Embedded Quantum Computing Algorithms in Molecular Dynamics and Density Functional Theory

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Quantum computers promise to enable accurate simulation of chemical systems which cannot be simulated by classical computers. While classical computers are able to accurately simulate small systems and simple interactions, reactions which involve strongly quantum mechanical effects cannot be simulated. Similarly, as the size of the molecules to be simulated increases, classical computers quickly become overwhelmed, lacking the necessary memory and processing power. Quantum computers, which process information using quantum mechanical effects, are well suited to simulate naturally occurring quantum systems like molecules. The current generation of quantum processors are limited in their number of qubits, restricting simulations to small molecules, which classical computers are capable of simulating. We therefore aim to develop quantum algorithms to divide the simulation task into two parts - one for classicalprocessors and one for quantum processors. Crucially, we aim to develop an algorithm which allows us to obtain maximum benefit from quantum computation, by selecting the number of qubits to be used. In this way, we will develop a method which is flexible enough to benefit from improvements in quantum computing hardware, while utilising existing quantum processors to perform more accurate and complex simulations than are currently possible. This approach will extend so-called "embedding" algorithms used in chemistry simulations to date, in which an accurate but computationally expensive approach is used for a small part of a simulation, with this then embedded into a larger, but less computationally demanding, simulation of the rest of the system.