Abstract

We consider a family of unstructured optimization problems, for which we propose a method for constructing analogue, continuous-time (not necessarily adiabatic) quantum algorithms that are faster than their classical counterparts. In this family of problems, which we refer to as' scrambled input'problems, one has to find a minimum-cost configuration of a given integer-valued n-bit black-box function whose input values have been scrambled in some unknown way. Special cases within this set of problems are Grover's search problem of finding a marked item in an unstructured database, certain random energy models, and the functions of the Deutsch–Josza problem. We consider a couple of examples in detail. In the first, we provide an O (1) deterministic analogue quantum algorithm to solve the seminal problem of Deutsch and Josza, in which one has to determine whether an n-bit boolean function is constant …

Date

2014

Authors

Itay Hen

Journal

Journal of Physics A: Mathematical and Theoretical

Volume

47

Issue

4

Pages

045305

Publisher

IOP Publishing