Collaborative Research: Practical strategies for implementing quantum chemistry on near-term quantum computers

在化学系化学理论、模型和计算方法（CTMC）项目的支持下，乔治城大学的James Freericks和密歇根大学的Dominika Zgid正在合作开发量子化学问题在当前或即将到来的下一代量子计算机上的实际实现。量子化学被认为是量子计算最有前途的应用之一。但是，目前可用的量子硬件平台被认为是嘈杂的中尺度量子（NISQ）时代设备，这意味着只能在其上运行短程序。Freericks和Zgid将采用混合量子-经典方法来减轻量子噪声的存在，并且只在NISQ机器上运行最重要的计算部分，而其余部分将在经典计算机上执行。通过这种方式，量子计算机被视为完整计算的加速器或使能器。Freericks和Zgid将研究两个问题：(i)如何有效地通过增加噪声测量的数量来权衡程序的长度？（ii）通过一个适合在NISQ设备上运行的虚拟的稀疏哈密顿量来近似真实的量子化学哈密顿量，同时仍然产生优秀的分子能量和动力学，能有多精确？在这个项目的教育部分，Freericks博士将为一本名为《没有微积分的量子力学》的书设计特定的化学材料；一本致力于发展量子力学课程的书，数学先决条件要低得多。Dominika Zgid将为F.E.M.M.E.S.（女性在数学、工程和科学方面更出色）组织准备一系列研讨会。原则上，存在许多算法和策略，用于在量子计算机上解决化学中的电子结构问题，但在理论可能性和近期设备的计算现实之间仍然存在巨大鸿沟。Freericks和Zgid打算通过提供在量子计算机上解决电子结构问题的实际实现来跨越这一鸿沟。Freericks和他的团队将采用一种分解形式的统一耦合簇分析（UCC），在波函数分析中处理少量精确项，因此在准备好的波函数中需要优化少量参数。然后，在UCC分析的振幅中，将能量期望值扩展到二阶，以补充大量额外的“虚拟”振幅。然后通过在经典计算机上解决行缩减问题来实现优化。这就牺牲了电路深度来进行测量。为了进一步减少电路深度，Zgid和她的团队将采用一种有效的方法来产生适合NISQ器件的超稀疏哈密顿量。该方法基于分子自能，并假设自能的动力学部分可以通过动态自能映射方法（DSEM）从精确分子系统转换为稀疏哈密顿函数描述的系统。对于更广泛的影响，Freericks的工作使用了所谓的因子分解方法，使用算子方法（不同于波函数和矩阵方法），更适合培养学生在未来的研究工作中，因为研究通常涉及到与算子的工作。Zgid更广泛的影响工作主要包括一个外联计划，旨在激励中学年龄女孩未来从事科学事业。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

With support from the Chemical Theory, Models and Computational Methods (CTMC) program in the Division of Chemistry, James Freericks of Georgetown University and Dominika Zgid of the University of Michigan are collaborating to develop practical implementations for quantum chemistry problems on current or near future generation of quantum computers. Quantum chemistry is viewed as one of the most promising applications of quantum computing. But, currently available quantum hardware platforms are regarded as noisy intermediate scale quantum (NISQ) era devices, implying only short programs can be run on them. Freericks and Zgid will employ hybrid quantum-classical methodologies to mitigate the presence of the quantum noise and run only the most important part of the calculation on a NISQ machine, while the remainder will be executed on a classical computer. In this way, the quantum computer is viewed as an accelerator or enabler for the full calculation. Freericks and Zgid will investigate two questions: (i) How efficiently can one trade off the length of the program by increasing the number of noisy measurements? and (ii) How accurately can a real quantum chemistry Hamiltonian be approximated via a fictitious sparse Hamiltonian that is suitable to be run on a NISQ device, while still yielding excellent molecular energies and dynamics. In the educational component of this project, Dr. Freericks will design chemistry-specific materials for a book entitled Quantum Mechanics without Calculus; a book devoted to developing quantum mechanics curriculum with a much lower mathematics prerequisite. Dominika Zgid will prepare a series of workshops for the F.E.M.M.E.S. (women excelling more in math, engineering and sciences) organization.Many algorithms and strategies exist, in principle, for solving the electronic structure problem in chemistry on a quantum computer, but there remains a huge chasm between the theoretical possibilities and the computational realities of near-term devices. Freericks and Zgid intend to cross that chasm by providing practical implementations for electronic structure problems to be solved on quantum computers. Freericks and his group will employ a factorized form of the unitary coupled cluster ansatz (UCC) with a small number of exact terms treated in the wavefunction ansatz, and hence a small number of parameters that will need to be optimized in the prepared wavefunction. It is then supplemented by an expansion of the energy expectation value to second order in the amplitudes for the UCC ansatz for a large number of additional "virtual" amplitudes. Optimization is then accomplished by solving a row-reduction problem on the classical computer. This trades off circuit depth for measurements. To further minimize circuit depths, Zgid and her group will employ an effective approach to produce ultra-sparse Hamiltonians suitable for NISQ devices. This approach is based on molecular self-energy and assumes that the dynamical part of the self-energy will be translatable from the exact molecular system to a system described by the sparse Hamiltonian via the dynamical self-energy mapping methodology (DSEM). For the broader impacts, the work by Freericks uses the so-called factorization method, employing operator methods (different from both wavefunction and matrix methods), and more suitable for training students in future research work, since research usually involves working with operators. The broader impact work of Zgid consists largely in an outreach program that is designed to excite middle-school-age girls for future careers in science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.