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)计划的支持下，乔治敦大学的James Freericks和密歇根大学的Dominika Zgid正在合作开发在当前或不久的将来新一代量子计算机上解决量子化学问题的实用工具。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视为噪声中等规模的量子(NISQ)时代的设备，这意味着只能在它们上运行短程序。Freericks和Zgid将使用量子-经典混合方法来缓解量子噪声的存在，并只在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推进器。Freericks和Zgid将研究两个问题：(I)通过增加噪声测量的数量来权衡程序长度的效率如何？以及(Ii)通过适合于在NISQ设备上运行的虚拟稀疏哈密顿量来近似真实的量子化学哈密顿量，同时仍然产生优异的分子能量和动力学。在这个项目的教育部分，弗里克斯博士将为一本名为《没有微积分的量子力学》一书设计特定于化学的材料，这本书致力于开发数学前提条件低得多的量子力学课程。Dominika Zgid将为F.E.M.E.S.(在数学、工程和科学方面更出色的女性)组织准备一系列研讨会。原则上，有许多算法和策略可以在量子计算机上解决化学中的电子结构问题，但在近期设备的理论可能性和计算现实之间仍然存在巨大的鸿沟。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和他的团队将使用一种因式分解形式的么正耦合团簇ansatz(UCC)，其中具有在波函数ansatz中处理的少量精确项，因此需要在所准备的波函数中优化少量参数。然后，将UCC ansatz的能量期望值扩展到幅度的二阶，以获得大量额外的“虚拟”幅度。然后，通过在经典计算机上解决行减少问题来完成优化。这在测量电路深度之间进行了权衡。为了进一步最小化电路深度，Zgid和她的团队将采用一种有效的方法来产生适用于NISQ设备的超稀疏哈密顿量。这种方法是建立在分子自能的基础上的，并假定自能的动力学部分可以通过动态自能映射法从精确的分子体系转化为稀疏哈密顿所描述的体系。对于更广泛的影响，Freericks的工作使用了所谓的因式分解方法，使用了算子方法(不同于波函数和矩阵方法)，更适合于在未来的研究工作中训练学生，因为研究通常涉及与算子的工作。ZGID更广泛的影响力工作主要包括一个外展计划，旨在激发中学年龄的女孩未来在科学领域的职业生涯。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.