Simulating the Hamiltonian of dimer atomic spin model of one-dimensional optical lattice on quantum computers

Abstract

The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin system in the presence of magnetic field can be obtained from the Ising model. We simulate the above Hamiltonian by designing a quantum circuit with precise gate measurement and execute with the IBMQ experience platform through different [Formula: see text] states with controlled energy separation where we can check quantum synchronization in a dissipative lattice system. Our result shows the relation between various entangled states, the relation between the different energy separation ([Formula: see text]) with the spin–spin coupling ([Formula: see text]) in the lattice, along with fidelity calculations for several iterations of the model used. We also estimate the ground and first excited energy states of Ising-Hamiltonian using VQE algorithm and investigate the lowest energy values varying the number of layers of ansatz.