arXiv subjects
Publications and source records attributed to M. Sipser.
Suppose an oracle is known to hold one of a given set of D two-valued functions. To successfully identify which function the oracle holds with k classical queries, it must be the case that D is at most 2^k. In this paper we derive a bound for how many functions can be distinguished with k quantum queries.
We consider the problem of inserting a new item into an ordered list of N-1 items. The length of an algorithm is measured by the number of comparisons it makes between the new item and items already on the list. Classically, determining the insertion point requires log N comparisons. We show that, for N large, no quantum algorithm can reduce the number of comparisons below log N/(2 loglog N).
Consider a function f which is defined on the integers from 1 to N and takes the values -1 and +1. The parity of f is the product over all x from 1 to N of f(x). With no further information about f, to classically determine the parity of f requires N calls of the function f. We show that any quantum algorithm capable of determining the parity of f contains at least N/2 applications of the unitary operator which evaluates f. Thus for this problem, quantum computers cannot outperform classical computers.