Reducing qubit requirements while maintaining numerical precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach

TL;DR

This paper introduces a basis-set-free method for the variational quantum eigensolver that uses adaptive, system-specific representations to reduce qubit requirements while maintaining high numerical accuracy, enabling more efficient quantum simulations.

Contribution

The authors develop a novel approach that determines qubit Hamiltonians without global basis sets, significantly reducing qubit needs for accurate molecular simulations.

Findings

Achieved accurate results with up to 20 qubits using compact Hamiltonians.

Reduced qubit requirements from 40-100 to 20 for similar systems.

Demonstrated the method's potential for efficient quantum chemistry calculations.

Abstract

We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wavefunctions. Our approach directly determines system-specific representations of qubit Hamiltonians while fully omitting globally defined basis sets. In this work, we use directly determined pair-natural orbitals on the level of second-order perturbation theory. This results in compact qubit Hamiltonians with high numerical accuracy. We demonstrate initial applications with compact Hamiltonians on up to 20 qubits where conventional representation would for the same systems require 40-100 or more qubits.