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

Hideaki Fukuhara, Eiji Takimoto

Research output: Contribution to journalArticle

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 - Jan 1 2010

Fingerprint

Boolean functions

All Science Journal Classification (ASJC) codes

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

Cite this

Lower bounds on quantum query complexity for read-once formulas with XOR and MUX operators. / Fukuhara, Hideaki; Takimoto, Eiji.

In: IEICE Transactions on Information and Systems, Vol. E93-D, No. 2, 01.01.2010, p. 280-289.

Research output: Contribution to journalArticle

@article{e5165f31a85f4a24934a125c3ca5eabb,
title = "Lower bounds on quantum query complexity for read-once formulas with XOR and MUX operators",
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.",
author = "Hideaki Fukuhara and Eiji Takimoto",
year = "2010",
month = "1",
day = "1",
doi = "10.1587/transinf.E93.D.280",
language = "English",
volume = "E93-D",
pages = "280--289",
journal = "IEICE Transactions on Information and Systems",
issn = "0916-8532",
publisher = "一般社団法人電子情報通信学会",
number = "2",

}

TY - JOUR

T1 - Lower bounds on quantum query complexity for read-once formulas with XOR and MUX operators

AU - Fukuhara, Hideaki

AU - Takimoto, Eiji

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77950240567&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950240567&partnerID=8YFLogxK

U2 - 10.1587/transinf.E93.D.280

DO - 10.1587/transinf.E93.D.280

M3 - Article

AN - SCOPUS:77950240567

VL - E93-D

SP - 280

EP - 289

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 2

ER -