TY - JOUR

T1 - Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers

T2 - the Cartesian component-separated approach

AU - Poirier, Bill

AU - Jerke, Jonathan

N1 - Publisher Copyright:
© the Owner Societies.

PY - 2022/2

Y1 - 2022/2

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=85124798372&partnerID=8YFLogxK

U2 - 10.1039/d1cp02036f

DO - 10.1039/d1cp02036f

M3 - Article

C2 - 35113096

AN - SCOPUS:85124798372

SN - 1463-9076

VL - 24

SP - 4437

EP - 4454

JO - Physical Chemistry Chemical Physics

JF - Physical Chemistry Chemical Physics

IS - 7

ER -