Complexity measures and decision tree complexity: a survey

TL;DR: An O(N/sup k/(k+1)/) query quantum algorithm is given for the generalization of element distinctness in which the authors have to find k equal items among N items.

TL;DR: In this article, the authors used quantum walks to construct a new O(n 2/3 ) query quantum algorithm for element distinctness and its generalization, which was later improved to O(k/(k+1) ).

TL;DR: Algebraic relativization or algebraic algebrization as discussed by the authors is a new barrier to progress in complexity theory, and it has been shown that relativizing some complexity class inclusion should give the simulating machine access not only to an oracle A, but also to a low-degree extension of A over a finite field or ring.

TL;DR: Some of quantum algorithms for search problems are reviewed: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on quantum walks.

TL;DR: This book inchides well-known classics such as "On the Criteria to be used in Decomposing Systems into Modules," "On a 'Buzzword': Hierarchical Structure," and "Software Aging."

TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.

TL;DR: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms, and is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it!