A Novel Quantum Machine Learning Algorithm Based on Kronecker Reed-Muller Forms

During an evening quantum computing seminar at Portland State University, Professor Marek Perkowski discussed the relatively new area of quantum machine learning. As the lecture continued, I gradually realized that I had come across a field with an ideal intersection between my passions for mathematics and machine learning. Following this seminar, I started reading published works in the field which introduced quantum analogs of algorithms ranging from support vector machines to k-nearest neighbors … My proposed quantum machine learning algorithm is a novel approach which converts the learning samples into an incompletely specified Boolean function for classification problems. An incompletely specified Boolean function is a function with multiple don’t know values (values which are not covered by the training data) along with values 0 or 1 corresponding to negative and positive decisions, respectively. A complex system can have multiple incompletely specified Boolean functions to handle multiple inputs and outputs. A new Kronecker Reed-Muller (KRO) spectral transform, to convert the Boolean function into a KRO form, is used to minimize such functions (i.e. with as many zero spectral coefficients as possible). Spectral coefficients are defined as the constants corresponding to each product term in a KRO form. There are a total of 3-to-the-n KRO forms (informally proven in Section 2.2) and the proposed algorithm is able to identify the exact minimum expression out of all such forms which cover each don’t know for a function of n input variables …

• Mathematics