Development of blind source separation methods adapted to the adiabatic quantum computing paradigm

• Grant number: 24/23830-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2025
• End date: March 31, 2027
• Field of knowledge: Engineering - Electrical Engineering - Telecommunications
• Principal Investigator: Leonardo Tomazeli Duarte
• Grantee: Maria Carolina Aragão de Andrade
• Host Institution: Faculdade de Ciências Aplicadas (FCA). Universidade Estadual de Campinas (UNICAMP). Limeira , SP, Brazil
• Company: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação (FEEC)
• Associated research grant: 20/09838-0 - BI0S - Brazilian Institute of Data Science, AP.PCPE

Abstract

Blind source separation (BSS) has been extensively studied in the fields of signal processing and machine learning. The goal of BSS is to recover a set of signals (sources) solely from the observation of mixtures of these sources, which constitutes an unsupervised learning task. Aiming to contribute to the search for new optimization strategies in the context of BSS, we shall investigate an optimization approach based on a quantum computing paradigm known as adiabatic quantum computing. In this context, it is necessary to develop a formulation of BSS as a QUBO (Quadratic Unconstrained Binary Optimization) problem. Our approach will consider objective functions based on kurtosis, a fourth-order moment widely used in BSS. We shall also investigate paradigms based on second-order statistics. We also aim at understanding the limitations of the adiabatic quantum computing paradigm in BSS, especially regarding the limited precision of available quantum computers (which have few qubits) and the need to use integer variable representations for continuous variables. Finally, we intend to validate the obtained algorithm in a real problem related to the separation of chemical signals from sensors for ion concentration detection. Our experiments will be conducted on adiabatic quantum computer simulation systems, as well as on the D-Wave quantum computer.