The use of trapped ions for quantum information processing is reviewed. Quantum simulations employ well controlled quantum systems to make predictions on another quantum system under investigation. With trapped ions quantum relativistic effects and spin systems are simulated.
The use of trapped atomic ions in the field of quantum information processing is briefly reviewed. We summarize the basic mechanisms required for logic gates and the use of the gates in demonstrating simple algorithms. We discuss the potential of trapped ions to reach fault-tolerant error levels in a large-scale system, and highlight some of the problems that will be faced in achieving this goal. Possible near-term applications in applied and basic science, such as in metrology and quantum simulation, are briefly discussed.
The control of internal and motional quantum degrees of freedom of laser-cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of quantum information science, the ability to deterministically prepare and measure quantum states of trapped ions is unprecedented. This expertise may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations. Here, we give an overview of current theoretical proposals and experiments for such quantum simulations with trapped ions. This includes various spin models (e.g. the quantum transverse Ising model or a neural network), the Bose–Hubbard Hamiltonian, the Frenkel–Kontorova model, and quantum fields and relativistic effects.
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
The role of trapped atomic ions in the field of quantum information processing is briefly reviewed. We discuss some of the historical developments that enabled ions to enter the field and then summarize the basic mechanisms required for logic gates and the use of the gates in demonstrating simple algorithms. We describe potential pathways to reach fault-tolerant error levels and large-scale devices, and highlight some of the main problems that will be faced in achieving these goals. Possible near-term applications in applied and basic science, such as in metrology and quantum simulation, are discussed.