Effect of constraint and Tabu Search term on Variational Quantum Eigensolver and Subspace-Search Variational Quantum Eigensolver

Abstract

Subspace-Search Variational Quantum Eigensolver(SSVQE) is 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 promising method for quantum chemistry because ordinary Variational Quantum Eigensolver (VQE) can only calculate the excited states step by step from 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, that are added by Lagrange’s multiplier method so as to calculate the desired energy levels. We evaluated the advantage by calculating each energy levels 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 indicate higher that of the constrained VQE with Tabu search. We found it is beneficial for enhance 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.