On the de-randomization of space-bounded approximate counting problems

Dean Doron, Amnon Ta-Shma

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


It was recently shown that SVD and matrix inversion can be approximated in quantum log-space [1] for well formed matrices. This can be interpreted as a fully logarithmic quantum approximation scheme for both problems. We show that if prBQL=prBPL then every fully logarithmic quantum approximation scheme can be replaced by a probabilistic one. Hence, if classical algorithms cannot approximate the above functions in logarithmic space, then there is a gap already for languages, namely, prBQL prBPL. On the way we simplify a proof of Goldreich for a similar statement for time bounded probabilistic algorithms. We show that our simplified algorithm works also in the space bounded setting (for a large set of functions) whereas Goldreich's approach does not seem to apply in the space bounded setting.

Original languageEnglish
Pages (from-to)750-753
Number of pages4
JournalInformation Processing Letters
Issue number10
StatePublished - 15 Sep 2014
Externally publishedYes


  • Approximation algorithms
  • Computational complexity
  • Randomized algorithms
  • Space bounded approximation schemes
  • Space bounded computation
  • Space bounded quantum computation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


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