  Subspace-Search Variational Quantum Eigen solver (SSVQE) is a searching
method of multiple states and relies on the unitarity of transformations to
ensure the orthogonality of output states for multiple states. Therefore, this
method is thought to be a promising method for quantum chemistry because
ordinary Variational Quantum Eigen solver (VQE) can only calculate the excited
states step by step from the ground state based on Variational Quantum
deflation (VQD). We compare the advantage of VQE, SSVQE with/without the
constraint term and/or Tabu search term, which is added by the Lagrange
multiplier method so as to calculate the desired energy levels. We evaluated
the advantage by calculating each level of H2 and HeH, respectively. As there
simulation results, the accuracy calculated by constrained VQE with Tabu search
indicates higher accuracy than that of our other algorithm, for analysis on H2.
The accuracy calculated by constrained SSVQE indicates higher that of the
constrained VQE with Tabu search. We found it is beneficial for enhancing the
accuracy to use constraint terms decreasing convergence times to use Tabu
search terms according to the nature of molecules. We demonstrate that
constraint and Tabu search terms contribute to the accuracy and convergence
time on quantum chemical calculating.
