New Journal of Physics ( IF 2.8 ) Pub Date : 2021-04-14 , DOI: 10.1088/1367-2630/abe63d Kbra Yeter-Aydeniz 1, 2 , George Siopsis 3 , Raphael C Pooser 1, 2, 3
Time evolution and scattering simulation in phenomenological models are of great interest for testing and validating the potential for near-term quantum computers to simulate quantum field theories. Here, we simulate one-particle propagation and two-particle scattering in the one-dimensional transverse Ising model for 3 and 4 spatial sites with periodic boundary conditions on a quantum computer. We use the quantum Lanczos algorithm to obtain all energy levels and corresponding eigenstates of the system. We simplify the quantum computation by taking advantage of the symmetries of the system. These results enable us to compute one- and two-particle transition amplitudes, particle numbers for spatial sites, and the transverse magnetization as functions of time. The quantum circuits were executed on various IBM Q superconducting hardware. The experimental results are in very good agreement with the values obtained using exact diagonalization.
中文翻译:
使用量子 Lanczos 算法在 Ising 模型中进行散射本手稿由 UT-Battelle, LLC 撰写,与美国能源部签订的合同号为 DE-AC0500OR22725。美国政府保留,出版商通过接受文章出版,承认美国政府保留出版或复制本手稿的出版形式的非排他性、已付费、不可撤销的全球许可,或为了美国政府的目的,允许其他人这样做。能源部将根据 DOE 公共访问计划向公众提供这些联邦资助研究结果的访问权限。
现象学模型中的时间演化和散射模拟对于测试和验证近期量子计算机模拟量子场论的潜力具有重要意义。在这里,我们在量子计算机上模拟具有周期性边界条件的 3 和 4 个空间位点的一维横向 Ising 模型中的单粒子传播和两粒子散射。我们使用量子 Lanczos 算法来获得系统的所有能级和相应的本征态。我们通过利用系统的对称性来简化量子计算。这些结果使我们能够计算单粒子和双粒子跃迁幅度、空间位置的粒子数以及作为时间函数的横向磁化强度。量子电路在各种 IBM Q 超导硬件上执行。