Reducing Qubit Requirements while Maintaining Numerical Precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach

The Journal of Physical Chemistry Letters, vol. 12, pp. 663–673

Abstract

We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wave functions. 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 22 qubits where conventional representation would for the same systems require 40-100 or more qubits. We further demonstrate reductions in the quantum circuits through the structure of the pair-natural orbitals.

Authors 4

1. Jakob S. Kottmann corresponding

   University of Toronto

   Affiliation as printed

   Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada

   Department of Computer Science, University of Toronto, Toronto, Canada

2. Philipp Schleich Aachen Center for Computational Engineering Science

   RWTH Aachen University

   Affiliation as printed

   Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany

3. Teresa Tamayo-Mendoza

   Harvard University · University of Toronto

   Affiliation as printed

   Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, United States

   Department of Computer Science, University of Toronto, Toronto, Canada

4. Alán Aspuru‐Guzik corresponding

   Canadian Institute for Advanced Research · University of Toronto · Vector Institute

   Affiliation as printed

   Canadian Institute for Advanced Research (CIFAR) Lebovic Fellow, Toronto, Canada

   Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Canada

   Department of Computer Science, University of Toronto, Toronto, Canada

   Vector Institute for Artificial Intelligence, Toronto, Canada