Subspace Selected Variational Quantum Configuration Interaction with a Partial Walsh Series

TL;DR

This paper introduces a variational quantum eigensolver that efficiently finds ground state energies of quantum systems by encoding CI wavefunctions with Walsh operators, applicable to large molecules and avoiding classical diagonalizations.

Contribution

It presents a novel VQE Ansatz using Walsh operators for encoding CI wavefunctions, enabling efficient quantum solutions for electronic ground states without classical diagonalizations.

Findings

Achieves exact and near-exact ground state energies for molecules.

Demonstrates effectiveness on quantum simulators and hardware.

Applicable to any Hamiltonian in a qubit basis.

Abstract

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.