Tools for analysing configuration interaction wavefunctions

V. A. Sidorovich

A new operator approach to the solution of the non-relativistic Schrödinger equation for few-body quantum systems with pair-wise interaction is presented. The problem is solved on the basis of the sequential account of configurations (SAC) method proposed. The wave-function of a few-body system determined with allowance for the configuration interaction (CI-wavefunction) is expressed in terms of the one-configuration wavefunctions with use of the configuration mixing operator (±) introduced in the paper. The examination is carried out with an example of a few-electron atomic system. An analytical expression for the (±) -operator has been represented and an integral equation for the CI-wavefunction has been obtained. It is shown that: (I) the correlation interaction inside an isolated configuration does not destroy the independent particle approximation; (ii) in the framework of the present approach the self-action is excluded. The present approach has enabled to receive an analytical expression for the (±) -operator without applying the non-physical procedure of 'switching-on' the interconfiguration interaction.

Anatoliy V. Luzanov

Koray Aydoğan, Anna R. Spak, Kade Head-Marsden +1 more

Estimating the ground-state energy of a quantum system is one of the most promising applications for quantum algorithms. Here we propose a variational quantum eigensolver (VQE) \emph{Ansatz} for finding ground state configuration interaction (CI) wavefunctions. We map CI for fermions to a quantum circuit using a subspace superposition, then apply diagonal Walsh operators to encode the wavefunction. The algorithm can be used to solve both full CI and selected CI wavefunctions, resuling in exact and near-exact solutions for electronic ground states. Both the subspace selection and wavefunction \emph{Ansatz} can be applied to any Hamiltonian that can be written in a qubit basis. The algorithm bypasses costly classical matrix diagonalizations, which is advantageous for large-scale applications. We demonstrate results for several molecules using quantum simulators and hardware.

D. G. Kanhere, Mihir Arjunwadkar

Mario Van Raemdonck

Zhendong Li, Garnet Kin‐Lic Chan

Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.