Subspace Selected Variational Quantum Configuration Interaction with a Partial Walsh Series

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.