A Novel Quantum Machine Learning Algorithm Based on Kronecker Reed-Muller Forms
By Bryan Lee
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 …