Embedded Quantum Computing Algorithms in Molecular Dynamics and Density Functional Theory

量子计算机有望实现经典计算机无法模拟的化学系统的精确模拟。虽然经典计算机能够精确地模拟小系统和简单的相互作用，但涉及强烈量子力学效应的反应却无法模拟。同样，随着要模拟的分子的大小增加，传统计算机很快就会变得不堪重负，缺乏必要的内存和处理能力。量子计算机利用量子力学效应处理信息，非常适合模拟自然发生的量子系统，如分子。当前这一代量子处理器的量子位数量有限，将模拟限制在传统计算机能够模拟的小分子上。因此，我们的目标是开发量子算法，将模拟任务分为两部分-一部分用于经典处理器，另一部分用于量子处理器。至关重要的是，我们的目标是开发一种算法，通过选择要使用的量子位的数量，使我们能够从量子计算中获得最大的收益。通过这种方式，我们将开发一种足够灵活的方法，以受益于量子计算硬件的改进，同时利用现有的量子处理器来执行比目前可能的更精确和更复杂的模拟。这种方法将扩展迄今为止化学模拟中使用的所谓“嵌入”算法，在这种算法中，精确但计算代价高昂的方法用于模拟的一小部分，然后将其嵌入到系统其余部分的更大但计算要求更低的模拟中。

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.