A Lie-algebraic criterion using Borel-de Siebenthal theory with incommensurate-spectrum generators yields a polynomial-time test for universality of exponentiated qudit gates and shows two generators are always sufficient.
Universality of single-qudit gates,
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A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates
A Lie-algebraic criterion using Borel-de Siebenthal theory with incommensurate-spectrum generators yields a polynomial-time test for universality of exponentiated qudit gates and shows two generators are always sufficient.