Implementation of the measurement-based variational quantum eigensolver on the 1D anisotropic XXZ spin-chain

The measurement-based variational quantum eigensolver (MBVQE) was applied to the 1D anisotropic XXZ Heisenberg model. Using Graphix, a Python-based software library capable of simulating MBQC patterns, and a classical optimizer, the anisotropy parameter was varied from J_z = -1.5 to J_z = 1.5 in half-integer increments for N = 2, 3, 4, 5 qubits. Optimization techniques were also applied to the system to ensure proper flow structure.