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Finding cliques by quantum adiabatic evolution

Authors:

Andrew M. Childs,

Edward Farhi,

Jeffrey Goldstone,

Sam GutmannAuthors Info & Claims

Quantum Information & Computation, Volume 2, Issue 3

Pages 181 - 191

Published: 01 April 2002 Publication History

Abstract

Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph with high probability and runs in a time polynomial in n. For the small graphs we are able to investigate (n ≤ 18), the quantum algorithm appears to require only a quadratic run time.

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Cited By

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Chen YBlum RSadler B(2021)Ordering for Communication-Efficient Quickest Change Detection in a Decomposable Graphical ModelIEEE Transactions on Signal Processing10.1109/TSP.2021.307730269(4710-4723)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1109/TSP.2021.3077302
Sharma ATulapurkar A(2021)Preparation of spin eigenstates including the Dicke states with generalized all-coupled interaction in a spintronic quantum computing architectureQuantum Information Processing10.1007/s11128-021-03063-720:5Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s11128-021-03063-7
Chakraborty KChoi BMaitra AMaitra S(2014)Efficient quantum algorithms to construct arbitrary Dicke statesQuantum Information Processing10.1007/s11128-014-0797-813:9(2049-2069)Online publication date: 1-Sep-2014
https://dl.acm.org/doi/10.1007/s11128-014-0797-8
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Finding cliques by quantum adiabatic evolution
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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Published In

Quantum Information & Computation Volume 2, Issue 3

April 2002

76 pages

ISSN:1533-7146

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Publisher

Rinton Press, Incorporated

Paramus, NJ

Publication History

Published: 01 April 2002

Revised: 15 February 2002

Received: 28 November 2001

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Chen YBlum RSadler B(2021)Ordering for Communication-Efficient Quickest Change Detection in a Decomposable Graphical ModelIEEE Transactions on Signal Processing10.1109/TSP.2021.307730269(4710-4723)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1109/TSP.2021.3077302
Sharma ATulapurkar A(2021)Preparation of spin eigenstates including the Dicke states with generalized all-coupled interaction in a spintronic quantum computing architectureQuantum Information Processing10.1007/s11128-021-03063-720:5Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s11128-021-03063-7
Chakraborty KChoi BMaitra AMaitra S(2014)Efficient quantum algorithms to construct arbitrary Dicke statesQuantum Information Processing10.1007/s11128-014-0797-813:9(2049-2069)Online publication date: 1-Sep-2014
https://dl.acm.org/doi/10.1007/s11128-014-0797-8
Karimi KDickson NHamze FAmin MDrew-Brook MChudak FBunyk PMacready WRose G(2012)Investigating the performance of an adiabatic quantum optimization processorQuantum Information Processing10.5555/2124660.212469311:1(77-88)Online publication date: 1-Feb-2012
https://dl.acm.org/doi/10.5555/2124660.2124693
Schaller GSchützhold R(2010)The role of symmetries in adiabatic quantum algorithmsQuantum Information & Computation10.5555/2011438.201144710:1(109-140)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.5555/2011438.2011447
Rao M(2007)Bounding run-times of local adiabatic algorithmsProceedings of the 4th international conference on Theory and applications of models of computation10.5555/1767854.1767897(450-461)Online publication date: 22-May-2007
https://dl.acm.org/doi/10.5555/1767854.1767897
Aharonov DTa-Shma ALarmore LGoemans M(2003)Adiabatic quantum state generation and statistical zero knowledgeProceedings of the thirty-fifth annual ACM symposium on Theory of computing10.1145/780542.780546(20-29)Online publication date: 9-Jun-2003
https://dl.acm.org/doi/10.1145/780542.780546

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