Quantum Computational Signal Classification

人工智能的发展为人机合作开辟了新的途径。例如，脑机接口（BCI）技术提取和解释大脑活动产生的信息，而不依赖于任何外部设备或肌肉干预。改善人机交互需要分析和解释生理信号，以有效地评估个体状态。这些信号通常是非平稳的、有噪声的和非线性的，并且当前的信号处理方法可能失败。将信号嵌入点云，这个项目，量子计算信号分类（QuATOMIC）遵循信号的严格性质，并考虑检测信号点云的形状模式。这些形状模式的特征在于它们的相关拓扑属性，这些属性在持久性图中进行了总结。持久性图由二维点组成，其定位突出了信号的特征，并将其与任何潜在的噪声去卷积。另一方面，点云由许多离散点组成，这些图的计算是一项相当艰巨的任务。实际上，二次采样通常会导致重要信息的丢失。 PI将采用量子拓扑框架，该框架考虑点云中的所有点，并依赖于量子机器学习算法的原理。此外，当涉及到信号及其相关图表的实际分析时，可能需要（i）计算它们之间的距离，以便区分它们，或者（ii）量化它们的不确定性并估计持久性图表空间上的概率密度函数。计算两个持久性关系图之间的距离需要解决一个最佳匹配问题。PI将开发一种以量子方式制定和计算的新距离。描述持久性图的分布以量化不确定性需要计算随机点过程的分布。这是一个非平凡的，高度组合的问题，QuATOMIC将通过考虑基于量子电路（门模型）或量子退火原理的量子计算方法来绕过这个问题。QuATOMIC拥有量化持久性图之间的差异及其不确定性的措施，将进一步为信号生成一种新的量子监督机器学习方案。该奖项反映了NSF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。

Developments in artificial intelligence are opening up new avenues for human-machine teaming. For example, the brain-computer interface (BCI) technology extracts and interprets information generated by brain activity without depending on any external device or muscle intervention. Improving human-machine interactions requires the analysis and interpretation of physiological signals to effectively assess individual states. These signals are typically nonstationary, noisy, and nonlinear, and current signal processing methods may fail. Embedding a signal into a point cloud, this project, Quantum Computational Signal Classifications (QuATOMIC) abides by the stringent nature of signals, and considers the detection of shape patterns of the signals’ point clouds. These shape patterns are characterized by their pertinent topological properties, which are summarized in a persistence diagram. A persistence diagram consists of two dimensional points whose positioning highlights signals’ features and deconvolves them from any underlying noise. On the other hand, point clouds consist of many discrete points, and the computation of these diagrams is a rather formidable task. Indeed, subsampling typically takes place leading to loss of vital information. The PIs will adopt a quantum topological framework which considers all points in a point cloud, and relies on principles of quantum machine learning algorithms. Moreover, when it comes to actual analysis of signals and their associated diagrams, one may need (i) to compute a distance between them so that they are differentiated, or (ii) to quantify their uncertainty and estimate a probability density function on the space of persistence diagrams. Computing a distance between two persistence diagrams requires the solution of an optimal matching problem. The PIs will develop a novel distance that is formulated and computed in a quantum way. Propagating a distribution of a persistence diagram to quantify uncertainty requires to compute a distribution of a random point process. This is a non-trivial, highly combinatorial problem, which QuATOMIC will bypass by considering a quantum computing approach based on either quantum circuits (gate model), or the principles of quantum annealing. Having at hand a measure of quantifying the difference among persistence diagrams and their uncertainty, QuATOMIC will further generate a novel quantum supervised machine learning scheme for signals.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.