Discrete quantum walks hit exponentially faster

Julia Kempe

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This paper addresses the question: what processes take polynomial time on a quantum computer that require exponential time classically? We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one comer to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum walks. We provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We outline a possible application to sequential packet routing.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsSanjeev Asora, Amit Sahai, Klaus Jansen, Jose D.P. Rolim
PublisherSpringer-Verlag
Pages354-369
Number of pages16
ISBN (Print)3540407707, 9783540407706
StatePublished - Jan 1 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2764
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Fingerprint

Quantum Walk
Hitting Time
Hits
Polynomials
Quantum computers
Packet Routing
Quantum Computer
Exponential time
Hypercube
Random walk
Polynomial time
Discrete-time
Polynomial
Alternatives
Graph in graph theory

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kempe, J. (2003). Discrete quantum walks hit exponentially faster. In S. Asora, A. Sahai, K. Jansen, & J. D. P. Rolim (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 354-369). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2764). Springer-Verlag.

Discrete quantum walks hit exponentially faster. / Kempe, Julia.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Sanjeev Asora; Amit Sahai; Klaus Jansen; Jose D.P. Rolim. Springer-Verlag, 2003. p. 354-369 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2764).

Research output: Chapter in Book/Report/Conference proceedingChapter

Kempe, J 2003, Discrete quantum walks hit exponentially faster. in S Asora, A Sahai, K Jansen & JDP Rolim (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2764, Springer-Verlag, pp. 354-369.
Kempe J. Discrete quantum walks hit exponentially faster. In Asora S, Sahai A, Jansen K, Rolim JDP, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer-Verlag. 2003. p. 354-369. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Kempe, Julia. / Discrete quantum walks hit exponentially faster. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Sanjeev Asora ; Amit Sahai ; Klaus Jansen ; Jose D.P. Rolim. Springer-Verlag, 2003. pp. 354-369 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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