<title>Embedding of feature space for pattern recognition using quantum computing</title>

Abstract

ABSTRACT In order to deal with a general pattern recognition problem by quantum computing, this paper proposes an embedding method that corresponds a feature vector of n-dimensional space V n to a vector of the surface of Riemann sphere in the n+1 dimensional space V n+1 , keeping the topology among feature vectors. Because the radius of this Riemann sphere is one, the feature vectors are mapped into normalized vectors. This paper shows that multiple linear discriminant functions can be defined to separate two arbitrary clusters that are mapped onto the Riemann sphere in the space V n+1 . This paper also shows that we can define a unitary transformation that computes the signs of values of those multiple linear discriminant functions, in parallel by quantum computing. Keywords: quantum computer, pattern recognition, feature vector, clustering, Riemann sphere, linear discriminant function, unitary transformation 1. INTRODUCTION In 1985, for the first time, Deutsch presented the concept of Quantum Turing Machine (QTM) as a mathematical computer model based on quantum mechanics