Scattering in the Ising Model Using Quantum Lanczos Algorithm

TL;DR

This paper demonstrates simulating one- and two-particle scattering in a small transverse Ising model using a quantum Lanczos algorithm on IBM hardware, showing promising results for quantum field theory simulations.

Contribution

It introduces a quantum algorithm for simulating scattering in the Ising model and leverages symmetries to simplify quantum computations on near-term hardware.

Findings

Quantum Lanczos algorithm effectively computes energy levels and eigenstates.

Experimental results closely match exact diagonalization.

Simulations validate potential for quantum field theory studies on quantum computers.

Abstract

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 IBM 5-qubit superconducting hardware. The experimental results with readout error mitigation are in very good agreement with the values obtained using exact diagonalization.