Quantum Algorithms: Applicable Algebra and Quantum Physics

Abstract

Classical computer science relies on the concept of Turing machines as a unifying model of universal computation. According to the modern Church-Turing Thesis, this concept is interpreted in the form that every physically reasonable model of computation can be efficiently simulated on a probabilistic Turing machine. Recently this understanding, which was taken for granted for a long time, has required a severe reorientation because of the emergence of new computers that do not rely on classical physics but, rather, use effects predicted by quantum mechanics.