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.
Bibliographical noteFunding 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 .
O.P. was supported by ISF grant 1031/17; P.S. was supported by NSF grant DMS 1302952.
© 2017 Elsevier Inc.
- Quantum computing
- Ramanujan conjectures
- Strong approximation
- Unitary groups