Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms

• URL: http://arxiv.org/abs/2307.07067v1
• Date: Thu, 13 Jul 2023 21:17:58 GMT
• Title: Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms
• Authors: Taehee Ko and Xiantao Li and Chunhao Wang
• Abstract summary: Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. This article presents a quantum algorithm that has a linear scaling with respect to the number of atoms.
• Score: 1.4502611532302039
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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