Abstract:
This chapter reviews recent developments in the use of mixed-species ion chains in quantum information science, frequency metrology and spectroscopy. A growing number of experiments have demonstrated new methods in this area, opening up new possibilities for quantum state generation, quantum control of previously inaccessible ions, and the ability to maintain quantum control over extended periods. I describe these methods, providing details of the techniques which are required in order to work with such systems. In addition, I present perspectives on possible future uses of quantum logic spectroscopy techniques, which have the potential to extend precision control of atomic ions to a large range of atomic and molecular species.

Abstract:
Mesoscopic superpositions of distinguishable coherent states provide an analog to the Schr\"odinger's cat thought experiment. For mechanical oscillators these have primarily been realised using coherent wavepackets, for which the distinguishability arises due to the spatial separation of the superposed states. Here, we demonstrate superpositions composed of squeezed wavepackets, which we generate by applying an internal-state dependent force to a single trapped ion initialized in a squeezed vacuum state with 9 dB reduction in the quadrature variance. This allows us to characterise the initial squeezed wavepacket by monitoring the onset of spin-motion entanglement, and to verify the evolution of the number states of the oscillator as a function of the duration of the force. In both cases, we observe clear differences between displacements aligned with the squeezed and anti-squeezed axes. We observe coherent revivals when inverting the state-dependent force after separating the wavepackets by more than 19 times the ground-state root mean squared extent, which corresponds to 56 times the root mean squared extent of the squeezed wavepacket along the displacement direction. Aside from their fundamental nature, these states may be useful for quantum metrology or quantum information processing with continuous variables.

Abstract:
Quantum information processing will require combinations of gate operations and communication, with each applied in parallel to large numbers of quantum systems. These tasks are often performed sequentially, with gates implemented by pulsed fields and information transported either by moving the physical qubits or using photonic links. For trapped ions, an alternative approach is to implement quantum logic gates by transporting the ions through static laser beams, combining qubit operations with transport. This has significant advantages for scalability since the voltage waveforms required for transport can potentially be generated using micro-electronics integrated into the trap structure itself, while both optical and microwave control elements are significantly more bulky. Using a multi-zone ion trap, we demonstrate transport gates on a qubit encoded in the hyperfine structure of a beryllium ion. We show the ability to perform sequences of operations, and to perform parallel gates on two ions transported through separate trap locations using a single recycled laser beam. For the latter, we demonstrate independent quantum gates by controlling the speed of each of the ions. This work provides a scalable path to ion trap quantum computing without a dramatic increase in optical control complexity.

Abstract:
We study the problem of designing electrode structures that allow pairs of ions to be brought together and separated rapidly in an array of linear Paul traps. We show that it is desirable for the electrode structure to produce a d.c. octupole moment with an a.c. radial quadrupole. For the case where electrical breakdown limits the voltages that can be applied, we show that the octupole is more demanding than the quadrupole when the characteristic distance scale of the structure is larger than 1 to 10 microns (for typical materials). We present a variety of approaches and optimizations of structures consisting of one to three layers of electrodes. The three-layer structures allow the fastest operation at given distance r from the trap centres to the nearest electrode surface, but when the total thickness w of the structure is constrained, leading to w < r, then two-layer structures may be preferable.

Abstract:
onion plants (allium cepa l. var. baia piriforme precoce piracicaba), 70 days, old were grown in pots containing 7 kg of quartz sand. twice a day they were irrigated by percolation with complete solution. every 15 days from the 70 th day plants were harvested divided into aerial part and bulb. the parts were weighed and analysed for n, p, k, ca, mg and s. data obtained allowed for the following main conclusion: a) the initial rate of growth of the onion during the first 85 days is rather slow b) the uptake of nutrients is small until the 85 days, increasing at the 145 days. c) the following amounts of nutrients in kg/ha were absorved by a population of 166,666 plants with a production of 36,700 kg of onion: n 132.8 p 21.9 k 177.0 ca 15.9 mg 17.8 s 33.8

Abstract:
We investigate electrode geometries required to produce periodic 2-dimensional ion-trap arrays with the ions placed between two planes of electrodes. We present a generalization of previous methods for traps containing a single electrode plane to this new geometry, and show that for a given ion-electrode distance and applied voltages, the inter-ion distance can be reduced by a factor of up to 3 relative to single-plane traps. This represents an increase by a factor of 9 in the trap density and a factor of 27 in the exchange coupling between the oscillatory motion of neighboring ions. The resulting traps are also considerably deeper for bi-layer structures than for single-plane traps. These results could offer a useful path towards 2-dimensional ion arrays for quantum simulation. We also discuss issues with the fabrication of such traps.

Abstract:
The universal quantum computer is a device capable of simulating any physical system and represents a major goal for the field of quantum information science. Algorithms performed on such a device are predicted to offer significant gains for some important computational tasks. In the context of quantum information, "universal" refers to the ability to perform arbitrary unitary transformations in the system's computational space. The combination of arbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate is a gate set capable of achieving universal control of any number of qubits, provided that these gates can be performed repeatedly and between arbitrary pairs of qubits. Although gate sets have been demonstrated in several technologies, they have as yet been tailored toward specific tasks, forming a small subset of all unitary operators. Here we demonstrate a programmable quantum processor that realises arbitrary unitary transformations on two qubits, which are stored in trapped atomic ions. Using quantum state and process tomography, we characterise the fidelity of our implementation for 160 randomly chosen operations. This universal control is equivalent to simulating any pairwise interaction between spin-1/2 systems. A programmable multi-qubit register could form a core component of a large-scale quantum processor, and the methods used here are suitable for such a device.

Abstract:
We study quantum teleportation with the resource of non-orthogonal qubit states. We first extend the standard teleportation protocol to the case of such states. We investigate how the loss of teleportation fidelity resulting for the use of non-orthogonal states compares to a similar loss of fidelity when noisy or non-maximally entangled states as used as teleportation resource. Our analysis leads to certain interesting results on the teleportation efficiency of both pure and mixed non-orthgonal states compared to that of non-maximally entangled and mixed states.

Abstract:
Large-scale quantum information processors must be able to transport and maintain quantum information, and repeatedly perform logical operations. Here we demonstrate a combination of all the fundamental elements required to perform scalable quantum computing using qubits stored in the internal states of trapped atomic ions. We quantify the repeatability of a multi-qubit operation, observing no loss of performance despite qubit transport over macroscopic distances. Key to these results is the use of different pairs of beryllium ion hyperfine states for robust qubit storage, readout and gates, and simultaneous trapping of magnesium re-cooling ions along with the qubit ions.

Abstract:
We propose a new scheme for supplying voltages to the electrodes of microfabricated ion traps, enabling access to a regime in which changes to the trapping potential are made on timescales much shorter than the period of the secular oscillation frequencies of the trapped ions. This opens up possibilities for speeding up the transport of ions in segmented ion traps and also provides access to control of multiple ions in a string faster than the Coulomb interaction between them. We perform a theoretical study of ion transport using these methods in a surface-electrode trap, characterizing the precision required for a number of important control parameters. We also consider the possibilities and limitations for generating motional state squeezing using these techniques, which could be used as a basis for investigations of Gaussian-state entanglement.