Title :
How Low Can Approximate Degree and Quantum Query Complexity Be for Total Boolean Functions?
Author :
Ambainis, Andris ; de Wolf, Ronald
Author_Institution :
Univ. of Latvia, Riga, Latvia
Abstract :
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n/log log n), and we exhibit quantum algorithms for two functions where this bound is achieved.
Keywords :
Boolean functions; approximation theory; computational complexity; quantum computing; Boolean function; approximate degree; bounded-error quantum query complexity; quantum algorithms; Approximation algorithms; Approximation methods; Boolean functions; Complexity theory; Hamming distance; Polynomials; Quantum computing; Analysis of Boolean functions; approximate degree; lower bounds; quantum algorithms; query complexity;
Conference_Titel :
Computational Complexity (CCC), 2013 IEEE Conference on
Conference_Location :
Stanford, CA
DOI :
10.1109/CCC.2013.26
