Simulating the Hamiltonian of Dimer Atomic Spin Model of One Dimensional Optical Lattice on Quantum Computers

TL;DR

This paper simulates the Hamiltonian of a one-dimensional dissipative spin system using quantum circuits on IBMQ, exploring entanglement, energy relations, and energy state estimation with VQE.

Contribution

It introduces a quantum circuit design for simulating the dissipative Ising Hamiltonian and applies VQE to estimate energy states, demonstrating quantum simulation of complex spin models.

Findings

Relation between entangled states and energy separation

Energy dependence on spin-spin coupling and energy separation

Fidelity analysis across multiple iterations

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 $N$ 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 ($\omega$) with the spin-spin coupling ($\lambda$) 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.