Exploring complexity and scalability of Near-term Quantum Computing algorithms for Quantum Chemistry

目前的计算能力严重限制了分子系统的研究。随着分子系统的复杂性呈指数级增长，即使对于小系统，精确计算化学性质也变得具有挑战性。量子计算在更大的分子系统建模方面提供了许多希望，而不是我们目前所能做的经典。变分量子本征求解器（VQE）是近期有望在量子化学中找到应用的量子算法的主要例子之一。然而，它的可扩展性在很大程度上仍然存在问题。最近，Zhenyu Cai （Oxford）对50量子位Fermi-Hubbard模型的VQE模拟进行了资源估计，并讨论了在近期量子硬件背景下多核NISQ处理和更好的错误缓解的需求。VQE依赖于经典的预处理。特别是，我们必须首先计算系统的第二个量子化哈密顿量，对于N个轨道，它的计算代价已经是0 （N^4）。因此，它永远不会取代最广泛使用的计算量子化学方法，密度泛函理论（DFT），因为它的求解成本是O(N^3)，而不假设任何稀疏性（这将降低两种情况下的成本）。为了在计算上具有相关性，VQE首先必须能够产生比DFT更准确的结果。同时，合适的基准分析必须将VQE的结果和计算成本与更精确的量子化学方法（如全构型相互作用（FCI））进行比较。Rahko目前正在领导一个旨在研究VQE可扩展性的项目。这家初创公司正在寻找一名CASE博士研究生，合作进一步开展这项研究，并对近期将量子计算用于量子化学的可行性进行正式研究。特别是，学生将研究量子化学量子算法的最新文献（超越VQE），并建立一种方法来评估其可扩展性，与DFT和FCI等最佳实践相比较。作为该项目的一部分，学生将定义最先进的方法来实现量子算法，并将在整个程序堆栈中识别瓶颈和可能的改进。该学生将获得Rahko的量子开发平台Hyrax，并将通过Rahko和UCL的合作伙伴关系获得真正的量子计算机（例如AWS bracet， Azure quantum， IMBQ）和超级计算机。

The study of molecular systems is heavily limited by current computing capabilities. As molecular systems grow in complexity exponentially, accurate computation of chemical properties becomes challenging even for small systems. Quantum computing offers many promises in terms of much larger modelling molecular systems than what we can currently do classically. The Variational Quantum Eigensolver (VQE) is one of the main examples of near-term quantum algorithms that are expected to find application in quantum chemistry. However, its scalability is still largely under question. Recently Zhenyu Cai (Oxford) has implemented resource estimates for VQE simulations of the 50-qubit Fermi-Hubbard Model, and discussed the requirement of multi-core NISQ processing to and better error mitigation in the context of near-term quantum hardware. The VQE, relies on classical pre-processing. In particular, we must first compute the second quantised Hamiltonian of the system, which already has a computational cost of O(N^4) for N orbitals. As such it will never replace the most widely used computational quantum chemistry method, Density Functional Theory (DFT) as its cost of solving is O(N^3) not assuming any sparsity (this would bring the cost in either case down). To be computationally relevant, the VQE must first and foremost be able to produce significantly more accurate results than DFT. At the same time, a suitable benchmarking analysis must compare the result and computational cost of VQE to a more accurate Quantum Chemistry method such as Full Configuration Interaction (FCI)/Rahko is currently leading a project aiming at studying the scalability of the VQE. The start-up is looking for a CASE PhD student to collaborate on furthering this research and conduct a formal study of the feasibility of using near-term quantum computing for quantum chemistry.In particular, the student will be researching the latest literature on Quantum algorithms for quantum chemistry (beyond VQE) and build a methodology for assessing their scalability in comparison to the best practices for the likes of DFT and FCI. As part of this project, the student will define the state-of-the-art methods to implement quantum algorithms and will identify bottlenecks and possible improvements for their scalability throughout the programme stack. The student will be given access to Rahko's quantum development platform, Hyrax , and will gain access to real quantum computers (e.g. AWS Braket, Azure Quantum, IMBQ) and supercomputers through Rahko's and UCL's partnerships.