Implementation of the measurement-based variational quantum eigensolver on the 1D anisotropic XXZ spin-chain
Abstract
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 Jz = −1.5 to Jz = 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. The results showed that the constructed MBVQE has strong approximations for cases N = 2 and N = 3 whilst the cases N = 4 and N = 5 had weaker correlations between the approximation and the exact ground state energies. The study also observed that the MBVQE is not necessarily more costly than its circuit-based counterpart if proper flow structure and optimization techniques are applied.
