J. Benhelm

Scalable multiparticle entanglement of trapped ions

The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are non-interacting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions or five photons has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a non-exponential scaling of resources with particle number. Among the various kinds of entangled states, the ‘W state’ plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, ‘Greenberger–Horne–Zeilinger’ entangled states with up to six ions have been created and analysed in Boulder.

Deterministic quantum teleportation with atoms

Teleportation of a quantum state encompasses the complete transfer of information from one particle to another. The complete specification of the quantum state of a system generally requires an infinite amount of information, even for simple two-level systems (qubits). Moreover, the principles of quantum mechanics dictate that any measurement on a system immediately alters its state, while yielding at most one bit of information. The transfer of a state from one system to another (by performing measurements on the first and operations on the second) might therefore appear impossible. However, it has been shown that the entangling properties of quantum mechanics, in combination with classical communication, allow quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated, but such techniques are probabilistic, requiring post-selection of measured photons. Here, we report deterministic quantum-state teleportation between a pair of trapped calcium ions. Following closely the original proposal, we create a highly entangled pair of ions and perform a complete Bell-state measurement involving one ion from this pair and a third source ion. State reconstruction conditioned on this measurement is then performed on the other half of the entangled pair. The measured fidelity is 75%, demonstrating unequivocally the quantum nature of the process.

Towards fault-tolerant quantum computing with trapped ions

Like their classical counterparts, quantum computers can, in theory, cope with imperfections—provided that these are small enough. The regime of fault-tolerant quantum computing has now been reached for a system based on trapped ions, in which a gate operation for entangling qubits has been implemented with a fidelity exceeding 99%. Today, ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics1,2. For the implementation of arbitrary operations, a quantum computer requires a universal set of quantum logic gates. As in classical models of computation, quantum error correction techniques3,4 enable rectification of small imperfections in gate operations, thus enabling perfect computation in the presence of noise. For fault-tolerant computation5, it is believed that error thresholds ranging between 10−4 and 10−2 will be required—depending on the noise model and the computational overhead for realizing the quantum gates6,7,8—but so far all experimental implementations have fallen short of these requirements. Here, we report on a Molmer–Sorensen-type gate operation9,10 entangling ions with a fidelity of 99.3(1)%. The gate is carried out on a pair of qubits encoded in two trapped calcium ions using an amplitude-modulated laser beam interacting with both ions at the same time. A robust gate operation, mapping separable states onto maximally entangled states is achieved by adiabatically switching the laser–ion coupling on and off. We analyse the performance of a single gate and concatenations of up to 21 gate operations.

Absolute frequency measurement of the 40Ca+ 4s(2)S_(1/2)-3d(2)D_(5/2) clock transition.

We report on the first absolute transition frequency measurement at the 10 -15 level with a single, laser-cooled 40 Ca + ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40 Ca + 4s 2 S 1/2 -3d 2 D 5/2 electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency v Ca + = 411 042 129 776 393.2 (1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Lande g factor of the 3d 2 D 5/2 level to be g 5/2 = 1.2003340(3).

Experimental quantum-information processing withC43a+ions

For quantum information processing (QIP) with trapped ions, the isotope 43Ca+ offers the combined advantages of a quantum memory with long coherence time, a high fidelity read out and the possibility of performing two qubit gates on a quadrupole transition with a narrow-band laser. Compared to other ions used for quantum computing, 43Ca+ has a relatively complicated level structure. In this paper we discuss how to meet the basic requirements for QIP and demonstrate ground state cooling, robust state initialization and efficient read out for the hyperfine qubit with a single 43Ca+ ion. A microwave field and a Raman light field are used to drive qubit transitions, and the coherence times for both fields are compared. Phase errors due to interferometric instabilities in the Raman field generation do not limit the experiments on a time scale of 100 ms. We find a quantum information storage time of many seconds for the hyperfine qubit.

Quantum teleportation with atoms: quantum process tomography

The performance of a quantum teleportation algorithm implemented on an ion trap quantum computer is investigated. First the algorithm is analysed in terms of the teleportation fidelity of six input states evenly distributed over the Bloch sphere. Furthermore, a quantum process tomography of the teleportation algorithm is carried out which provides almost complete knowledge about the algorithm.

Absolute Frequency Measurement of the 40Ca+ 4s 2S1/2 -3d2D5/2 Clock Transition

We report on the first absolute transition frequency measurement at the 10 -15 level with a single, laser-cooled 40 Ca + ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40 Ca + 4s 2 S 1/2 -3d 2 D 5/2 electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency v Ca + = 411 042 129 776 393.2 (1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Lande g factor of the 3d 2 D 5/2 level to be g 5/2 = 1.2003340(3).

ABSOLUTE FREQUENCY MEASUREMENT OF THE 40Ca+ 4s 2S1/2 - 3d 2D5/2 CLOCK TRANSITION

We report on the first absolute transition frequency measurement at the 10;{-15} level with a single, laser-cooled 40Ca+ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40Ca+ 4s ;{2}S_{1/2}-3d ;{2}D_{5/2} electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency nu_{Ca;{+}}=411 042 129 776 393.2(1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Landé g factor of the 3d;{2}D_{5/2} level to be g_{5/2}=1.200 334 0(3).

Quantum computing with trapped ions

The paper reports on the investigation of single Ca/sup +/ ions and crystals of Ca/sup +/ ions confined in a linear Paul trap. These are also investigated for quantum information processing. Recent experimental advancements towards a quantum computer with such a system are also discussed.

QUANTUM COMPUTATION WITH TRAPPED IONS

Trapped ions can be prepared, manipulated and analyzed with high fidelities. In ad-dition, scalable ion trap architectures have been proposed (Kielpinski et al., Nature417, 709 (2001).). Therefore trapped ions represent a promising approach to large scalequantum computing. Here we concentrate on the recent advancements of generatingentangled states with small ion trap quantum computers. In particular, the creationof W–states with up to eight qubits and their characterization via state tomography isdiscussed.Keywords: entanglement; quantum information; ion traps