Demonstration of magic state power of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> a

Abstract We consider a lattice of d = 6 qudits that supports <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="bold">S</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> non-Abelian anyons. We present a method for implementing both braiding and fusion evolutions using only the operators that create and measure anyons, without requiring additional dynamical control. This provides a minimal protocol demonstrating that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="bold">S</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> anyons can generate magic states, thereby establishing their universality for quantum computation. Furthermore, we show that the entire scheme can be encoded in just two qudits, offering a compact blueprint that is inherently scalable and readily implementable in current quantum platforms.