Issue 7, 2022

Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers: the Cartesian component-separated approach

Abstract

Traditional methods in quantum chemistry rely on Hartree–Fock-based Slater-determinant (SD) representations, whose underlying zeroth-order picture assumes separability by particle. Here, we explore a radically different approach, based on separability by Cartesian component, rather than by particle [J. Jerke and B. Poirier, J. Chem. Phys., 2018, 148, 104101]. The approach appears to be very well suited for 3D grid-based methods in quantum chemistry, and thereby also for so-called “first-quantized” quantum computing. We first present an overview of the approach as implemented on classical computers, including numerical results that justify performance claims. In particular, we perform numerical calculations with four explicit electrons that are equivalent to full-CI matrix diagonalization with nearly 1015 SDs. We then present an implementation for quantum computers for which the number of quantum gates (and to a lesser extent, the number of qubits) can be dramatically reduced, in comparison with other quantum circuitry that has been envisioned for implementing first-quantized “quantum computational chemistry” (QCC).

Graphical abstract: Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers: the Cartesian component-separated approach

Article information

Article type
Paper
Submitted
08 may 2021
Accepted
18 yan 2022
First published
19 yan 2022

Phys. Chem. Chem. Phys., 2022,24, 4437-4454

Author version available

Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers: the Cartesian component-separated approach

B. Poirier and J. Jerke, Phys. Chem. Chem. Phys., 2022, 24, 4437 DOI: 10.1039/D1CP02036F

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