CRII: FET: Quantum Bayesian network simulation through efficient representation, transpilation, and uncertainty quantification

传感、数据收集、算法和高性能计算的进步催生了一种新的科学发现范式，称为数据驱动的科学发现，其中基于可用数据训练不同类型的数据驱动模型，以进行知识发现和推理、预测和系统性能预测。由于数据的噪声和不精确性，这些分析需要在存在不确定性的情况下进行。贝叶斯网络构成了一种可用于表示噪声和不精确数据的模型，并且已应用于从原子级系统到宇宙学、医疗保健以及运输、制造、民用基础设施和航空航天系统等各种工程领域的应用。在过去的十年中，由于量子计算在解决某些类型的问题方面优于传统计算范式的计算性能，人们对量子计算领域也产生了极大的兴趣。该项目正在研究量子计算范式中贝叶斯网络的有效表示和模拟。该项目的成果正在被纳入 STEM 课程中。作为该项目的一部分，多名本科生和研究生正在接受培训，并且正在开发几个简短的教学模块，通过年度夏令营对高中生进行量子计算方面的培训。该项目研究了在当前可用的噪声中尺度量子 (NISQ) 设备上模拟量子贝叶斯网络 (QBN) 的基本问题。拟议的研究正在研究一种有效 QBN 模拟的多管齐下的方法。首先，我们正在研究一种通过旋转角度分解的新型 QBN 表示框架，该框架具有较低的分析复杂度且不损失准确性。其次，正在研究用于转译的混合优化强化学习方法，以解决组合的量子位布局和路由问题，以有效地将任何给定的 QBN 电路映射到基于门的硬件架构。最后，正在研究一种非参数统计方法，以获得 QBN 复杂性与 QBN 状态概率所需精度所需的量子电路运行次数之间的经验关系。所提出的方法不仅限于量子贝叶斯网络，而是通用的，适用于任何量子算法。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。

Advances in sensing, data collection, algorithms, and high-performance computing have resulted in a new paradigm of scientific discovery called the data-driven scientific discovery, where different types of data-driven models are trained based on the available data for knowledge discovery and reasoning, forecasting, and system-performance prediction. Due to the noisy and imprecise nature of data, these analyses need to be performed in the presence of uncertainty. Bayesian networks constitute one model that can be used to represent noisy and imprecise data, and that has been employed in applications ranging from atomic-level systems to cosmology, healthcare, and in various engineering domains such as transportation, manufacturing, civil infrastructure, and aerospace systems. In the last decade, there has also been tremendous interest in the field of quantum computing due to its superior computational performance over conventional computing paradigms in solving certain types of problems. This project is investigating efficient representation and simulation of Bayesian networks in the quantum-computing paradigm. The results from this project are being incorporated into STEM courses. Multiple undergraduate and graduate students are being trained as part of this project, and several short teaching modules are being developed to train high-school students in quantum computing through annual summer camps. The proposed project investigates the fundamental question of simulating a Quantum Bayesian Network (QBN) on currently available Noisy Intermediate Scale Quantum (NISQ) devices. The proposed research is investigating a multi-pronged approach for efficient QBN simulation. First, a novel QBN representation framework through rotation angle decomposition, which has a lower analysis complexity without losing the accuracy is being investigated. Second, a mixed optimization-reinforcement learning approach for transpilation is being investigated for combined qubit placement and routing problem to efficiently map any given QBN circuit on to gate-based hardware architectures. Finally, a non-parametric statistical approach is being investigated to obtain an empirical relationship between QBN complexity and the number of quantum circuit runs required for a desired accuracy in QBN state probabilities. The proposed methods are not limited to quantum Bayesian networks but are generic and applicable to any quantum algorithm.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.