  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.
