Generating equiprobable superpositions of arbitrary sets for a new generalization of the deutsch-jozsa algorithm

Abstract

We examine the problem of generating equal-probability superpositions of sets whose cardinalities are not necessarily powers of two. Alternative quantum circuits for this purpose are compared with respect to complexity and precision, and a variant based on the Grover iteration is shown to yield an algorithm with one-sided error for a generalization of the Deutsch-Jozsa problem, where the task is to decide whether a specified subset of the oracle function is constant or balanced. © Springer-Verlag 2004.