Implementation of the Density-functional Theory on Quantum Computers

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.