In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Amba...
We show that any quantum algorithm to decide whether a function f : [n] → [n] is a permutation or far from a permutation must make Ω n1/3 /w queries to f, even if the algorith...
We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pa...
We show that Graph Isomorphism is in the complexity class SPP, and hence it is in ⊕P (in fact, it is in ModkP for each k ≥ 2). We derive this result as a corollary of a more g...
A strong direct product theorem (SDPT) states that solving n instances of a problem requires ˝.n/ times the resources for a single instance, even to achieve success probability 2 ...