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European Quantum Electronics Conference (EQEC)

Quantum computing with trapped ions

Hartmut Häffner, Christian F. Roos, Christoph Becher, W. Hänsel, T. Körber, Ferdinand Schmidt‐Kaler, Mark Riebe, Jan Benhelm, Gavin P. T. Lancaster, D. Chek-al-kar, R. Blatt

Published Jan 18, 2006• 4 citations
Publisher

Abstract

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.
DOI
10.1109/eqec.2005.1567473

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Quantum information processing is performed with single trapped Ca(+) ions, stored in a linear Paul trap and laser-cooled to the ground state of their harmonic quantum motion. Composite laser-pulse sequences were used to implement SWAP gate, phase gate and controlled-NOT gate operations. Stark shifts on the quantum-bit transitions were precisely measured and compensated. For a demonstration of quantum information processing, a Deutsch-Jozsa algorithm has been implemented using two quantum bits encoded on a single ion.
Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40 Ca + ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm.
Richard Feynman first proposed the idea of quantum computers thirty years ago. Since then, efforts have been undertaken to realize large-scale, fault-tolerant quantum computers that can factor large numbers much more quickly than classical computers, which would have significant implications for computer security. While there is no universally agreed upon technology for experimentally realizing quantum computers, many researchers look to ion traps as a promising technology. This thesis focuses on ion traps, how they fulfill the Divincenzo criteria, what obstacles must be overcome, and recent achievements in this field. We examine the physical principles of a linear Paul trap, including the confining potential and its quantum dynamics. In addition, we built a mechanical analogue of an ion trap for pedagogical purposes, and we provide an analysis of its trapping potential and compare it to a real ion trap, the Paul trap. Furthermore, we provide guidance for building a course module on ion trap based quantum computing; our guidance is based on course materials from several institutions.
The potential for quantum computers to perform some computational tasks significantly more quickly than traditional computers is exciting. where using trapped ions provided one of the most important theoretical and experimental benefits for building a quantum computer. This paper covers the theoretical research for some quantum gates which using in quantum information. The basic building blocks for computations and algorithms are logic gates. Quantum logic gates also the basic building blocks of quantum algorithms are implemented using trapped ions. The 40Ca+ trapped ions were employed in that study as an example of a quantum qubit in a Paul linear trap because they were contained in one dimension and could be easily handled and manipulated in the quantum state. We used the simulation system in the MATLAB program to present the logic gates that using in Quantum circuits, and illustrate the processes of rotation and manipulation of the quantum state by represented it on a Bloch sphere.