Quantum simulators are controllable quantum systems that can be used to simulate other quantum systems. Being able to tackle problems that are intractable on classical computers, quantum simulators would provide a means of exploring new physical phenomena. We present an overview of how quantum simulators may become a reality in the near future as the required technologies are now within reach. Quantum simulators, relying on the coherent control of neutral atoms, ions, photons, or electrons, would allow studying problems in various fields including condensed-matter physics, high-energy physics, cosmology, atomic physics, and quantum chemistry.

Remarkable progress towards realizing quantum computation has been achieved using natural and artificial atoms as qubits. This article presents a brief overview of the current status of different types of qubits. On the one hand, natural atoms (such as neutral atoms and ions) have long coherence times, and could be stored in large arrays, providing ideal "quantum memories". On the other hand, artificial atoms (such as superconducting circuits or semiconductor quantum dots) have the advantage of custom-designed features and could be used as "quantum processing units". Natural and artificial atoms can be coupled with each other and can also be interfaced with photons for long-distance communications. Hybrid devices made of natural/artificial atoms and photons may provide the next-generation design for quantum computers.

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We investigate the structure of one-component and multicomponent planar Coulomb crystals in RF traps. Due to the RF confinement particular features emerge, especially in the case of multicomponent crystals. After briefly discussing one-component planar crystals, we consider the case of multicomponent crystals and, in particular, planar bicrystals. We show that in the multicomponent case, the spatial separation among components depends on the strength of axial confinement which also imposes a limit on the number of ions that can exist in the innermost shell. These theoretical results are confirmed by molecular dynamics simulations. Finally, we discuss some experimental issues.

Recently, quantum random walks ͑QRWs͒ have been thoroughly studied in order to develop new quantum algorithms. In this paper we propose scalable quantum networks for discrete QRWs on circles, lines, and also in higher dimensions. In our method the information about the position of the walker is stored in a quantum register and the network consists of only one-qubit rotation and ͑controlled͒ n -NOT gates, therefore it is purely computational and independent of the physical implementation. As an example, we describe the experimental realization in an ion-trap system.