  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.
