Title

A PROMISEBQP-COMPLETE STRING REWRITING PROBLEM

Authors

Authors

D. Janzing;P. Wocjan

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Quantum Inform. Comput.

Keywords

PromiseBQP; PromiseBQP-complete problems; QUANTUM ALGORITHMS; COMPUTERS; SYSTEMS; Computer Science, Theory & Methods; Physics, Particles & Fields; Physics, Mathematical

Abstract

We consider the following combinatorial problem. We are given three strings s, t, and t' of length L over some fixed finite alphabet and an integer in that is polylogarithmic in L. We have a symmetric relation on substrings of constant length that specifies which substrings are allowed to be replaced with each other. Let Delta(n) denote the difference between the numbers of possibilities to obtain t from s and t' from s after n is an element of N replacements. The problem is to determine the sign of A(m). As promises we have a gap condition and a growth condition. The former states that Delta(m) >= is an element of c(m) where is inverse polylogarithmic in L and c > 0 is a constant. The latter is given by Delta(n) <= c(n) for all n. We show that this problem is PromiseBQP-complete, i.e., it represents the class of problems that can be solved efficiently on a quantum computer.

Journal Title

Quantum Information & Computation

Volume

10

Issue/Number

3-4

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

234

Last Page

257

WOS Identifier

WOS:000276214700005

ISSN

1533-7146

Share

COinS