Primitive quantum gates for an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> discrete subgroup: Binary octahedral
Erik Gustafson, Henry Lamm, Felicity Lovelace
Abstract
We construct a primitive gate set for the digital quantum simulation of the 48-element binary octahedral (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="double-struck">BO</a:mi></a:mrow></a:math>) group. This non-Abelian discrete group better approximates <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>S</d:mi><d:mi>U</d:mi><d:mo stretchy="false">(</d:mo><d:mn>2</d:mn><d:mo stretchy="false">)</d:mo></d:math> lattice gauge theory than previous work on the binary tetrahedral group at the cost of one additional qubit—for a total of six—per gauge link. The necessary primitives are the inversion gate, the group multiplication gate, the trace gate, and the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:mi mathvariant="double-struck">BO</h:mi></h:mrow></h:math> Fourier transform. Published by the American Physical Society 2024