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## Quantum Information Processing and Quantum Control with Trapped Atomic Ions

Venue: | Phys. Scr. 2009 |

Citations: | 1 - 0 self |

### Citations

1178 |
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Citation Context ... a variable number of detection cycles to reach a certain measurement fidelity. 3.2. Tests of quantum correlations and entanglement With the continued interest in Einstein–Podolsky–Rosen correlations =-=[92]-=- and Bell-type inequalities [93], trapped ions have been able to probe these fundamental aspects of quantum mechanics in some new regimes. By producing entangled pairs of ions, Bell’s inequalities of ... |

1109 | Algorithms for quantum computation: discrete logarithms and factoring
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Citation Context ...lour only in the electronic version.) 1. Introduction Following Shor’s development of a quantum-mechanical algorithm for efficient number factoring and its recognized potential practical applications =-=[1]-=-, there was a dramatic increase of activity in the field of quantum information science. The possible realization of general-purpose quantum information processing (QIP) is now explored in many settin... |

1001 |
On the Einstein Podolsky Rosen paradox
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Citation Context ...cycles to reach a certain measurement fidelity. 3.2. Tests of quantum correlations and entanglement With the continued interest in Einstein–Podolsky–Rosen correlations [92] and Bell-type inequalities =-=[93]-=-, trapped ions have been able to probe these fundamental aspects of quantum mechanics in some new regimes. By producing entangled pairs of ions, Bell’s inequalities of the CHSH form [94] have been mea... |

433 | K.: Quantum mechanics helps in search for a needle in a haystack. Phys
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Citation Context ...be required to reach fault-tolerant levels. 3. Beginning applications Although primary drivers for the field of QIP have been a factoring machine [1] and a device for performing unstructured searches =-=[78, 79]-=-, it is very likely that other applications will emerge first. Some of these are described briefly here. 3.1. Spectroscopy and metrology Some potential applications are motivated by the idea of using ... |

135 |
Simulating Physics with Computers, Int
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Citation Context ...ors [101]. 3.3. Towards quantum simulation In the early 1980s, Richard Feynman proposed that one quantum system might be used to efficiently simulate the dynamics of other quantum systems of interest =-=[102, 103]-=-. This is now a highly anticipated application of QIP, and will likely occur well before useful factorization is performed. Of course the universality of a large-scale quantum computer will allow it t... |

79 | Experimental issues in coherent quantum-state manipulation of trapped atomic ions.
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Citation Context ...io frequency (RF) transition caused the electron’s cyclotron-motion quantum state to change conditioned on its spin state. This example has a close relation to the current trapped-ion QIP experiments =-=[10, 17]-=-. By 1990, trapped-ion experiments had reached the point where the mechanical motion of the ions could be cooled to the ground state [18]; this could be verified by an excitation of the ion’s internal... |

75 | The physical implementation of quantum computation
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Citation Context ...rocessing (QIP) is now explored in many settings, including condensed-matter, atomic and optical systems. Trapped atomic ions have proven to be a useful system in which to study the required elements =-=[2]-=- for such a device. Ions are attractive, in part, because qubits based on their internal states are also useful for atomic clocks and have very long coherence times, in some cases exceeding ten minute... |

71 | Electromagnetic traps for charged and neutral particles, - Paul - 1990 |

70 |
Demonstration of a fundamental quantum logic gate,
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Citation Context ...ween the internal state qubits of ions that are selected by focused laser beams (see text). the two selected ions. The logic gate between the motion qubit and internal-state qubit was demonstrated in =-=[31]-=- (a variation of this gate that depends on the motional wavepacket size [32] was implemented in [33]). The complete Cirac/Zoller gate between two selected qubits was demonstrated in [34]. More streaml... |

66 | Experimental violation of a Bell’s inequality with efficient detection.
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Citation Context ... photon-based experiments where not every pair produced results in a measurement. This feature enabled experiments that showed a violation of Bell’s inequalities and overcame the ‘detection loophole’ =-=[95, 96]-=-. These experiments also provided the first such tests on massive particles that employed a complete set of correlation measurements. Some experiments have explored other aspects of entanglement such ... |

63 |
Exploring the Quantum,
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Citation Context ...nresonant beams [46–48]). If we assume ωL = ω0 −ωz (laser tuned to the ‘red sideband’), the resonant term gives HI ' h̄ηei(φ+pi/2)S+a + H.C., which is the Jaynes–Cummings Hamiltonian from cavity QED =-=[49]-=-. This interaction and 3 Phys. Scr. T137 (2009) 014007 D J Wineland the ‘blue sideband’ interaction (for ωL = ω0 +ωz) provide a simple form of coupling between internal states and motion. When address... |

59 |
Quantum computations with cold trapped ions,” Phys
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Citation Context ...lly separated qubits. With the use of focused laser beams, this enables selective qubit addressing, coherent manipulations, and high-fidelity qubit-state readout with state-dependent laser scattering =-=[5, 6]-=-. With these tools, simple algorithms have been demonstrated [6]. However, current operation fidelities are significantly below those required for fault tolerance, and efforts towards scaling to a lar... |

42 | A “Schrodinger Cat” Superposition State of an Atom. - Monroe, Meekhof, et al. - 1996 |

41 | Generation of nonclassical motional states of a trapped atom. - Meekhof, Monroe, et al. - 1996 |

39 |
Laser cooling to the zero-point energy of motion Phys.
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Citation Context ... close relation to the current trapped-ion QIP experiments [10, 17]. By 1990, trapped-ion experiments had reached the point where the mechanical motion of the ions could be cooled to the ground state =-=[18]-=-; this could be verified by an excitation of the ion’s internal state conditioned on its motional quantum state. When coupled with optical pumping to a given internal state, this would provide an inte... |

39 |
Spin squeezing and reduced quantum noise in spectroscopy”,
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Citation Context ...e first. Some of these are described briefly here. 3.1. Spectroscopy and metrology Some potential applications are motivated by the idea of using entangled states to improve spectroscopic sensitivity =-=[21, 24, 25, 29, 80]-=-, and simple demonstrations of this increased sensitivity have been made [28, 29, 74, 80]. The improvements in sensitivity derived from these techniques assume that noise is dominated by ‘projection n... |

39 |
Squeezed atomic states and projection noise in spectroscopy”,
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Citation Context ...e first. Some of these are described briefly here. 3.1. Spectroscopy and metrology Some potential applications are motivated by the idea of using entangled states to improve spectroscopic sensitivity =-=[21, 24, 25, 29, 80]-=-, and simple demonstrations of this increased sensitivity have been made [28, 29, 74, 80]. The improvements in sensitivity derived from these techniques assume that noise is dominated by ‘projection n... |

34 |
Quantum computers can search arbitrarily large databases by a single query
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Citation Context ...be required to reach fault-tolerant levels. 3. Beginning applications Although primary drivers for the field of QIP have been a factoring machine [1] and a device for performing unstructured searches =-=[78, 79]-=-, it is very likely that other applications will emerge first. Some of these are described briefly here. 3.1. Spectroscopy and metrology Some potential applications are motivated by the idea of using ... |

32 |
Realization of the Cirac–Zoller controlledNOT quantum gate,”
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Citation Context ...monstrated in [31] (a variation of this gate that depends on the motional wavepacket size [32] was implemented in [33]). The complete Cirac/Zoller gate between two selected qubits was demonstrated in =-=[34]-=-. More streamlined versions of such deterministic multiqubit logic gates have now been realized (below), but they all employ the basic idea that the ions’ collective motion provides the data bus for s... |

30 | Optimal frequency measurements with maximally correlated states,”
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Citation Context ...e first. Some of these are described briefly here. 3.1. Spectroscopy and metrology Some potential applications are motivated by the idea of using entangled states to improve spectroscopic sensitivity =-=[21, 24, 25, 29, 80]-=-, and simple demonstrations of this increased sensitivity have been made [28, 29, 74, 80]. The improvements in sensitivity derived from these techniques assume that noise is dominated by ‘projection n... |

30 |
Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer. Nature 421
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Citation Context ... detuning from allowed transitions [60, 61]. The use of single- and multiqubit gates has enabled the demonstration of several (deterministic) QIP algorithms. These include the Deutsch–Jozsa algorithm =-=[62]-=-, dense coding [63], qubit teleportation [64, 65], quantum error correction [66], entanglement-assisted detection [67], the quantum Fourier transform [68], Grover’s search algorithm [69], entangled st... |

30 |
A decoherence-free quantum memory using trapped ions.
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Citation Context ...ts of entanglement such as size, by production of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state [74]. Longevity has been explored with the production of decoherence-free subspace Bell states =-=[96, 97]-=- with coherence lifetimes of 7 s in [98] and 34 s in [73]. In [99], Bell’s inequalities were violated for entangled states between an ion and a photon. Distance scales for entanglement have been explo... |

24 |
Toward Heisenberg-limited spectroscopy with multiparticle entangled states
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Citation Context |

24 |
Quantum projection noise: Population fluctuations in two-level systems,” Phys
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Citation Context ...ty derived from these techniques assume that noise is dominated by ‘projection noise,’ the fundamental noise arising from the fluctuations in which state the system is projected into upon measurement =-=[81, 82]-=-. However, if significant additional phase noise is present in either the atoms themselves [83], or the interrogating radiation [10, 84], the gain from entanglement can be lost. This puts a premium on... |

23 |
Entanglement of single-atom quantum bits at a distance.
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Citation Context ...es were violated for entangled states between an ion and a photon. Distance scales for entanglement have been explored by producing entangled spins over length scales from sub-millimeter [6] to ∼ 1 m =-=[100]-=-. The highest fidelity (0.993) of deterministic entanglement in any system has been reported in [58]. A recent verification of (state-independent) contextuality in quantum mechanics has been made in [... |

17 |
Arbitrary control of a quantum electromagnetic field.
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Citation Context ...], the Toffoli gate [72] and the production of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state [74]. A technique to generate arbitrary motional state superpositions, proposed by Law and Eberly =-=[75]-=-, was demonstrated in [76]. (this method has recently been applied with great success to the fields in a strip-line cavity coupled to a Josephson junction phase qubit [77]). Although the basic feature... |

13 | Simplified quantum logic with trapped ions. Phys
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Citation Context ...ams (see text). the two selected ions. The logic gate between the motion qubit and internal-state qubit was demonstrated in [31] (a variation of this gate that depends on the motional wavepacket size =-=[32]-=- was implemented in [33]). The complete Cirac/Zoller gate between two selected qubits was demonstrated in [34]. More streamlined versions of such deterministic multiqubit logic gates have now been rea... |

13 |
et al. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate
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Citation Context ...nts of AC Stark shifts. Since the AC Stark shifts are usually different for the two qubit states, geometric phases lead to entangling gates. Two-qubit phase gates have been implemented in the z-basis =-=[55, 56]-=- and in the x–y basis [47, 57–59]. In the Innsbruck experiment of [58] a state with fidelity of 0.993 with respect to a Bell state was produced, setting a standard for all QIP experiments. Qubits are ... |

13 |
Shimony A and Holt R A 1969 Proposed experiment to test local hidden-variable theories Phys
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Citation Context ... inequalities [93], trapped ions have been able to probe these fundamental aspects of quantum mechanics in some new regimes. By producing entangled pairs of ions, Bell’s inequalities of the CHSH form =-=[94]-=- have been measured. Since the pairs are produced deterministically, correlation measurements can be performed in every experiment, as opposed to, for example, photon-based experiments where not every... |

12 | A 303 MHz frequency standard based on trapped Be+ ions
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Citation Context ...or such a device. Ions are attractive, in part, because qubits based on their internal states are also useful for atomic clocks and have very long coherence times, in some cases exceeding ten minutes =-=[3, 4]-=-. In addition, due to their mutual Coulomb repulsion, trapped ions naturally form into arrays of spatially separated qubits. With the use of focused laser beams, this enables selective qubit addressin... |

11 |
et al. Long-lived qubit memory using atomic ions
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Citation Context ...on of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state [74]. Longevity has been explored with the production of decoherence-free subspace Bell states [96, 97] with coherence lifetimes of 7 s in =-=[98]-=- and 34 s in [73]. In [99], Bell’s inequalities were violated for entangled states between an ion and a photon. Distance scales for entanglement have been explored by producing entangled spins over le... |

10 |
Bell States of Atoms with Ultralong Lifetimes and Their Tomographic State Analysis.
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Citation Context ... photon-based experiments where not every pair produced results in a measurement. This feature enabled experiments that showed a violation of Bell’s inequalities and overcame the ‘detection loophole’ =-=[95, 96]-=-. These experiments also provided the first such tests on massive particles that employed a complete set of correlation measurements. Some experiments have explored other aspects of entanglement such ... |

10 |
Universal quantum simulators Science
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Citation Context ...ors [101]. 3.3. Towards quantum simulation In the early 1980s, Richard Feynman proposed that one quantum system might be used to efficiently simulate the dynamics of other quantum systems of interest =-=[102, 103]-=-. This is now a highly anticipated application of QIP, and will likely occur well before useful factorization is performed. Of course the universality of a large-scale quantum computer will allow it t... |

9 |
2008 Entangled states of trapped atomic ions Nature 453
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Citation Context ...lly separated qubits. With the use of focused laser beams, this enables selective qubit addressing, coherent manipulations, and high-fidelity qubit-state readout with state-dependent laser scattering =-=[5, 6]-=-. With these tools, simple algorithms have been demonstrated [6]. However, current operation fidelities are significantly below those required for fault tolerance, and efforts towards scaling to a lar... |

8 | A et al 2000 Experimental entanglement of four particles Nature 404 - Sackett |

8 |
D et al 2004 Deterministic quantum teleportation of atomic qubits Nature 429 737–9
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Citation Context ...The use of single- and multiqubit gates has enabled the demonstration of several (deterministic) QIP algorithms. These include the Deutsch–Jozsa algorithm [62], dense coding [63], qubit teleportation =-=[64, 65]-=-, quantum error correction [66], entanglement-assisted detection [67], the quantum Fourier transform [68], Grover’s search algorithm [69], entangled state purification [70], entanglement swapping [71]... |

7 |
Deterministic entanglement and tomography of ion spin qubits
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Citation Context ...nts of AC Stark shifts. Since the AC Stark shifts are usually different for the two qubit states, geometric phases lead to entangling gates. Two-qubit phase gates have been implemented in the z-basis =-=[55, 56]-=- and in the x–y basis [47, 57–59]. In the Innsbruck experiment of [58] a state with fidelity of 0.993 with respect to a Bell state was produced, setting a standard for all QIP experiments. Qubits are ... |

7 |
et al 2004 Deterministic quantum teleportation with atoms Nature 429 734–7
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Citation Context ...The use of single- and multiqubit gates has enabled the demonstration of several (deterministic) QIP algorithms. These include the Deutsch–Jozsa algorithm [62], dense coding [63], qubit teleportation =-=[64, 65]-=-, quantum error correction [66], entanglement-assisted detection [67], the quantum Fourier transform [68], Grover’s search algorithm [69], entangled state purification [70], entanglement swapping [71]... |

7 |
et al 2005 Scalable multiparticle entanglement of trapped ions Nature 438 643–6
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Citation Context ...[67], the quantum Fourier transform [68], Grover’s search algorithm [69], entangled state purification [70], entanglement swapping [71], the Toffoli gate [72] and the production of an 8-qubit W-state =-=[73]-=- and a 6-qubit ‘spin-cat’ state [74]. A technique to generate arbitrary motional state superpositions, proposed by Law and Eberly [75], was demonstrated in [76]. (this method has recently been applied... |

7 |
et al 2005 Creation of a six-atom “Schrödinger cat” state Nature 483 639–42
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Citation Context ...[68], Grover’s search algorithm [69], entangled state purification [70], entanglement swapping [71], the Toffoli gate [72] and the production of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state =-=[74]-=-. A technique to generate arbitrary motional state superpositions, proposed by Law and Eberly [75], was demonstrated in [76]. (this method has recently been applied with great success to the fields in... |

6 |
Experiments on the Structure of an Individual Elementary Particle,” Science 247
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Citation Context ...mogeneous magnetic field and subsequently projected onto one of the possible correlated outcomes. A more recent example is the single electron ‘AC Stern–Gerlach’ g-2 experiments of Hans Dehmelt et al =-=[16]-=-, where an entangling radio frequency (RF) transition caused the electron’s cyclotron-motion quantum state to change conditioned on its spin state. This example has a close relation to the current tra... |

6 |
C F and Blatt R 2008 Towards fault-tolerant quantum computing with trapped ions Nat. Phys
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Citation Context ...r the two qubit states, geometric phases lead to entangling gates. Two-qubit phase gates have been implemented in the z-basis [55, 56] and in the x–y basis [47, 57–59]. In the Innsbruck experiment of =-=[58]-=- a state with fidelity of 0.993 with respect to a Bell state was produced, setting a standard for all QIP experiments. Qubits are typically composed of states separated by optical energies or two stat... |

6 |
et al. (2004), Realization of quantum error correction, Nature 432
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Citation Context ...ates has enabled the demonstration of several (deterministic) QIP algorithms. These include the Deutsch–Jozsa algorithm [62], dense coding [63], qubit teleportation [64, 65], quantum error correction =-=[66]-=-, entanglement-assisted detection [67], the quantum Fourier transform [68], Grover’s search algorithm [69], entangled state purification [70], entanglement swapping [71], the Toffoli gate [72] and the... |

6 |
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Citation Context ...3], qubit teleportation [64, 65], quantum error correction [66], entanglement-assisted detection [67], the quantum Fourier transform [68], Grover’s search algorithm [69], entangled state purification =-=[70]-=-, entanglement swapping [71], the Toffoli gate [72] and the production of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state [74]. A technique to generate arbitrary motional state superpositions, ... |

5 |
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Citation Context ...or such a device. Ions are attractive, in part, because qubits based on their internal states are also useful for atomic clocks and have very long coherence times, in some cases exceeding ten minutes =-=[3, 4]-=-. In addition, due to their mutual Coulomb repulsion, trapped ions naturally form into arrays of spatially separated qubits. With the use of focused laser beams, this enables selective qubit addressin... |

5 |
C F and Blatt R 2008 Quantum computing with trapped ions Phys
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Citation Context ...focused laser beams would be lost, and crosstalk between zones, particularly for single qubit rotations, could be problematical. These effects can in principle be mitigated by use of composite pulses =-=[14]-=- and proper shielding between zones. 4.4. Lasers A significant source of decoherence in many experiments stems from laser-driven transitions. For qubits based on optical transitions, the fundamental l... |

5 | Ion–trap quantum information processing: experimental status - Kielpinski - 2008 |

5 |
Kielpinski D, Sackett C
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Citation Context ...tial applications are motivated by the idea of using entangled states to improve spectroscopic sensitivity [21, 24, 25, 29, 80], and simple demonstrations of this increased sensitivity have been made =-=[28, 29, 74, 80]-=-. The improvements in sensitivity derived from these techniques assume that noise is dominated by ‘projection noise,’ the fundamental noise arising from the fluctuations in which state the system is p... |

5 | Observation of ordered structures of laser-cooled ions in a quadrupole storage ring,’’ Phys - Waki, Kassner, et al. - 1992 |

5 | Linear trap for high-accuracy spectroscopy of stored ions - Raizen, Bergquist, et al. - 1992 |

5 |
et al 2006 Microfabricated surface-electrode ion trap for scalable quantum information processing Phys
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Citation Context ...ane as indicated by the dashed line. (b) Photographs of a single-zone surface-electrode trap in which gold electrodes are deposited on a quartz substrate with the use of lithographic techniques (from =-=[40]-=-). Other examples are described in [39]. Advantages of such a geometry include the ability to fabricate many traps in the same number of steps required to fabricate a single trap, and the precise elec... |

5 | S and James D F V 2000 Ion trap quantum computing with warm ions Fortschr. Phys - Milburn, Schneider |

5 |
dense coding with atomic qubits
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Citation Context ...wed transitions [60, 61]. The use of single- and multiqubit gates has enabled the demonstration of several (deterministic) QIP algorithms. These include the Deutsch–Jozsa algorithm [62], dense coding =-=[63]-=-, qubit teleportation [64, 65], quantum error correction [66], entanglement-assisted detection [67], the quantum Fourier transform [68], Grover’s search algorithm [69], entangled state purification [7... |

5 |
Enhanced quantum state detection efficiency through quantum information processing
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Citation Context ...several (deterministic) QIP algorithms. These include the Deutsch–Jozsa algorithm [62], dense coding [63], qubit teleportation [64, 65], quantum error correction [66], entanglement-assisted detection =-=[67]-=-, the quantum Fourier transform [68], Grover’s search algorithm [69], entangled state purification [70], entanglement swapping [71], the Toffoli gate [72] and the production of an 8-qubit W-state [73]... |

5 |
A S, Schindler P, Chwalla M, Hennrich M and Blatt R 2009 Realization of the quantum Toffoli gate with trapped ions Phys
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Citation Context ... 65], quantum error correction [66], entanglement-assisted detection [67], the quantum Fourier transform [68], Grover’s search algorithm [69], entangled state purification [70], entanglement swapping =-=[71]-=-, the Toffoli gate [72] and the production of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state [74]. A technique to generate arbitrary motional state superpositions, proposed by Law and Eberly [... |

5 |
Spectroscopy using quantum logic, Science 309
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Citation Context ...ve, it is possible to transfer the states of interest in the spectroscopy ion to a mode of the ions’ coupled motion and then transfer this information to the logic ion, which is subsequently measured =-=[86, 87]-=-. This technique has been used to detect optical transitions in 27Al+ ions by transferring the relevant state amplitudes to a 9Be+ logic ion, which is then measured [87]. It is now used routinely in a... |

4 |
Macchiavello C, Pellizzari T, Ekert A K, Plenio M
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Citation Context ...tal noise arising from the fluctuations in which state the system is projected into upon measurement [81, 82]. However, if significant additional phase noise is present in either the atoms themselves =-=[83]-=-, or the interrogating radiation [10, 84], the gain from entanglement can be lost. This puts a premium on finding probe oscillators that are stable enough that the projection noise dominates for the d... |

3 |
C and Wineland D 2003 Quantum dynamics of single trapped ions Rev
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Citation Context ...e been linear RF quadrupole Paul traps, shown schematically in figure 1 [35–38]. These traps are basically RF quadrupole mass analyzers that are plugged on the ends with appropriate static potentials =-=[12]-=-. To a first approximation, they can be viewed as providing a three-dimensional (3D) harmonic well with the strength of the well along the trap axis made relatively weak compared with the transverse d... |

3 | Observation of quantum jumps in a single atom Phys - Bergquist, Hulet, et al. - 1986 |

3 |
et al 2005 Hyperfine coherence in the presence of spontaneous photon scattering Phys
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Citation Context ... driven by stimulated-Raman transitions have the disadvantage of spontaneous emission decoherence, which can be reduced only by the use of high laser power and large detuning from allowed transitions =-=[60, 61]-=-. The use of single- and multiqubit gates has enabled the demonstration of several (deterministic) QIP algorithms. These include the Deutsch–Jozsa algorithm [62], dense coding [63], qubit teleportatio... |

3 |
et al 2007 Errors in trapped-ion quantum gates due to spontaneous photon scattering Phys
- Ozeri
(Show Context)
Citation Context ... driven by stimulated-Raman transitions have the disadvantage of spontaneous emission decoherence, which can be reduced only by the use of high laser power and large detuning from allowed transitions =-=[60, 61]-=-. The use of single- and multiqubit gates has enabled the demonstration of several (deterministic) QIP algorithms. These include the Deutsch–Jozsa algorithm [62], dense coding [63], qubit teleportatio... |

3 |
et al 2005 Implementation of the semiclassical quantum Fourier transform in a scalable system Science 308 997–1002
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Citation Context ...ms. These include the Deutsch–Jozsa algorithm [62], dense coding [63], qubit teleportation [64, 65], quantum error correction [66], entanglement-assisted detection [67], the quantum Fourier transform =-=[68]-=-, Grover’s search algorithm [69], entangled state purification [70], entanglement swapping [71], the Toffoli gate [72] and the production of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state [74]... |

3 |
et al 2009 Synthesizing arbitrary quantum states in a superconducting resonator Nature 459 546–9
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Citation Context ..., proposed by Law and Eberly [75], was demonstrated in [76]. (this method has recently been applied with great success to the fields in a strip-line cavity coupled to a Josephson junction phase qubit =-=[77]-=-). Although the basic features of these algorithms were observed, in all cases, considerable technical effort will be required to reach fault-tolerant levels. 3. Beginning applications Although primar... |

3 |
Riebe M and Blatt R 2006 ‘Designer atoms’ for quantum metrology Nature 443
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(Show Context)
Citation Context |

3 |
et al 2008 Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place Science 319
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(Show Context)
Citation Context ... optical transitions in 27Al+ ions by transferring the relevant state amplitudes to a 9Be+ logic ion, which is then measured [87]. It is now used routinely in an accurate optical clock based on 27Al+ =-=[88]-=- and might also be extended to molecular ions [89]. The information transfer and readout process employed in [87, 88] typically had a fidelity of about 0.85, limited by errors caused by the ions’ moti... |

3 |
Rosenband T and Wineland D J 2007 High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements Phys
- Hume
(Show Context)
Citation Context ... therefore be repeated to gain better information on the 27Al+ ion’s state. By use of real-time Bayesian analysis on successive detection cycles, the readout fidelity was improved from 0.85 to 0.9994 =-=[90]-=-. This experiment shares similarities with those of Serge Haroche’s group, where successive atoms are used to perform QND measurements of the field in a cavity [91]. In [90], the same atom (9Be+) is r... |

2 | Lukin M 2008 Remapping the quantum frontier Phys - Monroe |

2 |
Robust probabilistic quantum information processing with atoms, photons and atomic ensembles Advances in Atomic, Molecular and Optical Physics vol 55,
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- 2008
(Show Context)
Citation Context ...ll involve significant technical challenges, but straightforward solutions are being explored. In the meantime, quantum communication systems that utilize trapped ions will likely soon be implemented =-=[7, 8]-=- and simple elements of QIP are already being used in metrology [6]. This paper briefly reviews a bit of the history and the ideas behind QIP with trapped ions, and summarizes current capabilities, pr... |

2 | Linear ion trap based atomic frequency standard - Restage, Dick, et al. - 1990 |

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2 |
Sørensen A and Lukin M D 2004 Stability of atomic clocks based on entangled atoms Phys
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Citation Context ...ns in which state the system is projected into upon measurement [81, 82]. However, if significant additional phase noise is present in either the atoms themselves [83], or the interrogating radiation =-=[10, 84]-=-, the gain from entanglement can be lost. This puts a premium on finding probe oscillators that are stable enough that the projection noise dominates for the desired probe duration. Another interestin... |

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Precision spectroscopy with two correlated atoms
- Chwalla, Kim, et al.
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Citation Context ...ium on finding probe oscillators that are stable enough that the projection noise dominates for the desired probe duration. Another interesting use of entanglement in spectroscopy was demonstrated in =-=[80, 85]-=-. Here, a precise measurement of the quadrupole moment of 40Ca+ was made by performing spectroscopy on an entangled state of two ions in which the spectroscopy yielded the quadrupole moment, but was i... |

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Dotsenko I, Sayrin C, Bernu J, Brune M, Raimond J M and Haroche S 2008 Reconstruction of non-classical cavity field states with snapshots of their decoherence Nature 455 510–4
- Deléglise
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Citation Context ...ty was improved from 0.85 to 0.9994 [90]. This experiment shares similarities with those of Serge Haroche’s group, where successive atoms are used to perform QND measurements of the field in a cavity =-=[91]-=-. In [90], the same atom (9Be+) is reset after each detection cycle and used again. Also, because the detection was accomplished in real time, the procedure was adaptive, requiring on each run a varia... |

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et al 2002 Trapped-ion quantum simulator; experimental application to nonlinear interferometers Phys
- Leibfried
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Citation Context ...ossible to simulate the phase sensitivity of a Mach–Zehnder interferometer comprised of two nth-order nonlinear optical beam splitters, showing the increased gain in sensitivity from the nonlinearity =-=[105]-=-. Currently, there is considerable interest in, and efforts are underway in several laboratories to use, QIP interactions to simulate condensed-matter systems. Some of the basic ideas for how this mig... |

1 | Parkins A S, Blatt R and Zoller P 1996 Non-classical states of motion in ion traps - Cirac |

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K A, Deslauriers L, Haljan P C, Duan L M and Monroe C 2005 Phase control of trapped ion quantum gates
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Citation Context ...ework, the main difference being whether the forces act on the spins in the z-basis (eigenstates | ↓〉, | ↑〉) or in the x–y basis (eigenstates of the form 1√ 2 (| ↓〉+ eiξ | ↑〉, 1√ 2 (| ↓〉 − e−iξ | ↑〉) =-=[13]-=-. The state-dependent forces required for the displacements are optical-dipole forces, which arise from spatial gradients of AC Stark shifts. Since the AC Stark shifts are usually different for the tw... |

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2006 Electron g-2, entanglement and trapped-ion quantum information processing An Isolated Atomic Particle at Rest in Free Space ed
- Wineland
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Citation Context ...io frequency (RF) transition caused the electron’s cyclotron-motion quantum state to change conditioned on its spin state. This example has a close relation to the current trapped-ion QIP experiments =-=[10, 17]-=-. By 1990, trapped-ion experiments had reached the point where the mechanical motion of the ions could be cooled to the ground state [18]; this could be verified by an excitation of the ion’s internal... |

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1 | Parkins A S, Blatt R and Zoller P 1993 ‘Dark’ squeezed states of the motion of a trapped ion Phys - Cirac |

1 | A S and Zoller P 1993 Preparation of Fock states by observation of quantum jumps in an ion trap Phys - Cirac, Blatt, et al. |

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et al 2002 Experimental demonstration of a controlled-NOT wave-packet gate Phys
- DeMarco
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Citation Context ...selected ions. The logic gate between the motion qubit and internal-state qubit was demonstrated in [31] (a variation of this gate that depends on the motional wavepacket size [32] was implemented in =-=[33]-=-). The complete Cirac/Zoller gate between two selected qubits was demonstrated in [34]. More streamlined versions of such deterministic multiqubit logic gates have now been realized (below), but they ... |

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Microfabricated chip traps for ions arXiv:0812.3907
- Amini, Britton, et al.
- 2008
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Citation Context ...) Photographs of a single-zone surface-electrode trap in which gold electrodes are deposited on a quartz substrate with the use of lithographic techniques (from [40]). Other examples are described in =-=[39]-=-. Advantages of such a geometry include the ability to fabricate many traps in the same number of steps required to fabricate a single trap, and the precise electrode alignment provided by lithography... |

1 | Itano W M and Drullinger R E 1980 Double-resonance and optical-pumping experiments on electromagnetically confined, laser-cooled ions Opt - Wineland, Bergquist |

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Steane A and Lucas D 2008 High-fidelity readout of trapped-ion qubits
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Citation Context ...tion efficiency can be quite high [41–44] and nearly unit detection efficiency is possible. With the use of this technique, detection fidelities in trapped-ion QIP experiments have now reached 0.9999 =-=[45]-=-. 2.3. Qubit gates For the basic gate scheme outlined above, we need to efficiently couple an ion’s internal states to its motion. Laser beams provide a good means for this because the gradient of the... |

1 | Drewsen M 2002 Trapped-ion quantum logic utilizing position-dependent AC Stark shifts Phys. Rev. A 66 - Staanum |

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Gerritsma R, Kleinmann M, Gühne O
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Citation Context ...]. The highest fidelity (0.993) of deterministic entanglement in any system has been reported in [58]. A recent verification of (state-independent) contextuality in quantum mechanics has been made in =-=[48]-=-. By transferring entanglement from spin states to the motion of ion pairs held in different locations, entanglement has been created between separated mechanical oscillators [101]. 3.3. Towards quant... |

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L M and Monroe C 2009 Entanglement and tunable spin–spin couplings between trapped ions using multiple transverse modes Phys
- Kim, Chang, et al.
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Citation Context ...ct that phase gates between ions i and j invoke a spin–spin-like interaction of the form σûiσû j , where û ∈ {x̂, ŷ, ẑ}. Spin rotations about a direction û act like magnetic fields along û. In =-=[59, 115]-=-, these basic interactions have been implemented on a few ions and efforts are underway to scale to much larger numbers. One interesting application is to study quantum phase transitions by varying th... |

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Deslauriers L and Monroe C 2005 Implementation of Grover’s quantum search algorithm in a scalable system Phys. Rev. A 72
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Citation Context ...zsa algorithm [62], dense coding [63], qubit teleportation [64, 65], quantum error correction [66], entanglement-assisted detection [67], the quantum Fourier transform [68], Grover’s search algorithm =-=[69]-=-, entangled state purification [70], entanglement swapping [71], the Toffoli gate [72] and the production of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state [74]. A technique to generate arbitr... |

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Ben-Kish A et al 2003 Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-1/2 particle
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Citation Context ...nd the production of an 8-qubit W-state [73] and a 6-qubit ‘spin-cat’ state [74]. A technique to generate arbitrary motional state superpositions, proposed by Law and Eberly [75], was demonstrated in =-=[76]-=-. (this method has recently been applied with great success to the fields in a strip-line cavity coupled to a Josephson junction phase qubit [77]). Although the basic features of these algorithms were... |

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J C and Walls F L 1982 Proposed stored 201Hg+ ion frequency standards
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Citation Context ...ty derived from these techniques assume that noise is dominated by ‘projection noise,’ the fundamental noise arising from the fluctuations in which state the system is projected into upon measurement =-=[81, 82]-=-. However, if significant additional phase noise is present in either the atoms themselves [83], or the interrogating radiation [10, 84], the gain from entanglement can be lost. This puts a premium on... |

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2007 Blackbody thermometry with cold molecular ions and application to ion-based frequency standards Phys. Rev. A 76 023413 Phys. Scr. T137 (2009) 014007
- Koelemeij, Roth, et al.
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Citation Context ... the relevant state amplitudes to a 9Be+ logic ion, which is then measured [87]. It is now used routinely in an accurate optical clock based on 27Al+ [88] and might also be extended to molecular ions =-=[89]-=-. The information transfer and readout process employed in [87, 88] typically had a fidelity of about 0.85, limited by errors caused by the ions’ motion. However, this detection process is a quantum-n... |

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Blinov B B and Monroe C 2004 Experimental Bell inequality violation with an atom and a photon Phys
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Citation Context ...73] and a 6-qubit ‘spin-cat’ state [74]. Longevity has been explored with the production of decoherence-free subspace Bell states [96, 97] with coherence lifetimes of 7 s in [98] and 34 s in [73]. In =-=[99]-=-, Bell’s inequalities were violated for entangled states between an ion and a photon. Distance scales for entanglement have been explored by producing entangled spins over length scales from sub-milli... |

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Entangled mechanical oscillators Nature 459 683–6
- Jost, Home, et al.
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Citation Context ...ics has been made in [48]. By transferring entanglement from spin states to the motion of ion pairs held in different locations, entanglement has been created between separated mechanical oscillators =-=[101]-=-. 3.3. Towards quantum simulation In the early 1980s, Richard Feynman proposed that one quantum system might be used to efficiently simulate the dynamics of other quantum systems of interest [102, 103... |

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Trapped-ion quantum simulator Phys
- Wineland, Monroe
- 1998
(Show Context)
Citation Context ...tain classes of physical problems. For trapped ions, it might be possible to use the interactions employed in the various gates to simulate other systems of interest such as nonlinear optical systems =-=[10, 104]-=-. Along these lines, it has been possible to simulate the phase sensitivity of a Mach–Zehnder interferometer comprised of two nth-order nonlinear optical beam splitters, showing the increased gain in ... |

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and Balzer C 2003 Quantum measurements and new concepts for experiments with trapped ions Adv
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Citation Context ...fferent magnetic moments, their confining wells are displaced spatially in a static gradient field; therefore, Franck–Condon-type overlap factors allow simultaneous change of spin and motional states =-=[106, 159, 160]-=-. On the other hand, when the qubit transition frequencies are independent of position, it should be possible to use inhomogeneous ac magnetic fields for sideband transitions and multiqubit gates on h... |