Approximate counting and quantum computation

M. Bordewich, M. Freedman, L. Lovász, D. Welsh

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Motivated by the result that an 'approximate' evaluation of the Jones polynomial of a braid at a 5th 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 νP and GapP have such an approximation scheme under certain natural normalizations. 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.

Original languageEnglish
Pages (from-to)737-754
Number of pages18
JournalCombinatorics Probability and Computing
Volume14
Issue number5-6
DOIs
Publication statusPublished - Nov 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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