Quantum algorithms via linear algebra. A primer
The book introduces principles of quantum computation by simple linear algebra. It omits any physical and philosophical problems or discussions, trying to be as simple as possible. For example, through the whole book the bracket notation is avoided and only introduced in the later chapters.NEWLINENEWLINEBasic linear algebra of the complex space and unitary matrices are introduced. Unitary matrices do not change the length of the vector in a Hilbert space. The relation between these matrices and graphs is presented, and the feasibility of Boolean functions is described.NEWLINENEWLINEThen the Hadamard matrices and Fourier matrices are introduced. Reversible computation is presented by the example of the Toffoli gate followed by the Householder reflection. The difference between the copying of the basis states and the non-cloning theorem is clarified.NEWLINENEWLINEThe idea of quantum algorithms is explained and highlighted by maze diagrams. The respective section is followed by Deutsch's algorithm; again the understanding of the algorithm is made clearer by the maze diagrams. In relation to the algorithm, the teleportation is presented. Deutsch's algorithm is extended to the Deutsch-Josza algorithm and Simon's algorithm.NEWLINENEWLINEThen the two main algorithms (you could call them as well principles) of quantum computation are presented: Shor's algorithm and Grover's amplification algorithm. The analysis of Grover's amplification algorithm leaves the easy path of simple linear algebra for the first time; as well, for the first time the bracket notation is introduced in the exercises section.NEWLINENEWLINEAfter that, the quantum random walk is introduced followed by quantum search by quantum walk algorithms. Then the controversial subject of speeding chess playing using quantum walk is presented. One should note that even the evaluation is able to execute faster than its classical counterpart; it relies on the representation of the formula that requires as well computing cost. The corresponding representation has to be determined dynamically during the performed alpha-beta search.NEWLINENEWLINEEach chapter of the book is followed by exercises. The book offers an easy innovative way to deal with quantum computation by the simple language of linear algebra and is highly recommended to anyone interested in quantum computation.
scientific article; zbMATH DE number 6353520