Deflation techniques in quantum chemistry: Excited states from ground states

Abstract

Applications of deflation techniques to the study of excited states of quantum systems are analyzed. It is demonstrated how these methods allow us to transform the excited state problem of one Hamiltonian, into the ground state problem of an auxiliary one. As an example, potential application in the density functional treatment of excited states is discussed. The inclusion of approximations in this scheme, such as the solution of the proposed model within a finite basis set is discussed. An extension of the Hartree-Fock (HF) method to excited states is presented. This new treatment includes previous self consistent field extensions to excited states and provides us with a way to obtain the HF extension to excited states of any ground state method. These results make the excited states of a system accessible through all ground state theoretical techniques.

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

“…Deflation has been the cornerstone of many classical algorithms in the past for obtaining excited states 63,64 and even a quantum algorithm as well with UCC-VQE. 65 But the formal reduction of our penalty procedure in Eq.S1 based on Theorem 2.1 to deflation offers a slightly different perspective.…”

“…This method using the penalty program in eq is formally equivalent to the deflation technique if one recognizes the idempotency of Ô = | g ⟩⟨ g |. Deflation has been the cornerstone of many classical algorithms in the past for obtaining excited states , and even a quantum algorithm as well with UCC-VQE . However, the formal reduction of our penalty procedure to deflation in eq based on Theorem 2.1 offers a slightly different perspective.…”

Communication: Kohn-Sham theory for excited states of Coulomb systems

“…3-5), although several time-independent approaches have also been given to treat excited states within DFT. [6][7][8][9][10][11][12][13][14][15][16][17][18] The subspace theory of Theophilou 6 and its generalization by Gross, Oliveira, and Kohn 7 are complicated by the requirement that a whole ensemble of states has to be considered. Individual excitedstates can be targeted using time-independent approaches based on the adiabatic connection 19 or the constrained search.…”