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.

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。