NDLI: Quantum speed-up of Markov chain based algorithms

Content Provider	IEEE Xplore Digital Library
Author	Szegedy, M.
Copyright Year	2004
Description	Author affiliation: Rutgers Univ., NJ, USA (Szegedy, M.)
Abstract	We develop a generic method for quantizing classical algorithms based on random walks. We show that under certain conditions, the quantum version gives rise to a quadratic speed-up. This is the case, in particular, when the Markov chain is ergodic and its transition matrix is symmetric. This generalizes the celebrated result of L. K. Grover (1996)and a number of more recent results, including the element distinctness result of Ambainis and the result of Ambainis, Kempe and Rivosh that computes properties of quantum walks on the d-dimensional torus. Among the consequences is a faster search for multiple marked items. We show that the quantum escape time, just like its classical version, depends on the spectral properties of the transition matrix with the marked rows and columns deleted.
Sponsorship	IEEE Comput. Soc. Tech. Soc. on Foundations of Comput
Starting Page	32
Ending Page	41
File Size	709317
Page Count	10
File Format	PDF
ISBN	0769522289
ISSN	02725428
DOI	10.1109/FOCS.2004.53
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-10-17
Publisher Place	Italy
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Quantum computing Quantum mechanics Symmetric matrices State-space methods Algorithm design and analysis Computational modeling Simulated annealing Genetic algorithms Monte Carlo methods Stochastic processes
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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