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Quantum simulation of a quantum field theory in a trapped ion system realized by Prof. Kihwan Kim’s group

Quantum simulation of a quantum field theory in a trapped ion system realized by Prof. Kihwan Kim’s group

Prof. Kihwan Kim’s trapped ion group at the Center of Quantum Information at the Institute for Interdisciplinary Information Sciences has realized the quantum simulation of a fundamental model in quantum field theory in a trapped ion system. The work was published in Nature Communications on January 15th,2018, and is entitled “Experimental quantum simulation of fermion-antifermion scattering via boson exchange in a trapped ion.”

Figure 1 Fermion-antifermion scattering process and its mapping to a 171Yb+ ion system. (a) Diagram of the interactions between a fermion, an antifermion, and bosons. (b) Diagram of the encoding and operation to implement the interaction Hamiltonian with a 171Yb+ trapped ion.

The field of quantum simulations with controllable quantum systems is rapidly developing and the time when a quantum simulator can outperform classical computational capacities does not look that far away. Such a quantum simulation device is expected to execute complicated computational tasks, such as involved computations in the frames of quantum field theory or quantum chemistry. Quantum field theories are among the most successful descriptions of the physical world, from elementary particles to condensed matter systems. One of the most prominent approaches to analyze the theories is to perturbatively expand the Dyson series using Feynman diagrams. However, certain regimes of theories cannot be studied in perturbation theory, where couplings are much stronger than the system energies, for example. A quantum simulator, on the other hand, can be a powerful tool to simulate quantum field theories much more efficiently than classical computers.

In this paper, Prof. Kihwan Kim’s group demonstrate experimentally how a trapped ion system can simulate phenomena in quantum field theories, such as particle creation and annihilation or self-interaction processes. In their experiment, they performed a proof-of-principle quantum simulation of a fermion-antifermion scattering process mediated by bosonic modes. For the simulation, they exploited the vibrational modes of the ion to encode the simulated bosonic modes, while they mapped the fermionic ones onto four of the electronic levels of the ion. This is the first time that a trapped ion system has been used to simultaneously simulate bosons and fermions by profiting from the different degrees of freedom of the ion. Moreover, their approach was not restricted to perturbative regimes, as is the case in the standard classical or quantum computational approaches; instead they were able to observe the exact dynamics of the scattering process in highly non-perturbative regimes, something that would be cumbersome to compute even with dozens of qubits in a digital quantum computer. It is believed that their experiment opens the door to the digital-analog scalable quantum simulation of quantum field theories in perturbative and non-perturbative regimes. 

Figure 2 Trapped-ion simulation results of quantum field theories. Fermion and antifermion annihilation process in the strong coupling, where both the self-interaction and pair production processes strongly influence the dynamics.

The corresponding authors are an assistant research scientist, Jing-Ning Zhang, and tenured associate professor,Kihwan Kim. The equally contributing first authors are Zhang Xiang and Zhang Kuan, a Ph.D. candidate in IIIS, who carried out the experiments with Yangchao Shen and Shuaining Zhang. Zhang Xiang graduated from IIIS and is currently working principally in Renmin University. The assistant research scientist Jing-Ning Zhang, Prof. Man-Hong Yung from the Southern University of Science and Technology, and the team of Prof. Enrique Solano in the University of the Basque Country, Dr. Julen Pedernales, Dr. Jorge Casanova, and Dr. Lucas Lamata, provided the theoretical support. The research was funded by the National Basic Research Program of China, and the National Natural Science Foundation of China.

The full paper is available at: https://www.nature.com/articles/s41467-017-02507-y

Contributor: The Institute for Interdisciplinary Information Sciences
Editor: Guo Lili