Full-Dimensional Schr\"odinger Wavefunction Calculations using Tensors and Quantum Computers: the Cartesian component-separated approach

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. 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 $10^{15}$ SDs. We then present an implementation for quantum computers, for which both the number of qubits, and the number of quantum gates, may be substantially reduced in comparison with other quantum circuitry that has been envisioned for implementing first-quantized "quantum computational chemistry" (QCC).