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International Conference on Quantum Information

Quantum Simulations with Trapped Ions

R. Blatt

Published Jan 1, 2011• 122 citations
Publisher

Abstract

Quantum simulation makes use of a well controlled quantum system to make predictions on another quantum system under investigation. Here, we report on quantum simulations using trapped ions to investigate quantum relativistic effects and spin systems.
DOI
10.1364/icqi.2011.qwb1

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Quantum simulations with trapped ions

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Quantum simulation makes use of a well controlled quantum system to make predictions on another quantum system under investigation. Here, we report on quantum simulations using trapped ions to investigate quantum relativistic effects and spin systems.

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•Jan 1, 2005•2 citations

Quantum Simulation with Trapped Ions

James K. Freericks

In this chapter, we examine ion-trap-based quantum simulators. This is the same type of hardware that is employed for ion-trap quantum computers, but we do not describe gated quantum computing in this book. Instead, we focus on examining the complex quantum dynamics in systems where individual ions can be trapped and manipulated. These systems are one of the hallmarks of the second quantum revolution, where we can manipulate quantum systems at the single-quantum level. We describe the phonon modes for ions in a trap, Raman transitions, spin-dependent forces that lead to effective spin models, how to prepare spin ground states, and extensions to the Lipkin-Meshkov-Glick and Dicke models.

Springer eBooks•Jan 1, 2026•0 citations
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.
Coupling internal and vibrational states of a string of trapped ions has proven to be an effective way of entangling the ions' internal states. This mechanism can be used for high-fidelity quantum gates, QND measurements of spin correlations and creation of large entangled states. However, spin-motion interactions are also of interest for the purpose of quantum simulations where the motional state no longer acts as an auxiliary quantum system only. Here, we describe an experiment where a laser-cooled trapped ion is set to behave as a free relativistic quantum particle.
We show that trapped ions are ideally suited for the simulation of quantum spin systems and for the observation of a rich variety of quantum phase transitions. By changing the laser intensities and polarizations, the dynamics of the internal states of the ions can be controlled in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analog quantum simulator of spin systems with trapped ions and to observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins. The requirements for our proposal are met by current technology: it does not rely on the use of quantum gates, and striking many-body effects can be observed even when the fidelity of the simulation is smaller than the one required for quantum computation. Our proposal with trapped ions would solve many of the problems that are faced in the implementation of quantum simulations with neutral atoms in optical lattices.
In this chapter, we examine ion-trap-based quantum simulators. This is the same type of hardware that is employed for ion-trap quantum computers, but we do not describe gated quantum computing in this book. Instead, we focus on examining the complex quantum dynamics in systems where individual ions can be trapped and manipulated. These systems are one of the hallmarks of the second quantum revolution, where we can manipulate quantum systems at the single-quantum level. We describe the phonon modes for ions in a trap, Raman transitions, spin-dependent forces that lead to effective spin models, how to prepare spin ground states, and extensions to the Lipkin-Meshkov-Glick and Dicke models.