Title

A Promisebqp-Complete String Rewriting Problem

Keywords

Promisebqp; Promisebqp-complete problems

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 m 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 Δ(n) denote the difference between the numbers of possibilities to obtain t from s and t′ from s after n ∈ N replacements. The problem is to determine the sign of Δ(m). As promises we have a gap condition and a growth condition. The former states that |Δ(m)| ≥ ∈ cm where ∈ is inverse polylogarithmic in L and c > 0 is a constant. The latter is given by Δ(n) ≤ cn 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. © Rinton Press.

Publication Date

3-1-2010

Publication Title

Quantum Information and Computation

Volume

10

Issue

3-4

Number of Pages

234-257

Document Type

Article

Personal Identifier

scopus

Socpus ID

77953880274 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/77953880274

This document is currently not available here.

Share

COinS