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Super-Golden-Gates for PU(2)
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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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Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits
Unitaries over the rings Z[1/2], Z[1/√2], Z[1/i√2], and Z[1/2,i] are exactly the circuits over four Clifford+T-derived gate sets.
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