A project to study analogue and digital quantum simulations and analyse their robustness against noises. The noise model implemented for analogue quantum simulation is referred to as physical noise model. The noise model implemented for digital quantum simulation is referred to as quantum depolarizing channel model. A 1D transverse and longitudinal field Ising-like Hamiltonian with polynomially decaying spin-spin coupling over distance is engineered as a case study. This Hamiltonian is given by,
,
where and
are Pauli operators acting on sites i and j respectively. This 1D Ising chain satisfies free boundary conditions. Therefore, the first spin is not adjacent to the last spin.