6533b856fe1ef96bd12b2825

RESEARCH PRODUCT

How Low Can Approximate Degree and Quantum Query Complexity Be for Total Boolean Functions?

Andris AmbainisRonald De Wolf

subject

Computational complexity theoryGeneral MathematicsFOS: Physical sciences0102 computer and information sciences02 engineering and technology01 natural sciencesUpper and lower boundsTheoretical Computer ScienceComplexity indexCombinatorics0202 electrical engineering electronic engineering information engineeringBoolean functionMathematicsQuantum computerDiscrete mathematicsQuantum PhysicsApproximation theoryDegree (graph theory)TheoryofComputation_GENERALApproximation algorithmComputational MathematicsComputational Theory and Mathematics010201 computation theory & mathematics020201 artificial intelligence & image processingQuantum algorithmQuantum Physics (quant-ph)Quantum complexity theory

description

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

yearjournalcountryeditionlanguage
2012-06-042013 IEEE Conference on Computational Complexity
https://doi.org/10.1109/ccc.2013.26