Orbital-free density functional theory with first-quantized quantum subroutines

In this study, we propose a quantum-classical hybrid scheme for performing orbital-free density functional theory (OFDFT) using probabilistic imaginary-time evolution (PITE), designed for the era of fault-tolerant quantum computers (FTQC), as a material calculation method for large-scale systems. PITE is applied to the part of OFDFT that searches the ground state of the Hamiltonian in each self-consistent field (SCF) iteration, while the other parts such as electron density and Hamiltonian updates are performed by existing algorithms on classical computers. When the simulation cell is discretized into $N_\mathrm{g}$ grid points, combined with quantum phase estimation (QPE), it is shown that obtaining the ground state energy of Hamiltonian requires a circuit depth of $O(\log N_\mathrm{g})$. The ground state calculation part in OFDFT is expected to be accelerated, for example, by creating an appropriate preconditioner from the estimated ground state energy for the locally optimal block preconditioned conjugate gradient (LOBPCG) method.