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Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments are discussed. Furthermore, we review some implementations of quantum algorithms such as a deterministic teleportation of quantum information and an error correction scheme.
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the bidimensional relat
We propose the quantum simulation of the quantum Rabi model in all parameter regimes by means of detuned bichromatic sideband excitations of a single trapped ion. We show that current setups can reproduce, in particular, the ultrastrong and deep stro
Thermodynamics is one of the oldest and well-established branches of physics that sets boundaries to what can possibly be achieved in macroscopic systems. While it started as a purely classical theory, it was realized in the early days of quantum mec
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
Measurement-based quantum computation (MBQC) represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the one-way qu