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Approximate counting and quantum computation

Bordewich, M.; Freedman, M.; Lovasz, L.; Welsh, D.

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M. Freedman

L. Lovasz

D. Welsh


Motivated by the result that an `approximate' evaluation of the Jones polynomial of a braid at a $5^{th}$ root of unity can be used to simulate the quantum part of any algorithm in the quantum complexity class BQP, and results relating BQP to the counting class GapP, we introduce a form of additive approximation which can be used to simulate a function in BQP. We show that all functions in the classes \#P and GapP have such an approximation scheme under certain natural normalisations. However we are unable to determine whether the particular functions we are motivated by, such as the above evaluation of the Jones polynomial, can be approximated in this way. We close with some open problems motivated by this work.


Bordewich, M., Freedman, M., Lovasz, L., & Welsh, D. (2005). Approximate counting and quantum computation. Combinatorics, Probability and Computing, 14(5-6), 737-754.

Journal Article Type Article
Publication Date 2005-10
Deposit Date Oct 7, 2008
Publicly Available Date Oct 7, 2008
Journal Combinatorics, Probability and Computing
Print ISSN 0963-5483
Electronic ISSN 1469-2163
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 14
Issue 5-6
Pages 737-754
Keywords Quantum computing, Complexity, Approximation, Jones polynomial, Tutte polynomial.


Published Journal Article (186 Kb)

Copyright Statement
© Cambridge University Press 2005.

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