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Author Hallgren, Sean ♦ Moore, Cristopher ♦ Rtteler, Martin ♦ Russell, Alexander ♦ Sen, Pranab
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2010
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Graph isomorphism ♦ Hidden subgroup problem ♦ Quantum algorithms ♦ Quantum computation
Abstract It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by solving instances of the HSP. A common feature of the resulting algorithms is the use of quantum coset states, which encode the hidden subgroup. An open question has been how hard it is to use these states to solve graph isomorphism. It was recently shown by Moore et al. [2005] that only an exponentially small amount of information is available from one, or a pair of coset states. A potential source of power to exploit are entangled quantum measurements that act jointly on many states at once. We show that entangled quantum measurements on at least $Ω(\textit{n}$ log $\textit{n})$ coset states are necessary to get useful information for the case of graph isomorphism, matching an information theoretic upper bound. This may be viewed as a negative result because in general it seems hard to implement a given highly entangled measurement. Our main theorem is very general and also rules out using joint measurements on few coset states for some other groups, such as $GL(n,F_{p^{m}})$ and $G^{n}$ where $\textit{G}$ is finite and satisfies a suitable property.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2010-11-05
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 57
Issue Number 6
Page Count 33
Starting Page 1
Ending Page 33


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Source: ACM Digital Library