{
  "id": "2307.07067",
  "version": "v1",
  "published": "2023-07-13T21:17:58.000Z",
  "updated": "2023-07-13T21:17:58.000Z",
  "title": "Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms",
  "authors": [
    "Taehee Ko",
    "Xiantao Li",
    "Chunhao Wang"
  ],
  "categories": [
    "quant-ph",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing the Hamiltonian, for which a classical algorithm typically requires a computational complexity that scales cubically with respect to the number of electrons. This limits DFT's applicability to large-scale problems with complex chemical environments and microstructures. This article presents a quantum algorithm that has a linear scaling with respect to the number of atoms, which is much smaller than the number of electrons. Our algorithm leverages the quantum singular value transformation (QSVT) to generate a quantum circuit to encode the density-matrix, and an estimation method for computing the output electron density. In addition, we present a randomized block coordinate fixed-point method to accelerate the self-consistent field calculations by reducing the number of components of the electron density that needs to be estimated. The proposed framework is accompanied by a rigorous error analysis that quantifies the function approximation error, the statistical fluctuation, and the iteration complexity. In particular, the analysis of our self-consistent iterations takes into account the measurement noise from the quantum circuit. These advancements offer a promising avenue for tackling large-scale DFT problems, enabling simulations of complex systems that were previously computationally infeasible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-13T21:17:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "density-functional theory",
      "quantum computers",
      "linear scaling",
      "implementation",
      "quantum singular value transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}