We present a quantum-classical algorithm for electronic structure calculations that dramatically reduces the quantum measurement cost of variational quantum eigensolver (VQE) approaches. While conventional VQE methods require measurements scaling as O(M^4) with system size M, the proposed occupation-number VQE (ON-VQE) reduces this cost to O(M/2) by avoiding reduced density matrix (RDM) measurements and relying exclusively on ONs. The method exploits only the diagonal elements of the one-particle RDM in the natural orbital representation, where occupations are obtained directly from computational-basis measurement outcomes. By restricting the variational ansatz to double excitations within orbital subspaces associated with electron pairs, the required measurements can be grouped into a small number of qubit-wise commuting observables, yielding an efficient and scalable measurement strategy. The approach is validated through simulations and executions on quantum hardware for the cubic H
8 cluster, demonstrating the feasibility of extracting accurate ONs from quantum measurements and evaluating electronic energies within the natural orbital functional (NOF) framework. Across representative molecular systems, the extracted ONs enable accurate energy evaluation with state-of-the-art NOFs while maintaining a dramatically reduced measurement cost. These results establish a scalable route toward quantum simulation of strongly correlated electronic systems, demonstrating that accurate electronic energies can be obtained from quantum measurements of ONs alone.
Accurate solutions to the electronic Schrödinger equation can provide valuable insight for electron interactions within molecular systems, accelerating the molecular design and discovery processes in many different applications. However, the availability of such accurate solutions are limited to small molecular systems due to both the extremely high computational complexity and the challenge of operating and executing these workloads on high-performance compute clusters. This work presents a massively scalable cloud-based quantum chemistry platform by implementing a highly parallelizable quantum chemistry method that provides a polynomial-scaling approximation to full configuration interaction (FCI). Our platform orchestrates more than one million virtual CPUs on the cloud to analyze the bond-breaking behaviour of carbon-fluoride bonds of per- and polyfluoroalkyl substances (PFAS) with near-exact accuracy within the chosen basis set. This is the first quantum chemistry calculation utilizing more than one million virtual CPUs on the cloud and is the most accurate electronic structure computation of PFAS bond breaking to date.
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum computers hold the promise of transcending such limitations although in the current era the size and noise of these devices militates against significant progress. Here we describe a new and chemically intuitive approach that permits a subdomain of the electronic structure of a molecule to be calculated accurately on a quantum device, while the rest of the molecule is described at a lower level of accuracy using density functional theory running on a classical computer. We demonstrate that our method produces improved results for molecules that cannot be simulated fully on quantum computers but which can be resolved classically at a lower level of approximation. Our algorithm is tunable, so that the size of the quantum simulation can be adjusted to run on available quantum resources. Therefore, as quantum devices become larger, our method will enable increasingly large subdomains to be studied accurately.