Recently, the Duan Luming Research Group of Tsinghua University has made important progress in the field of ion trap quantum simulation, and for the first time realized the Rabi-Hubbard model in the experiment, surpassing the simulation capabilities of the current classical supercomputer and is an important step towards large-scale ion trap quantum computing and simulation.
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The Rabbi-Hubbard model is a combination of two basic models in quantum optics and condensed matter physics, the Rabbi model and the Hubbard model. The Rabbinic model dates back to 1936 and describes the interaction of light fields with matter; the Hubbard model, which originated in 1963 as the most basic model for describing the interaction of particles in the lattice, has now developed as a starting point for many fields of condensed matter physics. The Rabbi-Hubbard model, on the other hand, includes the local rabbinic spin-phonon interaction and the phonon-phonon interaction between lattice points, which combine to show a wealth of physical properties. The experimental protocol for this model was originally proposed in a cavity quantum electrodynamic system, but it has not been experimentally realized before due to technical difficulties.
This time, the Duan Luming Research Group of the Institute for Interdisciplinary Information Sciences of Tsinghua University realized the aforementioned model for the first time in the experiment, and verified the quantum phase transition and quantum dynamics process of the model. By manipulating 16 ions and 16 simple harmonic vibration modes, the team reached the effective spatial dimension of the quantum simulation problem to 257, exceeding the simulation capabilities of existing classical supercomputers. The results were recently published in the Physical Review Letters.
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Thanks to the highly controllable nature of the ion trap quantum simulation platform, the researchers realized a controllable quantum simulation of the Rabbi-Hubbard model. Through the precise manipulation of the laser, the team realized the interaction between the ion qubits and the local phonons, and the Coulomb interaction in the ion trap system formed a local phonon exchange term between different ions.
In addition, the researchers also verified the successful realization of the Rabbi-Hubbard model through two aspects of quantum phase transition and quantum dynamics. In terms of quantum phase transition, the team achieved the conversion between coherent and incoherent phases through adiabatic evolution, and in the process successfully observed the quantum phase transition phenomenon in ion arrays of different sizes by measuring the sequence parameter of spatial spin association, which was consistent with the results of the approximate calculation of the DMRG method. DMRG, or density matrix reorganization group, is a numerical algorithm used to accurately calculate quantum multibody systems, proposed in 1992 by American physicist Steven R. White.
Evolution of order parameters and quantum phase transitions of the Rabbi-Hubbard model, image from Tsinghua University
In terms of quantum dynamics, the Rabbi-Hubbard model incorporates the coupling of the spin mode of ions and the vibration mode of space, which significantly increases the effective Hilbert Space dimension of the system, making classical simulations more difficult. The researchers observed quantum dynamics evolutions that met the expectations of classical simulations under small-scale systems (i.e., 2 ions and 4 ions), and together with the quantum phase transition, proved that the team successfully implemented the Rabbi-Hubbard model in the experiment.
In large-scale systems (i.e., 16 ions) and strongly coupled parameter intervals, the commonly used classical approximation method will no longer be applicable. The active spatial dimension of tsinghua team experimental system is as high as 257, and the relevant dynamic processes are difficult to simulate and calculate by classical computers.
Evolution of spin dynamics of the Rabbi-Hubbard model, image from Tsinghua University
The above research demonstrates the quantum multibody simulation based on the ion trap platform, which introduces the degrees of freedom of space vibration into the quantum simulation, realizes the scale of the problem that is difficult for classical computers to calculate, and is an important step towards the future large-scale ion trap quantum computing and quantum simulation.
The co-first authors of the paper are Mei Quanxin, Li Bowen, and Assistant Professor Wu Yukai, phD students of the Institute for Interdisciplinary Information Sciences of Tsinghua University, and the corresponding authors are Professor Duan Luming, and other authors include doctoral students Wang Ye, associate researcher Zhou Zichao, and researchers Cai Minglei and Yao Lin of Huayi Quantum Company. The project has received funding and support from Tsinghua University Independent Research Program, Beijing Institute of Quantum Information Science, National Key R&D Program, Frontier Science Center for Quantum Information of the Ministry of Education, Tsinghua University Mizuki Scholar Program, Postdoctoral International Exchange Program Introduction Project, and Tsinghua University Research Startup Fund.