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computational complexity

, Volume 23, Issue 2, pp 305–322 | Cite as

How Low can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?

  • Andris Ambainis
  • Ronald de Wolf
Article

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 Ω(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 Ω(log n/ log  log n), and we exhibit quantum algorithms for two functions where this bound is achieved.

Keywords

Quantum computing quantum algorithms Boolean functions polynomial approximations computational complexity 

Subject classification

68Q12 68Q17 41A10 06E30 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia
  2. 2.CWI and University of AmsterdamAmsterdamThe Netherlands

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