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

TL;DR

This paper investigates how adding constraint and Tabu search terms affects the accuracy and convergence time of Variational Quantum Eigensolver (VQE) and Subspace-Search VQE (SSVQE) in quantum chemistry, demonstrating improved performance with these methods.

Contribution

It introduces the combined use of constraint and Tabu search terms in VQE and SSVQE, showing their benefits for accuracy and convergence in quantum chemical calculations.

Findings

Constrained VQE with Tabu search yields higher accuracy than unconstrained methods.

Constrained SSVQE outperforms constrained VQE with Tabu search in accuracy.

Using constraints and Tabu search reduces convergence times for molecular energy calculations.

Abstract

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.