 3631
233. Turchette Q.A., Kielpinski B.E., King D., Leibfried D.M., Meekhof C.J., Myatt M.A., Rowe C.A., Sackett C.S., Wood W.M., Itano C., Monroe D.J., and Wineland. Heating of trapped ions from the quantum ground state. Phys. Rev. A 61 (2000) 063418
234. Vandersypen L.M., Steffen M., Breyta G., Yannoni C.S., Sherwood M.H., and Chuang I.L. Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance. Nature 414 6866 (2001) 883-887
235. Wallraff A., Schuster D.I., Blais A., Frunzio L., Huang R.-S., Majer J., Kumar S., Girvin S.M., and Schoelkopf R.J. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431 7005 (2004) 162-167
236. Walther P., Resch K.J., Rudolph T., Schenck E., Weinfurter H., Vedral V., Aspelmeyer M., and Zeilinger A. Experimental one-way quantum computing. Nature 434 7030 (2005) 169-176
237. Warren W.S. The usefulness of NMR quantum computing. Science 277 (1997) 1688
238. Weber E.W. Optical pumping of ions. Phys. Rev. 32 (1977) 123
239. Weihs G., Jennewein T., Simon C., Weinfurter H., and Zeilinger A. Violation of Bell's inequality under strict Einstein locality conditions. Phys. Rev. Lett. 81 23 (1998) 5039-5043
240. Wesenberg J.H., Epstein R.J., Leibfried D., Blakestad R.B., Britton J., Home J.P., Itano W.M., Jost J.D., Knill E., Langer C., Ozeri R., Seidelin S., and Wineland D.J. Fluorescence during Doppler cooling of a single trapped atom. Phys. Rev. A 76 (2007) 053416
241. White A.G., James D.F.V., Eberhard P.H., and Kwiat P.G. Nonmaximally entangled states: Production, characterization, and utilization. Phys. Rev. Lett. 83 16 (1999) 3103-3107
242. Wineland D., Bergquist J., Itano W., and Drullinger R. Double-resonance and optical-pumping experiments on electromagnetically confined, laser-cooled ions. Opt. Lett. 5 (1980) 254
243. Wineland D.J., Barrett M., Britton J., Chiaverini J., DeMarco B., Itano W.M., Jelenković B., Langer C., Leibfried D., Meyer V., Rosenband T., and Schätz T. Quantum information processing with trapped ions. Proc. R. Soc. Lond. A 361 1808 (2003) 1349-1361
244. Wineland D.J., Bergquist J.C., Itano W.M., Bollinger J.J., and Manney C.H. Atomic ion Coulomb clusters in an ion trap. Phys. Rev. Lett. 59 26 (1987) 2935-2938
245. Wineland D.J., and Dehmelt H.G. Principles of the stored ion calorimeter. J. App. Phys. 46 (1975) 919
246. Wineland D.J., and Itano W.M. Laser cooling of atoms. Phys. Rev. A 21 (1979) 1521
247. Wineland D.J., Monroe C., Itano W.M., Leibfried D., King B., and Meekhof D.M. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl. Inst. Stand. Technol. 103 (1998) 259
248. Wootters W.K., and Fields B.D. Optimal state determination by mutually unbiased measurements. Ann. Phys. 191 2 (1989) 363-381
249. Young B., Cruz F., Itano W., and Bergquist J. Visible lasers with subhertz linewidths. Phys. Rev. Lett. 82 (1999) 3799
250. + optical frequency standard: Recent progress. In: Blatt R., Eschner J., Leibfried D., and Schmidt-Kaler F. (Eds). Laser Spectroscopy, Proceedings of the XIV International Conference (1999), World Scientific, Singapore 61
251. Zeilinger A., Horne M., and Greenberger D. Higher-order quantum entanglement. NASA Conf. Publ. 3135 (1992) 73
252. Zhu S.-L., Monroe C., and Duan L.-M. Arbitrary-speed quantum gates within large ion crystals through minimum control of laser beams. Europhys. Lett. 73 (2006) 485