Lower bounds on quantum query complexity for read-once decision trees with parity nodes

Hideaki Fukuhara, Eiji Takimoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We introduce a complexity measure for decision trees called the soft rank, which measures how wellbalanced a given tree is. The soft rank is a somehow relaxed variant of the rank. Among all decision trees of depth d, the complete binary decision tree (the most balanced tree) has maximum soft rank √d, the decision list (the most unbalanced tree) has minimum soft rank √d, and any other trees have soft rank between d and d. We show that, for any decision tree T in some class G of decision trees which includes all read-once decision trees, the soft rank of T is a lower bound on the quantum query complexity of the Boolean function that T represents. This implies that for any Boolean function f that is represented by a decision tree in G, the deterministic query complexity of f is only quadratically larger than the quantum query complexity of f.

Original languageEnglish
Title of host publicationTheory of Computing 2009 - Proceedings of the Fifteenth Computing
Subtitle of host publicationThe Australasian Theory Symposium, CATS 2009
Publication statusPublished - Dec 1 2009
EventTheory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009 - Wellington, New Zealand
Duration: Jan 20 2009Jan 23 2009

Publication series

NameConferences in Research and Practice in Information Technology Series
Volume94
ISSN (Print)1445-1336

Other

OtherTheory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009
CountryNew Zealand
CityWellington
Period1/20/091/23/09

Fingerprint

Decision trees
Boolean functions

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Information Systems
  • Software

Cite this

Fukuhara, H., & Takimoto, E. (2009). Lower bounds on quantum query complexity for read-once decision trees with parity nodes. In Theory of Computing 2009 - Proceedings of the Fifteenth Computing: The Australasian Theory Symposium, CATS 2009 (Conferences in Research and Practice in Information Technology Series; Vol. 94).

Lower bounds on quantum query complexity for read-once decision trees with parity nodes. / Fukuhara, Hideaki; Takimoto, Eiji.

Theory of Computing 2009 - Proceedings of the Fifteenth Computing: The Australasian Theory Symposium, CATS 2009. 2009. (Conferences in Research and Practice in Information Technology Series; Vol. 94).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Fukuhara, H & Takimoto, E 2009, Lower bounds on quantum query complexity for read-once decision trees with parity nodes. in Theory of Computing 2009 - Proceedings of the Fifteenth Computing: The Australasian Theory Symposium, CATS 2009. Conferences in Research and Practice in Information Technology Series, vol. 94, Theory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009, Wellington, New Zealand, 1/20/09.
Fukuhara H, Takimoto E. Lower bounds on quantum query complexity for read-once decision trees with parity nodes. In Theory of Computing 2009 - Proceedings of the Fifteenth Computing: The Australasian Theory Symposium, CATS 2009. 2009. (Conferences in Research and Practice in Information Technology Series).
Fukuhara, Hideaki ; Takimoto, Eiji. / Lower bounds on quantum query complexity for read-once decision trees with parity nodes. Theory of Computing 2009 - Proceedings of the Fifteenth Computing: The Australasian Theory Symposium, CATS 2009. 2009. (Conferences in Research and Practice in Information Technology Series).
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