Exact quantum query complexity of $\rm{EXACT}_{k,l}^n$

TL;DR

This paper studies the exact quantum query complexity of a function that checks if exactly k or l bits are 1 among n input bits, providing optimal algorithms and bounds for this problem.

Contribution

It introduces new bounds and algorithms for the exact quantum query complexity of the EXACT_{k,l}^n function, advancing understanding of quantum query efficiency.

Findings

Established bounds on query complexity for the function

Developed optimal algorithms for specific cases

Provided insights into quantum query efficiency for exact functions

Abstract

In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal algorithm (for some cases), and a nontrivial general lower and upper bound on the minimum number of queries to the black box.