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arXiv:1106.1190 · Contemporary Physics

The trapped-ion qubit tool box

Roee Ozeri

Published Oct 27, 2011• 41 citations
arXivHTMLPDF

Abstract

In this tutorial we review the basic building blocks of Quantum Information Processing with cold trapped atomic ions. We mainly focus on methods to implement single-qubit rotations and two-qubit entangling gates, which form a universal set of quantum gates. Different ion qubit choices and their respective gate implementations are described.

DOI
10.1080/00107514.2011.603578

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In this tutorial we review the basic building blocks of Quantum Information Processing with cold trapped atomic ions. We mainly focus on methods to implement single-qubit rotations and two-qubit entangling gates, which form a universal set of quantum gates. Different ion qubit choices and their respective gate implementations are described.
In this tutorial we review the physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multi-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on off-resonant transitions associated with a qualitative estimation of the weak coupling regime and of the Lamb-Dicke regime is included in the Appendix.
In this tutorial we review the physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multiple-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on off-resonance transitions associated with a qualitative estimation of the weak-coupling regime is included in Appendix A and of the Lamb-Dicke regime in Appendix B.
Combining the strong, long-range interactions of cold Rydberg atoms with the controllability of trapped ions, trapped Rydberg ions provide a promising platform for scalable quantum information processing. As demonstrated in a breakthrough experiment [1], microwave dressing of Rydberg states induces permanent rotating dipole moments leading to strong interactions between highly excited ions. Due to the separation of timescales, the fast electronic dynamics of Rydberg ions decouple from the slower motional modes of the linear Coulomb crystal, which typically mediate entangling gates in ground-state ion systems. Therefore, Rydberg ions enable significantly faster gate operations. We demonstrate how the unique properties of trapped Rydberg ions can be exploited to realize fast and high-fidelity entangling gates, along with the associated challenges and strategies to overcome them. Different types of gate protocols for two- and three-qubit entangling gates with trapped Rydberg ions are presented and sources of infidelity are analyzed.