A Blind Source Separation Formulation Adapted for Adiabatic Quantum Computation-Assisted Optimization

Adiabatic Quantum Computing (AQC) is a paradigm focused on solving optimization problems. Considering that various tasks in areas such as machine learning and signal processing can be formulated as optimization problems, this paradigm has been widely explored in these domains. In this context, this work addresses the use of AQC in an unsupervised task in signal processing, known as Blind Source Separation (BSS). The challenge of formulating BSS in an AQC paradigm is to formulate it as a Quadratic Unconstrained Binary Optimization (QUBO). To this end, we listed essential steps, such as defining the objective function, incorporating constraints, and representing variables in binary format, among others. To evaluate the formulation and understand its limitations, we used a classical solver based on simulated annealing as a way to validate the proposal.