Z2-systolic freedom and quantum codes

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

Research output: Chapter in Book/Report/Conference proceedingChapter

47 Scopus citations


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 (US)
Title of host publicationMathematics of Quantum Computation
PublisherCRC Press
Number of pages34
ISBN (Electronic)9781420035377
ISBN (Print)1584882824, 9781584882824
StatePublished - Jan 1 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science(all)

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    Freedman, M. H., Meyer, D. A., & Luo, F. (2002). Z2-systolic freedom and quantum codes. In Mathematics of Quantum Computation (pp. 287-320). CRC Press.