Z2-systolic freedom and quantum codes

Michael H. Freedman, David A. Meyer, Feng Luo

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

A closely coupled pair of conjectures/questions—one in differential geometry (by M. Gromov), the other in quantum information theory—are both answered in the negative. The answer derives from a certain metrical flexibility of manifolds and a corresponding improvement to the theoretical efficiency of existing local quantum codes. We exhibit this effect by constructing a family of metrics on S2 × S1, and other three and four dimensional manifolds. Quantitatively, the explicit “freedom” exhibited is too weak (a log1/2 factor in the natural scaling) to yield practical codes but we cannot rule out the possibility of other families of geometries with more dramatic freedom.

Original languageEnglish
Title of host publicationMathematics of Quantum Computation
PublisherCRC Press
Pages287-320
Number of pages34
ISBN (Electronic)9781420035377
ISBN (Print)1584882824, 9781584882824
StatePublished - 1 Jan 2002
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2002 by Chapman & Hall/CRC.

ASJC Scopus subject areas

  • General Mathematics
  • General Computer Science

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