Super-Golden-Gates for PU(2)

Ori Parzanchevski, Peter Sarnak

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

To each of the symmetry groups of the Platonic solids we adjoin a carefully designed involution yielding topological generators of PU(2) which have optimal covering properties as well as efficient navigation. These are a consequence of optimal strong approximation for integral quadratic forms associated with certain special quaternion algebras and their arithmetic groups. The generators give super efficient 1-qubit quantum gates and are natural building blocks for the design of universal quantum gates.

Original languageEnglish (US)
Pages (from-to)869-901
Number of pages33
JournalAdvances in Mathematics
Volume327
DOIs
StatePublished - Mar 17 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Quantum computing
  • Ramanujan conjectures
  • Strong approximation
  • Unitary groups

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