Quantum-Accelerated Self-Consistent Field: A Hybrid Algorithm
arXiv:2606.20176
The paper proposes a hybrid quantum‑classical algorithm, GAS‑SCF, that uses Grover‑based adaptive search and amplitude amplification to accelerate self‑consistent field calculations in quantum chemistry, demonstrating a theoretical quadratic speed‑up and providing small‑scale simulations as proof of concept.
Abstract
We present the Grover adaptive search self-consistent field (GAS-SCF) algorithm. GAS-SCF leverages quantum arithmetic to construct an efficient oracle that marks target states (Fock states) which improve upon some initial classical energy estimate. Amplitude amplification then increases the probability of measuring these states. This approach offers a theoretical quadratic speed-up for the optimization problem encountered in SCF quantum chemistry and establishes a baseline against which structured optimization algorithms, such as QAOA and DQI may be compared. In this work, we classically simulate three examples as proofs of concept of the algorithm, the largest consisting of 26 qubits. We then extend our analysis to two larger systems, with O3 representing the largest case at 330 qubits. These examples are chosen to probe classically challenging SCF regimes. Achieving chemically relevant applications of GAS-SCF will require large-scale, fault-tolerant quantum hardware.
14 pages, (10 page SI), 6 Figures