Variational quantum excited state solvers

Abstract

The computation of ground and excited state energies of electronic Hamiltonians holds significant applications across various industries. The Variational Quantum Eigensolver (VQE) has been proposed for determining the ground-state energy of molecules, thereby boosting optimism for the near-term applications of quantum computers. In this thesis, we explore the extension of VQE for excited state calculation, specifically focusing on the Variational Quantum Deflation (VQD) algorithm and the Subspace Search Variational Quantum Eigensolver (SSVQE). We then propose a Joint Excited State Solver, which combines the VQD and SSVQE for the efficient computation of multiple eigenstates of a given Hamiltonian. This approach aims to overcome the shortcoming of each method by the strengths of the other. To validate the concept and demonstrate the performance improvements achieved through this joint solver, we calculate the excited states of selected small molecules.