Topological Fermionic Quantum Simulation

量子物理学有可能在工业和经济上以重要的方式扩大计算机的能力。就像计算机已经成为人们生活中不可或缺的一部分一样，从长远来看，量子计算可能会变得同样有影响力。实现这一宏伟目标的道路需要沿途可以实现的里程碑，而量子模拟提供了许多这样的垫脚石。然而，为了利用量子计算来模拟物质，必须开发新的工具和方法来将费米子（例如电子和某些原子核）的模型系统映射到量子计算机上。该项目将开发包含拓扑思想的模型，帮助基于量子位的量子计算机模拟化学、物理和材料科学中发现的费米子系统。拓扑启发费米子到量子位映射的性质为在量子计算机的量子位上模拟电子结构开辟了新的可能性。这允许对非本地存储的信息进行本地寻址，这有助于简化量子模拟的算法。该项目的目标包括设计和实现可以在早期量子硬件上测试的新算法，并将其纳入开源代码集合中。该项目的成果将通过引入工具来服务于更广泛的科学界，这些工具将被整合到快速发展的量子技术中，从而超越传统计算机。该项目还包括通过与“女性参与科学项目”（Women in science project）合作，邀请大一和大二的女性实习生，努力增加在科学和技术领域代表性不足的群体的参与。作为了解如何最好地利用量子计算机的长期目标的一部分，拓扑费米子量子模拟项目旨在充实拓扑量子模拟算法。这项工作的中心假设是拓扑方法可以提高量子模拟的效率。这个假设是基于这个团队的初步发现，证明了基于编码自旋算子的局部性的费米子编码的好处。建议的工作有三个主要方向。第一部分深入研究了Bravyi-Kitaev超高速模型的自动化和实现，并探讨了其与toric代码的密切联系。第二个领域是考虑辅助费米子方法，其中包括额外的模式来减少自旋算子的局部性。第三，黑箱模拟的群论方法已经成熟，可以探索并与量子模拟这一不断发展的领域相结合。有两个交叉主题与项目的所有分支重叠：本地基础集设计和使用数值工具和现有量子硬件进行基准测试。基础集在确定任何模拟的效率和准确性方面起着至关重要的作用，而实际实现提供了成功的度量。基于拓扑的量子模拟算法的扩展对量子计算机的使用具有直接影响的潜力。此外，该项目开启了关于费米子本质的问题，提供了对模拟它们的局限性的见解，并告知量子模拟路径到量子霸权的要求。该项目由物理系的原子、分子和光学物理实验项目和化学系的化学理论、模型和计算方法项目（这两个部门都隶属于美国国家科学基金会数学和物理科学理事会）以及促进竞争性研究的既定计划（NSF EPSCoR计划）共同资助。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。

Quantum physics has the potential to expand computer power in industrially and economically significant ways. Just as computers have become an integral part of people's lives, quantum computation is likely to become equally impactful in the long term. The path to this grandiose goal needs achievable milestones along the way, and quantum simulation provides many such stepping stones. However, to take advantage of quantum computation for simulating matter, new tools and methods must be developed to map model systems of fermions (e.g. electrons and certain nuclei) onto quantum computers. This project will develop models that incorporate topological ideas that aid qubit-based quantum computers to simulate the fermion systems found throughout chemistry, physics, and materials science. The nature of topologically inspired fermion-to-qubit mappings opens new possibilities for simulating electronic structure on the qubits of a quantum computer. This allows local addressing of information that is stored non-locally which helps to simplify the algorithms for quantum simulation. The goals of this project include designing and implementing new algorithms that can be tested on early quantum hardware and incorporated into open-source code collections. The outcomes of this project will serve the broader scientific community by introducing tools that will be incorporated into rapidly developing quantum technology on the path to outpacing traditional computers. This project also include efforts to increase the inclusion of underrepresented groups in science and technology by inviting female freshmen and sophomore interns in conjunction with the Women In Science Project. As part of the long-term goal to understand how best to utilize a quantum computer, the Topological Fermionic Quantum Simulation project aims to flesh out topological quantum simulation algorithms. The central hypothesis of this work is that topological approaches can enhance the efficiency of quantum simulations. This hypothesis has been formulated based on this team's preliminary findings demonstrating benefits for fermionic encodings based on locality of the encoded spin operator. The proposed work has three major directions. The first delves into automation and implementation of the Bravyi-Kitaev Super-Fast model and explores its close connections to the toric code. The second area is to consider auxiliary fermion methods where additional modes are included to reduce the locality of the spin operators. Third, group theoretic approaches to black box simulation are ripe to explore and integrate with this growing area of quantum simulation. There are two cross-cutting themes that overlap with all branches of the project: local basis set design and benchmarking with numerical tools and with existing quantum hardware. The basis sets play a vital role in determining the efficiency and accuracy of any simulation while actual implementations provide metrics for success. Extension of quantum simulation algorithms based on topology has the potential for an immediate impact on the use of quantum computers. Additionally, this project opens questions about the nature of fermions, provides insights into the limitations of simulating them, and informs the requirements for the quantum simulation path to quantum supremacy.This project is jointly funded by the Atomic, Molecular, and Optical Physics Experiment program in the Division of Physics and the Chemical Theory, Models and Computational Methods program in the Division of Chemistry (both Divisions are in the NSF Directorate for Mathematical and Physical Sciences) as well as the Established Program to Stimulate Competitive Research (NSF EPSCoR program).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.