Super-Golden-Gates for PU(2)

Ori Parzanchevski, Peter Sarnak

Research output: Contribution to journalArticlepeer-review

20 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 languageAmerican English
Pages (from-to)869-901
Number of pages33
JournalAdvances in Mathematics
Volume327
DOIs
StatePublished - 17 Mar 2018

Bibliographical note

Funding Information:
The authors thank O. Regev and J. Vondrák for illuminating discussions on integer programming and NP-completeness. O.P. was supported by ISF grant 1031/17 ; P.S. was supported by NSF grant DMS 1302952 .

Funding Information:
O.P. was supported by ISF grant 1031/17; P.S. was supported by NSF grant DMS 1302952.

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

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

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