This is a textbook about quantum walks and quantum search algorithms. The readers will
take advantage of the pedagogical aspects and learn the topics faster and make less effort …

We use quantum walks to construct a new quantum algorithm for element distinctness and
its generalization. For element distinctness (the problem of finding two equal items among N …

Boolean circuit complexity is the combinatorics of computer science and involves many
intriguing problems that are easy to state and explain, even for the layman. This book is a …

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

Complexity theory is the theory of determining the necessary resources for the solution of
algorithmic problems and, therefore, the limits of what is possible with the available …

Abstract In 1950, John Nash sent a remarkable letter to the National Security Agency, in
which—seeking to build theoretical foundations for cryptography—he all but formulated what …

We prove that any algorithm for learning parities requires either a memory of quadratic size
or an exponential number of samples. This proves a recent conjecture of Steinhardt et …

A strong direct product theorem says that if we want to compute k independent instances of a
function, using less than k times the resources needed for one instance, then our overall …

We show that for several natural problems of interest, complexity lower bounds that are
barely non-trivial imply super-polynomial or even exponential lower bounds in strong …

We prove that for all positive integer k and for all sufficiently small/spl epsiv/> 0 if n is
sufficiently large then there is no Boolean (or 2-way) branching program of size less than …