Methods for simulating chemistry using quantum computers

电子结构计算通常被化学、材料科学、物理学和工程学的研究人员用于根据量子力学的公认定律来建模和预测分子性质和过程。它们在计算量子化学中发挥着核心作用，对于发现和合理设计新的化学品和材料（如催化剂，药物，光电器件和其他功能分子组装体）至关重要。然而，他们遭受了一个实际的困难：找到量子多粒子问题的精确解需要计算资源，其规模与模拟系统的大小呈指数级。这是可能解的空间的指数缩放的结果，作为在模拟中使用的自由度的数量的函数，其与模拟系统的大小成比例。因此，当在传统计算机上进行时，化学的量子模拟被限制在非常小的分子上，或者需要很强的近似，这严重限制了模拟的准确性。量子计算机可以比传统（“经典”）计算机更快地执行某些计算任务。特别是，它们可以绕过限制经典机器上量子模拟准确性的维数灾难。量子模拟被认为是量子计算机最有前途的应用之一，目前可用的量子器件虽然不完善且尺寸有限，但可以产生和控制越来越复杂的量子态。由于最近出现的噪声，中等规模的量子（NISQ）设备，许多研究都致力于寻找量子算法，可以利用这种近期的机器，以实现显着的速度时，模拟感兴趣的化学系统（前景，通常被称为“量子优势”）。然而，量子算法的研究涉及适用于NISQ以及长期容错量子计算机的技术。本DPhil项目旨在研究使用量子计算机有效模拟化学系统的方法。特别是，将开发新的方法来寻找将电子分子系统编码为量子比特状态的准确和有效的映射，以及可以利用量子计算机的独特能力来求解电子哈密顿量的本征态的算法。该项目属于EPSRC量子技术研究领域的福尔斯项目。该博士生将由牛津大学化学系的大卫·图教授和牛津大学材料系的西蒙·本杰明教授共同指导。这项工作将是理论性的，但将涉及与布里斯托大学Anthony Laing教授的量子光子学小组的合作，量子算法将在该小组开发的真实的量子设备上进行测试。

Electronic structure calculations are routinely used by researchers in chemistry, materials science, physics and engineering to model and predict molecular properties and processes from the well-established laws of quantum mechanics. They play a central role in computational quantum chemistry and are crucial for the discovery and rational design of new chemicals and materials such as catalysts, drugs, optoelectronic devices, and other functional molecular assemblies. However, they suffer from a practical difficulty: finding the exact solution to a quantum many-particle problem requires computational resources which scale exponentially with the size of the simulated system. This is a consequence of the exponential scaling of the space of possible solutions as a function of the number of degrees of freedom that are used in the simulation, which is proportional to the size of the simulated system. Hence, when performed on a conventional computer, quantum simulations of chemistry are constrained to very small molecules or require strong approximations which severely limit the accuracy of simulations.Quantum computers could perform certain computational tasks much faster than conventional ("classical") computers. In particular, they could circumvent the curse of dimensionality which limits the accuracy of quantum simulation on classical machines. Consequently, quantum simulation is widely believed to be one of the most promising applications of quantum computers.Currently available quantum devices can create and control quantum states with increasing complexity, despite being imperfect and limited in size. Due to the recent emergence of noisy, intermediate-scale quantum (NISQ) devices, much research is being devoted towards finding quantum algorithms which can exploit such near-term machines to achieve a significant speed-up when simulating chemical systems of interest (a prospect often termed "quantum advantage"). However, research on quantum algorithms involves techniques suited for both NISQ as well as long-term, fault tolerant quantum computers.This DPhil project will aim to investigate methods for efficiently simulating chemical systems using quantum computers. In particular, new approaches will be developed for finding accurate and efficient mappings which encode electronic molecular systems into states of qubits, as well as algorithms which can exploit the unique power of quantum computers to solve for the eigenstates of electronic Hamiltonians. Such developments could enable a fundamental leap forward in electronic structure calculations and unlock the possibility of accurate computational quantum-mechanical modeling of complex molecular systems.The project falls within the EPSRC Quantum Technologies research area.The DPhil student will be co-supervised by Prof. David Tew (Department of Chemistry, University of Oxford) and Prof. Simon Benjamin (Department of Materials, University of Oxford). The work will be theoretical but will involve a collaboration with the Quantum Photonics group of Prof. Anthony Laing, University of Bristol, where quantum algorithms will be tested on real quantum devices developed in the group.