Lower bounds on quantum query complexity for read-once formulas with XOR and MUX operators

Hideaki Fukuhara, Eiji Takimoto

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a complexity measure r for the class ℱ of read-once formulas over the basis {AND,OR,NOT,XOR, MUX} and show that for any Boolean formula F in the class ℱ r(F) is a lower bound on the quantum query complexity of the Boolean function that F represents. We also show that for any Boolean function f represented by a formula in ℱ the deterministic query complexity of f is only quadratically larger than the quantum query complexity of f . Thus, the paper gives further evidence for the conjecture that there is an only quadratic gap for all functions.

Original languageEnglish
Pages (from-to)280-289
Number of pages10
JournalIEICE Transactions on Information and Systems
VolumeE93-D
Issue number2
DOIs
Publication statusPublished - 2010

All Science Journal Classification (ASJC) codes

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence

Fingerprint Dive into the research topics of 'Lower bounds on quantum query complexity for read-once formulas with XOR and MUX operators'. Together they form a unique fingerprint.

Cite this