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

作者：Ambainis Andris^*; de Wolf Ronald

来源：Computational Complexity, 2014, 23(2): 305-322.

DOI：10.1007/s00037-014-0083-2

• Quantum computing
• quantum algorithms
• Boolean functions
• polynomial approximations
• computational complexity

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.

• 出版日期2014-6