Phonon-mediated many-body quantum entanglement andlogic gates in ion traps

The high-fidelity multi-ion entangled states and quantum gates are the basis for trapped-ion quantumcomputing. Among the developed quantum gate schemes, Molmer-Sorensen gate is a relatively matureexperimental technique to realize multi-ion entanglement and quantum logic gates. In recent years, there havealso been schemes to realize ultrafast quantum entanglement and quantum logic gates that operate outside theLamb-Dicke regime by designing ultrafast laser pulse sequences. In such a many-body quantum system, theseentanglement gates couple the spin states between ions by driving either the phonon energy level or themotional state of the ion chain. To improve the fidelity of quantum gates, the modulated laser pulses or theappropriately designed pulse sequences are applied to decouple the multi-mode motional states. In this review,we summarize and analyze the essential aspects of realizing these entanglement gates from both theoretical andexperimental points of view. We also reveal that the basic physical process of realizing quantum gates is toutilize nonlinear interactions in non-equilibrium processes through driving the motional states of an ion chainwith laser fields.

Automated summary

This article discusses the implementation of high-fidelity multi-ion entangled states and quantum gates. It introduces the Molmer-Sorensen gate and the design of ultrafast laser pulse sequences. The spin states between ions are coupled by driving either the phonon energy level or the motional state of the ion chain. Modulated laser pulses or appropriately designed pulse sequences are applied to improve the fidelity of quantum gates.