Bibliographic Details
| Title: |
Limitations of Quantum Coset States for Graph Isomorphism. |
| Authors: |
HALLGREN, SEAN1 hallgren@cse.psu.edu, MOORE, CRISTOPHER2 moore@cs.unm.edu, MARTIN RÖTTELER3 mroetteler@nec-labs.com, RUSSELL, ALEXANDER4 acr@cse.uconn.edu, SEN, PRANAB5 pgdsen@tcs.tifr.res.in |
| Superior Title: |
Journal of the ACM. Oct2010, Vol. 57 Issue 6, p34:1-34:33. 33p. 1 Diagram, 4 Charts. |
| Subject Terms: |
*COMPUTER algorithms, SET theory, ISOMORPHISMS, COMPUTATIONAL mathematics, COMPUTERS in graph theory, QUANTUM graph theory |
| 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(n log 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, Fpm) and Gn where G is finite and satisfies a suitable property. [ABSTRACT FROM AUTHOR] |
|
Copyright of Journal of the ACM is the property of Association for Computing Machinery and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| Database: |
Business Source Premier |