Title
A PROMISEBQP-COMPLETE STRING REWRITING PROBLEM
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
ISSN
1533-7146
Recommended Citation
"A PROMISEBQP-COMPLETE STRING REWRITING PROBLEM" (2010). Faculty Bibliography 2010s. 299.
https://stars.library.ucf.edu/facultybib2010/299
Comments
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