Short-depth trial-wavefunctions for the variational quantum eigensolver based on the problem Hamiltonian

TL;DR

This paper introduces a method for constructing efficient trial wavefunctions for the variational quantum eigensolver by selecting key Pauli terms from the problem Hamiltonian, resulting in short-depth circuits that achieve chemical accuracy.

Contribution

It proposes two novel approaches inspired by QAOA and imaginary-time evolution for generating trial wavefunctions using minimal Pauli terms, improving efficiency and scalability.

Findings

Achieves chemical accuracy with few Pauli terms

Produces short-depth quantum circuits with few variational parameters

Demonstrates scalability for larger molecules

Abstract

For the variational quantum eigensolver we propose to generate trial wavefunctions from a small amount of selected Pauli terms of the problem Hamiltonian. Two different approaches, one inspired by the quantum approximate optimization algorithm and the other by imaginary-time evolution, are proposed and studied in detail. Using numerical calculations, we study the efficiency of these trial wavefunctions for finding the ground-state energy of three molecules: H2, LiH and H2O. We find that only a small number of Pauli terms are needed to reach chemical accuracy, leading to short-depth quantum circuits with a small number of variational parameters. For the LiH molecule, the quantum circuit consists of 36 two-qubit gates, 45 one-qubit gates, and four variational parameters, with a favorable scaling for larger molecules.