EAGER: Collaborative: Tensor Networks Methods for Quantum Simulations

量子技术的最新进展最终使具有数十个量子比特的小型高质量量子计算机成为可能。虽然这些机器仍然太小，不足以对密码学等领域产生影响，但它们已经足够大，可以研究与材料科学和化学相关的物理和化学系统，从而帮助我们更好地了解某些材料性质的起源，以及某些重要的化学反应是如何发生的。该项目旨在开发新的模拟技术，以帮助对这些量子机进行基准测试。这些模拟将在普通计算机上运行，但将利用云计算服务尽可能扩大系统规模。这些模拟技术还将被用来研究与物理和材料科学相关的其他量子系统，这些系统还不能被量子硬件访问。提高这些领域的知识对于开发更好、更坚固的材料以及更快、更小的电子产品至关重要。这些项目将有额外的社会效益，在非常跨学科的研究领域培训研究生，在计算机科学和物理之间的交界处，从而帮助将备受欢迎的技能带入工作队伍。该项目包括开发和部署一种使用张量网络模拟量子多体系统的新方法。该方法基于Keldysh-Schwinger形式的量子动力学演化的态历史表示。因此，该方法不是使用张量网络来表示状态向量的概率幅度随时间的演变，而是使用张量网络来表示演变本身，使得网络的完全收缩直接计算诸如可观测的或两点相关函数的期望值之类的量。在这种方法中，纠缠度保持在较低的水平，导致网络链路上的键合维度较低，使收缩更容易进行精确计算。对于收缩，使用了两步收缩-抽取方案来折叠网络。更具体地说，该方案包括通过奇异值分解压缩信息来去除局部纠缠，然后通过选择性地去除网络的行或列来抽取网络。这一收缩计划将被编码为最佳地利用商业云计算服务的最大实例上的可用资源。在项目期间开发的代码将通过公共存储库提供。该奖项反映了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。

Recent advances in quantum technologies have made small, high-quality quantum computers with tens of qubits finally available. While these machines are still too small to make an impact on areas such as cryptography, they are big enough to study physical and chemical systems of relevance to materials science and chemistry, thus helping us better understand the origins of certain materials properties and how certain important chemical reactions take place. This project aims at developing novel simulation techniques to help benchmark these quantum machines. These simulations will run on ordinary computers, but will make use of cloud computing services to scale up the system sizes as far as possible. The simulation techniques will also be used to investigate other quantum systems of relevance to physics and materials science that are not yet accessible to quantum hardware. Advancing knowledge in those areas is essential for developing better and stronger materials, as well as faster and smaller electronics. These projects will have the additional societal benefit of training graduate students in a very interdisciplinary area of research, at the interface between computer science and physics, thus helping bring highly-sought skills into the workforce.The project consists of developing and deploying a novel method to simulate quantum many-body systems using tensor networks. The method is based on the state history representation of the quantum dynamical evolution, as expressed in the Keldysh-Schwinger formalism. Thus, rather than using the tensor network to represent the evolution of the probability amplitude of a state vector over time, the method uses the tensor network to represent the evolution itself, such that the full contraction of the network directly calculates quantities such as the expectation value of an observable or a two-point correlation function. In this approach, entanglement is kept low, resulting in low bond dimensions on the network links, making contractions more amenable to exact computations. For the contraction, a two-step contraction-decimation scheme is used to collapse the network. More specifically, the scheme consists of the removal of local entanglement by compressing the information via singular value decomposition, followed by the decimation of the network by selectively removing rows or columns of the network. This contraction scheme will be coded to optimally utilize the resources available on the largest instances of commercial cloud computing services. The codes developed during the project will be made available through public repositories.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.