Discrete quantum walks hit exponentially faster

Julia Kempe

Research output: Contribution to journalArticle

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 walk on the n-bit hypercube from one corner 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)
Pages (from-to)215-235
Number of pages21
JournalProbability Theory and Related Fields
Volume133
Issue number2
DOIs
StatePublished - Jan 1 2005

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

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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

In: Probability Theory and Related Fields, Vol. 133, No. 2, 01.01.2005, p. 215-235.

Research output: Contribution to journalArticle

Kempe, Julia. / Discrete quantum walks hit exponentially faster. In: Probability Theory and Related Fields. 2005 ; Vol. 133, No. 2. pp. 215-235.
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