Scalable approach to quantum simulation via projection-based embedding

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. Many believe quantum computers will transcend such limitations although in the current era the size and noise of these devices militates against significant progress. Here we describe a chemically intuitive approach that permits a subdomain of a molecule's electronic structure 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 this approach produces improved results for molecules that cannot be simulated fully on current quantum computers but which can be resolved classically at a cheaper level of approximation. The 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, this method will enable increasingly large subdomains to be studied accurately.