Super-Golden-Gates for PU(2)

Ori Parzanchevski; Peter Sarnak

doi:10.1016/j.aim.2017.06.022

Super-Golden-Gates for PU(2)

Ori Parzanchevski, Peter Sarnak

Mathematics

Research output: Contribution to journal › Article › peer-review

28 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 language	English (US)
Pages (from-to)	869-901
Number of pages	33
Journal	Advances in Mathematics
Volume	327
DOIs	https://doi.org/10.1016/j.aim.2017.06.022
State	Published - Mar 17 2018

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Quantum computing
Ramanujan conjectures
Strong approximation
Unitary groups

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10.1016/j.aim.2017.06.022

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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.",

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AB - 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.

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KW - Ramanujan conjectures

KW - Strong approximation

KW - Unitary groups

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Super-Golden-Gates for PU(2)

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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