Finite Temperature Simulation of Non-Markovian Quantum Dynamics in Condensed Phase using Quantum Computers

在化学系化学理论、模型和计算方法计划的支持下，乔治梅森大学的王飞将致力于开发高效的量子算法，在量子计算机上执行凝聚态量子动力学模拟。许多重要的物理和化学过程发生在凝聚相中，跨越溶液中的化学反应，半导体界面上的电荷转移，以及分子聚集体中的太阳能转换。对这些过程的科学研究不仅促进了我们对这些过程的基本理解，还为材料设计和环境可持续发展提供了实用的解决方案。由于这些过程中的许多都涉及电荷迁移和激发能量转移，涉及多个自由度的量子动力学对于描述它们是必不可少的。然而，这种模拟在经典计算机上是资源密集型的。另一方面，量子计算机天然地适合于量子模拟。随着算法的发展，王博士的目标是展示凝聚态量子动力学模拟的量子加速，并展示量子计算在量子模拟领域的实际应用。参与该项目的研究生和博士后研究人员将接受严格的量子信息科学培训，掌握最先进的量子模拟工具。通过为本科生和高中生提供实习计划，PI将支持代表性不足和经济困难的群体。这些努力不仅将鼓励广泛参与STEM(科学、技术、工程和数学)，而且还有助于培养未来的量子劳动力，以便在学术界和工业领域就业。这项工作的重点将是发展有限温度非马尔科夫时间演化的有效量子算法，这为凝聚相量子动力学提供了一个通用的框架。该项目的新进展将包括么正算子的构建、高效的量子电路编译、模型和真实系统模拟，以及不同类型量子设备之间的性能比较。我们将探索三种数学方法(么正膨胀、奇异值分解和酉算子的线性组合)来进行非酉化到酉化，并基于复杂性理论对它们的有效性进行评估。将研究两种通用的电路编译方法：一种执行精确的数学分解，另一种使用变分量子电路方法。将根据门计数和电路深度来确定最佳电路结构。该算法将在自旋-玻色子模型和现实系统上进行测试，并将比较囚禁离子和超导设备的性能。该算法的成功将为有限温度下多态非马尔可夫量子动力学的模拟提供量子加速。将提出一个用户友好和开源的平台，这样，只需输入参数，就可以在量子计算机上进行动态模拟并分析结果。这项工作可能会启发未来用于模拟开放量子系统动力学的量子算法设计。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 program in the Division of Chemistry, Fei Wang of George Mason University will work to develop efficient quantum algorithms to perform condensed phase quantum dynamics simulations on quantum computers. Many important physical and chemical processes occur in the condensed phase, spanning chemical reactions in solutions, charge transfer at semiconductor interfaces, and solar energy conversion in molecular aggregates. The scientific investigation of these processes not only promotes our fundamental understanding but also offers practical solutions to materials design and environmental sustainability. As many of these processes involve charge migration and excitation energy transfer, quantum dynamics involving many degrees of freedom is essential for their description. However, such simulations are resource intensive on classical computers. On the other hand, quantum computers are naturally suited for quantum simulations. With algorithm development, Dr. Wang is aiming to show quantum speedup for quantum dynamics simulations in condensed phases, and demonstrate practical applications of quantum computing in the area of quantum simulation. Graduate students and postdoctoral researchers involved in this project will receive rigorous training in quantum information science and master state-of-the-art quantum simulation tools. Through internship programs offered to undergraduate and high school students, the PI will support underrepresented and economically disadvantaged groups. These efforts will not only encourage broad participation in STEM (science, technology, engineering and mathematics), but also help to educate a future quantum workforce for careers in academia and industry. The focus of this work will be to develop efficient quantum algorithms for finite-temperature non-Markovian time evolution, which offers a general framework for condensed phase quantum dynamics. New advances in this project will cover unitary operator construction, efficient quantum circuit compilation, model and real system simulations, and performance comparison between different types of quantum devices. Three mathematical methods will be explored (unitary dilation, singular value decomposition, and linear combinations of unitary operators) for non-unitary to unitary conversion, and their effectiveness will be assessed based on complexity theory. Two general approaches will be investigated for circuit compilation: one performs the exact mathematical decomposition, and the other uses the variational quantum circuit method. The optimal circuit structure will be identified based on gate counts and circuit depth. The algorithm will be tested on spin-boson models as well as on realistic systems, and the performance of trapped ions and superconducting devices will be compared. The success of the algorithm will offer quantum speedup in simulations of multi-state non-Markovian quantum dynamics at finite temperature. A user-friendly and open-source platform will be put forward such that, with input parameters, dynamical simulations on a quantum computer can be carried out and the results analyzed. This work could potentially inspire future quantum algorithm design for simulating the dynamics of open quantum systems.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.