# Super-Golden-Gates for PU(2)

## TL;DR

This paper introduces a new set of topological generators for PU(2) derived from Platonic solid symmetries, enabling efficient quantum gate design through optimal approximation and navigation.

## Contribution

It presents a novel construction of generators for PU(2) based on Platonic symmetries, with applications to efficient quantum gate implementation.

## Key findings

- Generators exhibit optimal covering properties.
- Enable super-efficient 1-qubit quantum gates.
- Provide natural building blocks for universal quantum gates.

## 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.