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RESEARCH PRODUCT

Quantum Computing with Trapped Charged Particles

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The concept of quantum computing has no clear cut origin. It emerged from combinations of information theory and quantum mechanical concepts. A decisive step was taken by Feynman [414, 415] who considered the possibility of universal simulation, a quantum system which could simulate the physical behavior of any other. Feynman gave arguments which suggested that quantum evolution could be used to compute certain problems more efficiently than any classical computer. His device may be considered as not sufficiently specified to be called a computer. The next important step was taken in 1985 by Deutsch [310]. His proposal is generally considered to represent the first blueprint for a quantum computer. It is sufficiently specific and simple to allow real machines to be contemplated, but sufficiently versatile to be an universal quantum simulator. Deutsch’s system is essentially an ensamble of two-state systems building a register. He proved that if the two-state systems could be made to evolve by means of a specific small set of simple operations, then any unitary evolution could be produced, and therefore their evolution could be made to simulate that of any physical system. Deutsch’s simple operations are now called quantum “gates,” since they play a role analogous to that of binary logic gates in classical computer. Unfortunately, all that could be found were a few mathematical problems, until Shor elaborated in 1994 a method for using quantum computers to crack an important problem in number theory, namely factorization of huge numbers [416]. He showed how an ensemble of mathematical operations, designed specifically for a quantum computer, could be organized to enable such a machine to factor huge numbers extremely rapidly, much faster than is possible on conventional computers. Various authors have refined these basic concepts and since then many new ideas and proposals have emerged. Various physical systems are presently considered to implement quantum gates and perform logical operations such as Nuclear Magnetic Resonance, Quantum Dots, Optical Lattices, Cavity Quantum Electrodynamics, and others. Among them strings of ions confined in linear Paul traps are presently regarded as the most promising route toward realization of a quantum computer. In this chapter, we will outline the basic concept of ion trap quantum computing and mention various experimental attempts to perform quantum logical operations. A number of general reviews on this topic have been published in recent years [305, 417-424] and the reader is referred to these articles for further information.