Quantum Computational Signal Classification

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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.