Quantum Simulation of Electronic Structure using Quantum Density Functional Theory on a Programmable Integrated Photonic Circuit
Quantum simulations of molecular electronic structure hold the potential for computational advantage but are inherently limited by the linear scaling of qubit requirements with respect to system size. Quantum Density Functional Theory (Q-DFT) addresses this constraint by reformulating the interacting many-body problem in terms of a non-interacting Kohn--Sham reference system. Here, we present and experimentally validate a Q-DFT algorithm that requires only $\mathcal{O}(\log_2(N))$ qubits to simulate a system of $N$ orbitals, thereby reducing resource overhead. More precisely, we solve the Kohn--Sham problem for the lithium hydride (LiH) molecule using the ensemble extension of the variational quantum eigensolver paradigm that minimizes the energy of the system in the subspace spanned by the ground and first excited states. To execute this task, we encode the problem with qubits on a quantum photonic platform, utilizing an architecture that combines a deterministic quantum dot single-photon source with a programmable integrated photonic circuit. By evaluating the molecular ground- and first excited-state properties, this work establishes a pathway for simulating larger molecular systems, demonstrating the viability of integrating qubit-efficient algorithms with advanced reconfigurable photonic hardware for near-term quantum chemistry applications.